Both **heat capacity (C)** and **specific heat capacity (c) **deal with the amount of heat required to change a compound’s temperature by 1 Kelvin. Specific heat capacity (c) deals with changing 1 gram of a compound.

By using **calorimetry** we can measure the thermal energy of a reaction (system) by measuring the change in heat of the surroundings.

**Concept:** Heat capacity vs. Specific Heat Capacity

Welcome back guys! In this new video, we're going to take a look at calorimetry under a constant volume.

Now first we're going to say that every object has its own heat capacity. And just remember heat capacity uses a capital C, and this is just the amount of heat that's required to change an object's temperature by 1 Kelvin (K). Here we're just going to say heat capacity is simply heat/the change in temperature, so Final - Initial. And we're going to say the units are usually in Joules (J)/Kelvin or kiloJoules/Kelvin.

q J

C = ∆T [ in units of K ]

Sometimes your professor may even do it over Degrees Celsius, so just look to see what units were they want the answer to be in. That's what you always have to make sure so that you get the correct answer.

Now similar to heat capacity, there's another property. This property is known as Specific Heat Capacity, and notice that this one is lower case c, and this is the amount of heat that's required to change 1g of substance by 1K.

So here we're just going to introduce the concept of mass, and mass here would be in grams. So it's similar to heat capacity but more in depth, where talks about mass. Now what we're going to say here is if we know the specific heat capacity of a substance, we can rearrange this formula here so that we can solve for the amount of heat absorbed or released. So if we want to rearrange this equation up here, so C = q/m * change in temperature.

q

C = m * ∆T

Just multiply both sides by mass * change in temperature.

q

m * ∆T (C) = m * ∆T m * ∆T

And then you say that q = mcAT.

q = mc∆T

So just remember q = mcAT, just read the delta sign, the triangle as an A. So that's the easy way for you to remember the equation, q = mcAT. This is the equation that we use anytime they give us specific heat capacity, and we know that change in temperature, and they give us the mass of an object.

Now based on the concept we've just looked at let's take a look at this Question here. It says:

At constant volume, the heat of combustion of a particular compound is -4621.0 kJ/mol. We say when 2.319 grams of this compound (molar mass = 192.75 g/mol), remember it has a molar mass that I give to you, was burned in a bomb calorimeter, the temperature of the calorimeter (including its contents) rose by 3.138 oC. What is the heat capacity of the calorimeter in J/K?

First of all, this image that we have here is called a bomb calorimeter. It's a way of us actually figuring out how much energy does an object contain in it. The way it works is, we have our sample put inside to the small little bowl here, and that is placed inside of those water. This whole unit is referred to as a bomb. And what's going to happen is, we're going to actually use these rods here, and we're going to send an electrical current, and it's actually going to cause this sample to explode inside of the bomb calorimeter. So that's why it's called the bomb calorimeter because we actually cause the contents to explode. And when they explode, they're going to give off some heat. Now there's a temperature in the water, this temperature is actually going to record how much the water temperature increases by. In that way, we can figure out how much heat that that sample release and from that we can figure out how many calories it has, how much heat it started with, we could find out a lot of information. This is the way to do certain food sciences, to figure out the calories we have in a food. They use similar technique such as this.

Now we talked about Joules as being the standard type of energy for heat, but remember you could also have instead of Joules for q you could have kiloJoules, but you could also have calories, large calories, these are the calories that you see in food, and kilowatt-hours. So these are other units, energy conversion factors that we can use in place of Joules for q. Now we're not going to work on converting from Joules to calories or kilowatt-hours, I just want to give you guys these tables so that you can see all the different types of energy conversions that you should know for lecture.

Now let's take a look at this question, we want to calculate heat capacity. Remember this is capital C, and so heat capacity = q/change in temperature. And what we need to realize here is, we need to isolate Joules, we need to find Joules for q, and we need the temperature to be in Kelvin. We already have half of it right off the bat, the easy part. The easy part here is I told you that the temperature rose by this much.

**Concept:** Bomb Calorimeter

That right there represents our change in temperature, but the thing is we just need to change those oC into K. And how do we do that? Remember the goal from oC to K, you just add 273.15 to it, when we do that we get 276.288 K.

3.138 oC + 273.15 = 276.288 K

Now what we have to do is we have to isolate q, we have to find Joules. Now the closest place we're going to find Joules are right here in kiloJoules. So we need to find a way of isolating those kiloJoules there. Now the only way I can isolate those kiloJoules is if I find a way to cancel out these moles that we have. And the way I'm going to cancel out those moles is if I convert these grams that I gave to you into moles and multiply times this whole thing. So what we're going to do is we're going to start out with 2.319 g, now we can change this into moles because I gave you the molecular weight, the molar mass of the object. So we're going to say for every 1 mole of this substance it's 192.75 g, grams cancel out and we've just isolated our moles.

1 mol

2.319 g x 192.75 g

I'm going to take myself out of the image so that we'll have more room to work with guys. So we have moles now, now I can just multiply times the heat of combustion, so this would be -4621.0 kJ on top, 1 mol on the bottom. Moles cancel out and now I have kiloJoules isolated.

1 mol -4621.0 kJ

2.319 g x 192.75 g x 1 mol

But remember I don't want kiloJoules, I want Joules. So one more step, kiloJoules go on the bottom, Joules on the top. Kilo is a metric prefix, so for every 1 kilo it's 103. When we work all of that out that gives me -55 600 J, so that's my q. So I'm going to plug it up here. So divide that by the temperature we just isolated and you'll get -201 J/K.

1 mol -4621.0 kJ 10J

2.319 g x 192.75 g x 1 mol x 1 kJ

= - 55 600 J

So I'm going to plug it up here. So divide that by the temperature we just isolated and you'll get -201 J/K.

q

C = ∆T

= - 55 600 J

276.288 kJ

= - 201 J/K

Now this question seems like a lot of information into this, but the thing is just focus on what they're asking us to find, they wanted us to find heat capacity. Heat capacity is just simply q/change in temperature, we knew change in temperature immediately so we just convert it that to Kelvin and then you're now to work on isolating the one variable you needed, you needed kJ, you need to isolate kJ. We isolated that by changing the grams I gave you into moles and then multiplying times the heat of combustion. Now when they say heat of combustion, remember heat means q, but more importantly here it means delta H. They could have said that enthalpy of combustion, also that be the same exact thing. Okay so just remember heat and enthalpy is the same thing.

A **bomb calorimeter** measures the amount of calories within a substance through combustion. In other words, we “blow it up” and measure the amount of heat it releases.

If you are given energy or heat, with specific heat capacity and mass then you will most likely use **q = mcΔT**.

**Example:** In an experiment a 9.87 carat (1 carat = 0.200g) diamond is heated to 72.25^{o}C and immersed in 22.08 g of water in a calorimeter. If the initial temperature of the water was 31.0^{o}C what is the final temperature of the water? (c_{diamond} = 0.519) (c_{water} = 4.184 ).

**Problem:** A sample of copper absorbs 35.3 kJ of heat, which increases the temperature by 25 degrees Celsius, determine the mass (in kg) of the copper sample if the specific heat capacity of copper is 0.385 J/g *C.

When dealing with heat it is important to remember that if one compound is gaining heat that means another compound is losing heat.

**Problem:** 50.00 g of heated metal ore is placed into an insulated beaker containing 822.5 g of water. Once the metal heats up the final temperature of the water is 32.08 degrees Celsius. If the metal gains 14.55 kJ of energy, what is the initial temperature of the water?

The enthalpy or heat of a reaction can be calculated through the use of a coffee cup calorimeter.

**Concept:** Coffee Cup Calorimeter

Welcome back, guys! In this new video, we're going to take a look at chemical reactions when the calorimetry is done under constant pressure. What you’re going to see here is this image right here. We're going to say that this is called a coffee calorimeter. We're going to say it’s used basically to help us find the enthalpy of a reaction. Remember, enthalpy just means delta H. The coffee cup calorimeter has certain parts to it. Here we have the stirrer, which just helps us to mix the water that surrounds our sample. Here we’re going to have our thermometer, which measures the temperature change involved when the sample undergoes its chemical reaction. The sample was going to be releasing heat. The water is going to be absorbing that heat. The thermometer is just to calculate the change in temperature that the water undergoes. Here we’re going to have the two styrofoam cups that are placed together. They work as insulation. That way, no heat is lost to the outside environment. All the temperature or energy changes that occur are going to happen between the water and the sample. Here we're going to have our water. Our water acts as the surroundings. Here we're going to have our sample, which is going to undergo the chemical reaction. This represents our system.

Remember, under constant pressure it's possible for us to calculate the enthalpy of the reaction through the use of this coffee cup calorimeter.

**Concept:** Calculating the Heat of the Solution

Now let's take a look at it this example question. Here it says you place 50 ml of 0.100 molar NaOH into a coffee cup calorimeter at 50 degrees Celsius and carefully add 75 mls of 0.100 molar hydrochloric acid also at 50 degrees Celsius. After stirring, the final temperature of the solution is 76.12 degrees Celsius. Heat capacity and the density of water are also given.

From this, we have to calculate two parts. For part A, we have to figure out what is the heat or Q of the solution in joules. Since we're going to need room to do both of these questions, I'm going to take myself out of the image guys, so we have more room to work with.

What we should realize is that we need to find the heat of the solution. The problem is it's hard to do it directly. But we can find the Q of the water. If we know Q of water, we can then say Q of water equals negative Q of the solution. Remember, in this process, the sample will undergo a chemical reaction and release heat that's why it’s negative. The water will absorb that heat that's why it's positive. We can find the Q of water because we can say Q of water equals mCΔT. We already know the specific heat water. I gave it to you. I said it’s 4.184 joules over degrees times Celsius. Our temperature change, our final temperature is 76.12 degrees Celsius. Our initial for both samples when we mix them together were 50 degrees Celsius.

The harder part is just figuring out what the mass of the water is. But we can figure this out because when we say 50 ml and 75 ml, those two things actually represent the volume of water. What's really going on here that we have that many milliliters of water and dissolved within it are those moles of NaOH and HCl. We're going to take those 50 mls and that 75 ml and add them together to give me 125 mls of water. Since I know the density of water here, I can use that to find the grams of water. Multiply this times the density. Mls cancel out and I have 125 grams of water, which I can just plug into here.

When I multiply everything out, that gives me 13,660.8 joules as the Q of water. We can just plug it into here so we’re going to have 13,660.8 joules equals negative Q of solution. But I want Q of solution, not negative Q of solution. So then all you have to do is divide both sides by -1. Now, Q of solution equals negative 13,660.8 joules as your final answer. Here we’re not concerning ourselves with number of significant figures because here we’re just trying to figure out what the answer is. If you will get this type of question on your exam, your professor would specify do they want sig figs or not.

The **heat of the solution** can be determined by first determining the **heat of water**.

**Concept:** Calculating the enthalpy of the reaction

For B, we have to calculate the enthalpy, delta H, in joules per mole for the formation of water. Here we have to figure out the enthalpy of water. We're going to say delta H of reaction equals Q of solution divided by the moles of whatever they're asking us to find. Here, they’re asking for the formation water so it’s moles of water. We already have half of this because we just figured out what the Q of solution was, so we’ll just plug it in. Now what we have to do is we have to figure out how many moles of water we have.

What we should realize here is I give you information on NaOH and HCl. Remember, the word of when it’s in between two numbers means multiply. Remember, when I say big M that means molarity. Molarity equals moles over liters. When I say 0.100 molar NaOH, that really means 0.100 moles of NaOH over 1 liter. We always assume it's always moles over liters.

If you guys don’t remember this too well, go back to a few videos past where we talked about molarity and molarity in stoichiometry because to do this question, it's essential that you remember those steps from earlier. We’re going to work it out down here. Since I gave you information on two reactants and I'm asking you how much product do you have in moles, this is really a limiting reactant type of question. We're going to have to first do it with the molarity of NaOH, see how many moles of water that gives us then do the same thing with HCl. Since this is a limiting reactant type of question, the one that gives us a smaller amount of moles of water, those are those moles we’re going to use. We have 50 ml of 0.100 molar NaOH. I need to change my ml into liters. 1 ml on the bottom, 10 to the negative 3 liters on the top. Mls cancel out and I finally isolate liters. Now that I have liters, I can multiply it times the molarity to find the moles of NaOH. We need the moles of water though. We need to go from these moles I've given that we just found to our moles of unknown. Remember when we do that jump, we do a mole to mole comparison. We look at the coefficients in the balanced equation. According to our balanced equation, for every one mole of NaOH, we have one mole of water. NaOH on the bottom and mole of H2O what we’re looking for in the top. Since this is in 10 to the negative 3, put it in brackets. When we work it out, we get 0.005 moles of water.

Now we have to do the same thing with HCl. We have 75 ml of 0.100 molar HCl. Same thing, we change the mls into liters first then we multiply it times the molarity. For every one mole of HCl, we have one mole of H2O. Liters cancel out, moles cancel out. We have 0.0075 moles of water. Remember, since this is the limiting reactant type of question, we're going to go with the smaller moles of water. Those are the moles we're going to plug down here to find our enthalpy. When we plug that in, we get back negative 2.73 times 10 to the 6 joules per mole.

This question had a lot of parts to it. It became even harder because we had to incorporate concepts that we learned a few videos back. Just because we passed molarity and stoichiometry involved with them doesn't mean we don't have to see it again this semester. Those types of ideas always resurface at some point. We had to use them in order to solve this question. Remember, if we’re at constant pressure, that's when we use a coffee cup calorimeter. Its whole purpose is to help us find the enthalpy of a reaction. Remember, if your enthalpy, I may not have said that but if your enthalpy is positive, that means you’re absorbing energy or absorbing heat so you're endothermic. If you're releasing heat or releasing energy by the system, then it's exo. It’s negative delta H. Just remember the concepts that we covered here and the approaches we take. When you see a question like this, you'd be better prepared to do it.

A 428 g iron weight is added to 425 ml of water in a calorimeter at 22.6. The final temperature of the water was measured as 43.8. What was the initial temperature of the iron weight (assuming a perfectly insulated calorimeter)? You may omit units since the degree symbol cannot be included. The specific heat of iron is 0.449 J/(g * °C) and that of water is 4,184 J/(g ° C).

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Suppose you place 0.0300 g of magnesium chips in a coffee-cup calorimeter and then add 100 0 ml. of 1.00 M HCl. The reaction that occurs is

Mg(s) + 2 HCl(aq) → H2(g) + MgCl2(aq)

The temperature of the solution increases from 22.56 degree C (295.71 K) to 23.91 °C (297.06 K). What is the enthalpy change for the reaction per mole of Mg? Assume a specific heat capacity of the solution is 4.20 I/g • K and the density of the HCI solution is 1.00 g/mL. kJ/mol

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How much energy must be transferred to raise the temperature of a cup of coffee (250. mL) from 20.0 degree C (293.35 K) to 98.4 °C (371.55 K)? Assume that water and coffee have the same density (1.00 g/mL) and specific heat capacity (4 184 J/g •K).

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The heat capacity of an object indicates how much energy that object can absorb for a given increase in that Use the following values: object's temperature. In a system in which two objects of specific heat of water 4.18 J/(g.°C) different temperatures come into contact with one another, the warmer object will cool and the cooler object specific heat of steel 0.452 J/(g C) will warm up until the system is at a single equilibrium temperature.

Note the difference between the terms molar heat capacity, which has units of J/(mo C), and specific heat, which has units of J/(g. C).

A volume of 125 mL of H2O is initially at room temperature (22.00 C), A chilled steel rod at 2.00 C is placed in the water. If the final temperature of the system is 21.10C, what is the mass of the steel bar?

The specific heat of water is 4.18 J/(g. C). Calculate the molar heat capacity of water.

Express your answer to three significant figures and include the appropriate units.

°

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661 cal of heat is added to 5.00 g ice at -20.0 °C. What is the final temperature of the water?

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When a 2.331-g sample of a new organic material was combusted in a bomb calorimeter, the temperature of the calorimeter (and its contents) increased from 23.89 C to 28.30 C. If the heat capacity (calorimeter constant) of the calorimeter is 31.45 kJ/ C, what is the heat of combustion per gram of the material?

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Enter your answer in the provided box. A 595-g piece of copper tubing is heated to 89.5 C and placed in an insulated vessel containing 159 g of water at 22.8 C. Assuming no loss of water and a heat capacity for the vessel of 10.0 J/C, what is the final temperature of the system (c of copper = 0.387 J/g C)?

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Suppose that the microwave radiation has a wavelength of 12.4 cm. How many photons are required to heat 215 mL of coffee from 25.0 degree C to 62.0 degree C? Assume that the coffee has the same density, 0.997 g/mL, and specific heat capacity, 4.184 J/(g middot K), as water over this temperature range. Express the number of photons numerically.

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A 31.5 g water of pure gold initially at 69.3 degree C is submerged into 63.9 g of water at 27.6 degree C in an insulated container. What is the final temperature of both substances at thermal equilibrium?

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A volume of 110 mL of H_2O is initially at room temperature (22 00 degree C) A chilled steel rod at 2 00 degree C is placed n the water. If the final temperature of the system is 21.10 degree C, what is the mass of the steel bar?

Use the following values specific heat of water = 4.18 J/(g middot degree C) specific heal of steel = 0.452 J/(g middot degree C) Express your answer to three significant figures and include the appropriate units.

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The combustion of how many moles of ethane (C2H6) would be required to heat 884 g of water from 25.0 C to 98.0 C? (Assume liquid water is formed during the combustion.)

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Exactly 132.6 J will raise the temperature of 10.0 g of a metal from 25.0 C to 60.0 ºC. What is the specific heat capacity of the metal?

a. 0.379 J/g -C

b. 2.64 J/g - C

c. 23.2 J/g - C

d. 31.7 J/g -C

e. none of these

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A 2.90 g lead weight, initially at 11.1 ºC, is submerged in 7.64 g of water at 51.8 ºC in an insulated container. You may want to reference section 10.4 while completing this problem. What is the final temperature of both the weight and water at thermal equilibrium? Express the temperature in Celsius to three significant figures.

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A calorimeter was used to measure the heat change when an ionic compound dissolves in water. The final mass of the contents of the calorimeter was 50.73 g and the change in temperature was 2.35 ºC.

Calculate the heat change of the calorimeter contents Number given that its specific heat is 4.10 J (g ºC).

Calculate the heat change of the calorimeter, Number

Calculate the heat change of the solution process Number

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Calculate the amount of heat liberated (in kJ) from 366 g of mercury when it cools from 77.0°C to 12.0°C.

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A 6.22-kg piece of copper metal is heated from 20.5°C to 324.3°C. Calculate the heat absorbed (in kJ) by the metal.

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A piece of silver of mass 362 g has a heat capacity of 85.7 J/°C. What is the specific heat of silver?

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A 54.0 g block of an unknown metal is heated in a hot water bath to 100.0 C. When the block is placed in an insulated vessel containing 130.0 g of water at 25.0 C, the final temperature is 28.0 C. Determine the specific heat of the unknown metal. The Cs for water is 4.18 J/g-C.

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A sample of steam with a mass of 0.510 g and at a temperature of 100°C condenses into an insulated container holding 4.50 g of water at 2.0°C.( Δ*H*°_{vap }= 40.7 kJ/mol, water = 4.18 J/g•°C) Assuming that no heat is lost to the surroundings, what is the final temperature of the mixture?

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Four ice cubes at exactly 0°C with a total mass of 53.5 g are combined with 140 g of water at 85∘C in an insulated container. (Δ*H*°_{fus} = 6.02 kJ/mol, water = 4.18J/g•°C) If no heat is lost to the surroundings, what is the final temperature of the mixture?

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At 1 atm, how much energy is required to heat 55.0g of H_{2}O(s) at -22.0°C to H_{2}O(g) at 123.0°C? Answer in kJ and explain in detail.

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a. What is the specific heat of liquid water?

b. What is the molar heat capacity of liquid water?

c. What is the heat capacity of 185 g of liquid water?

d. How many k J of heat are needed to raise the temperature of 10.00 kg of liquid water from 24.6° C to 46.2°C?

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The enthalpy of neutralization for the reaction of HNO_{3} with KOH is given below.

HNO_{3} (aq) + KOH (aq) → H_{2}O (l) + KNO_{3} (aq) ΔH = -57.0 kJ

102.4 ml of 0.662 M HNO_{3} is combined with 102.4 ml of 0.662 M KOH in a coffee cup calorimeter. Both of the starting solutions were initially at a temperature of 30.64 °C. The density of each solution is 1.00 g/ml. Calculate the final temperature of the solution in the calorimeter (in °C).

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What is the heat capacity of 155 g of liquid water?

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At 1 atm, how much energy is required to heat 75.0 g of H _{2}O(s) at –22.0 °C to H_{2}O(g) at 145.0 °C? Helpful constants can be found below.

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Liquid sodium is being considered as an engine coolant. How many grams of liquid sodium (minimum) are needed to absorb 3.10 MJ of energy (in the form of heat) if the temperature of the sodium is not to increase by more than 10.0. Use Cm = 30.8 J/(K·mol) for Na(l).

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Liquid sodium is being considered as an engine coolant. How many grams of liquid sodium (minimum) are needed to absorb 5.90 MJ of energy (in the form of heat) if the temperature of the sodium is not increase by more than 10.0 degrees Celsius?

Use Cp=30.8J/(K*mol) for Na(l) at 500K.

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A 2.78g lead weight, initially at 11.0°C, is submerged in 7.66g of water at 52.3°C in an insulated container. What is the final temperature of both the weight and the water at thermal equilibrium?

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The specific heat of water is 4.18 J/(g • °C). Calculate the molar heat capacity of water. A volume of 115 mL of H_{2}O is initially at room temperature (22.00 °C). A chilled steel rod at 2.00 °C is placed in the water. If the final temperature of the system is 21.10 °C , what is the mass of the steel bar? Specific heat of water = 4.18 J/(g • °C) specific heat of steel = 0.452 J/(g • °C).

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Which one of the following statements is correct?

A) The SI unit of specific heat capacity is calories per gram (cal/g)

B) Specific heat capacity is a positive value for liquids and a negative value for solids

C) When heat is transferred from the surrounding to the system q is negative

D) The larger the heat capacity of an object the more thermal energy it can store

E) Heat is transformed from the systems to the surroundings in an endothermic process

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If you have 340.0 mL of water at 25.00 °C and add 120.0 mL of water at 95.00 °C, what is the final temperature of the mixture? Use 1.00 g/mL as the density of water.

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Use the information given below to calculate the energy involved in the conversion of 235 g of steam at 373 K to ice at 243 K. Be sure to use the correct sign and answer in kJ.

Specific Heat, J/g.°C

2.06 - ice

4.18 - water

2.03 - steam

Molar heat of fusion for water, kJ/mol - 6.02

Molar heat of vaporization for water, kJ/mol - 40.6

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Potassium nitrate, KNO_{3}, has a molar mass of 101.1 g/mol. In a constant-pressure calorimeter, 32.3 g of KNO_{3} is dissolved in 243 g of water at 23.00 °C.

KNO_{3}(s)+H_{2}O(aq) ---> KOH(aq)+HNO_{3}(aq)

The temperature of the resulting solution decreases to 17.90 °C. Assume the resulting solution has the same specific heat as water, 4.184 J/(g·°C), and that there is negligible heat loss to the surroundings.

1. How much heat was released by the solution?

2. What is the enthalpy of the reaction?

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Sucrose (table sugar) has the formula C_{12}H_{22}O_{11} (molar mass = 342.30 g/mol) and a food value of 6.49 kJ/g. Determine the calorimeter constant of the calorimeter in which the combustion of 0.995 g of sucrose raises the temperature by 4.21 degrees celsius (answer must be in kJ/degrees celsius).

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A 46.0 g sample of a metal is heated to 95.0°C and then placed in a calorimeter containing 120.0 g of water (c = 4.18 J/g°C) at 21.6°C. The final temperature of the water is 24.5°C. Which metal was used?

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A 2.78g lead weight, initially at 11.0°C, is submerged in 7.66g of water at 52.3°C in an insulated container. What is the final temperature of both the weight and the water at thermal equilibrium?

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The specific heat of water is 4.18 J/(g⋅^{∘}C). Calculate the molar heat capacity of water.

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Suppose a 50.0 g block of silver (specific heat = 0.2350 J/g.°C. at 100°C is placed in contact with a 50.0 g block of iron (specific heat = 0.4494 J/g.°C. at 0°C, and the two blocks are insulated from the rest of the universe. The final temperature of the two blocks

a) will be higher than 50°C.

b) will be lower than 50°C.

c) will be exactly 50°C.

d) is unrelated to the composition of the blocks.

e) cannot be predicted.

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Calculate q (in kJ) when 2.00 g of water is heated from 37°C to 47°C. The specific heat capacity of water is 4.184 J/g.°C.

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Determine the final temperature when a 25.0 g piece of iron at 85.0°C is placed into 75.0 g of water at 20.0°C. The heat capacity of the iron is 0.450 J/g °C.

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When 1.550 g of liquid hexane (C_{6}H_{14}) undergoes combustion in a bomb calorimeter, the temperature rises from 25.87 to 38.13 °C. Find the ∆E_{rxn} in kJ/mol of hexane. The heat capacity of the bomb calorimeter was found in a different experiment to be 5.73 kJ/°C.

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A chemistry student weighs a rock and finds its mass to be 4.7 g. She then finds that upon absorption of 57.2 J of heat, the temperature of the rock rises from 25°C to 57°C. Find the specific heat capacity of the substance composing the rock.

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The combustion of toluene has a ∆E_{rxn} of -3.91 x 10^{3} kJ/mol. When 1.55 g of toluene (C_{7}H_{8}) undergoes combustion in a bomb calorimeter, the temperature rises from 23.12 °C to 37.57 °C. Find the heat capacity of the bomb calorimeter.

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Which of the following statements are correct?

A. specific heat capacity is defined as the amount of heat energy required to raise the temperature of an object 1K

B. under conditions of constant pressure, no work is done on or by the system

C. molar heat capacity is defined as the amount of heat energy required to raise the temperature of 1 mole of a substance 1K

D. heat is always transferred from an object with a lower temperature to an object with a higher temperature

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What is the enthalpy change associated with heating 20g of Al from room temperature (23°C) to its melting point at 660°C and then melting it. (Specific heat of Al, C_{p} = 0.900J/kg °C; ΔH _{fus }= 437 kJ/mole)

Watch Solution

Consider a 1 kg block of ice at standard pressure. If it is initially at −5°C and is heated until it is steam at 109°C, how much total heat was added to the sample of water? Use the following thermodynamic values for your calculation:

c_{ice} = 2.09 J/g K

c_{water} = 4.184 J/g K

c_{steam} = 2.03 J/g K

∆H_{vap} = 2260 J/g

∆H_{fus} = 334 J/g

1. 3950 kJ

2. 2710 kJ

3. 2620 kJ

4. 3040 kJ

5. 28.7 kJ

Watch Solution

How much heat is absorbed by a pan made of iron, with a mass of 150 g whose temperature rises from 25.0°C to 100.0°C?

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When 75.4 J of energy is absorbed by 0.25 mol of CCl _{4}, what is the temperature change of CCl_{4}? The specific heat capacity of CCl _{4} is 0.861 J/g·°C. Molar mass of CCl _{4} is 153.81 g/mol.

A) 17.8°C

B) 21.9°C

C) 2.3°C

D) 9.1°C

E) 44.6°C

Watch Solution

When 5.50 g of Ba(*s*) is added to 100.00 g of water in a container open to the atmosphere, the reaction shown below occurs and the temperature of the resulting solution rises from 22.00°C to 61.16°C. If the specific heat capacity of the solution is 4.18 J/(g∙°C), calculate Δ*H*_{rxn} for the reaction, as written.

Ba(*s*) + 2 H_{2}O(*l*) → Ba(OH)_{2}(*aq*) + H_{2}(*g*) Δ*H*_{rxn }= ?

A) –431 kJ

B) –3.14 kJ

C) +3.14 kJ

D) +431 kJ

E) –17.2 kJ

Watch Solution

To raise 232 g of an unknown liquid from 15°C to 60°C, 17.9 kJ of energy are required. What is the specific heat capacity, *C*_{s}, of the liquid?

A) 5.41 J/(g ∙ °C)

B) 1.71 J/(g ∙ °C)

C) 3.48 J/(g ∙ °C)

D) 1.10 J/(g ∙ °C)

Watch Solution

Suppose a 50.0 g block of silver at 100°C is placed in contact with a 50.0 g block of iron at 0°C, and the two blocks are insulated from the rest of the universe. The final temperature of the two blocks

A) will be higher than 50°C.

B) will be lower than 50°C.

C) will be exactly 50°C.

D) is unrelated to the composition of the blocks.

E) cannot be predicted.

Watch Solution

Calculate the amount of heat necessary to raise the temperature of 12.0 g of water from 15.4°C to 93.0°C.

A) 0.027 J

B) 324 J

C) 389 J

D) 931 J

E) 3,890 J

Watch Solution

How much heat, in kJ, is required to raise the temperature of 125 g H _{2}O from 24.3°C to 64.9°C? The specific heat of water is 4.18 J g^{-1} °C^{-1}.

A) 21.2 kJ

B) 42.4 kJ

C) 12.7 kJ

D) 33.9 kJ

E) 523 kJ

Watch Solution

Calculate the amount of heat (in kJ) required to raise the temperature of a 79.0 g sample of ethanol from 298 K to 385 K. The specific heat capacity of ethanol is 2.42 J/g°C.

A) 12.9 kJ

B) 57.0 kJ

C) 73.6 kJ

D) 28.4 kJ

E) 16.6 kJ

Watch Solution

Calculate the amount of heat (in kJ) necessary to raise the temperature of 47.8 g benzene by 57 K. The specific heat capacity of benzene is 1.05 J/g°C

A) 2.59 kJ

B) 2.86 kJ

C) 3.85 kJ

D) 1.61 kJ

E) 16.6 kJ

Watch Solution

Determine the specific heat capacity of an alloy that requires 59.3 kJ to raise the temperature of 150.0 g alloy from 298 K to 398 K.

A) 4.38 J/g°C

B) 3.95 J/g°C

C) 2.29 J/g°C

D) 1.87 J/g°C

E) 2.53 J/g°C

Watch Solution

A sample of copper absorbs 43.6 kJ of heat, resulting in a temperature rise of 75°C, determine the mass (in kg) of the copper sample if the specific heat capacity of copper is 0.385 J/g°C.

A) 6.62 kg

B) 1.51 kg

C) 3.64 kg

D) 7.94 kg

E) 1.26 kg

Watch Solution

Determine the specific heat capacity of an alloy that requires 59.3 kJ to raise the temperature of 150.0 g alloy from 298 K to 398 K.

A) 3.95 J/g°C

B) 1.87 J/g°C

C) 2.29 J/g°C

D) 2.53 J/g°C

E) 4.38 J/g°C

Watch Solution

A 19.78 g piece of nickel (specific heat of nickel = 0.444 J/g ^{o}C) was heated to 103.5 ^{o}C and then plunged into a beaker containing 87.9 grams of water at 14.7 ^{o}C. Determine the final temperature of the metal after the system attains thermal equilibrium. (the specific heat of water is 4.184 J/g ^{o}C)

A. 59.1 ^{o}C

B. 44.4 ^{o}C

C. 16.8 ^{o}C

D. 12.5 ^{o}C

E. 55.6 ^{o}C

Watch Solution

A sample of calcium carbonate [CaCO_{3} (s)] absorbs 45.5 J of heat, upon which the temperature of the sample increases from 21.1^{o}C to 28.5^{o}C. If the specific heat of calcium carbonate is 0.82 J/g^{o}C, what is the mass (in grams) of the sample?

A. 0.20

B. 5.0

C. 7.5

D. 410

e. 5.0 x 10^{3}

Watch Solution

A student constructs a "coffee cup" calorimeter that contains 83.6 grams of water, at 19.7°C, in a double cup set up with a thermometer and a cork cover. A piece of copper with a mass of 101.7 grams was heated to a certain temperature and placed in the calorimeter. Then the calorimeter was allowed to equilibrate and the thermometer recorded a temperature of 28.3 °C after the equilibration. Determine the temperature to which the copper piece was heated initially. (The specific heat of copper is 0.385 J/g °C and the specific heat of water is 4.184 J/g °C)

a. 105.1 °C

b. 85.4 °C

c. 142.0 °C

d. 29.0 °C

e. 48.5 °C

Watch Solution

How much energy would be absorbed or released by the H _{2}O in the process.

30 grams H_{2}O(g) at 100°C → 30 grams H_{2}O(*l*) at 20°C?

1. 16.2 kcal absorbed

2. 16.2 kcal released

3. There would be no transfer of energy due to the first law of thermodynamics

4. 18.6 kcal released

5. 2.4 kcal released

Watch Solution

Two solids of equal mass, labeled X and Y, are placed in contact with each other. *Solid X* has an initial temperature of 100°C and *Solid Y* has an initial temperature of 25°C. After some time, both solids are at 40°C. Which statement is correct regarding the direction of heat transfer and specific heat capacity (Assume heat transfers only between X and Y):

**Direction of heat transfer Specific heat capacity**

A. From X to Y X has greater heat capacity

B. From X to Y Y has greater heat capacity

C. From Y to X X has greater heat capacity

D. From Y to X Y has greater heat capacity

Watch Solution

The molar heat capacity of silver is 25.35 J/mol•°C. Calculate how much energy (in kJ) it would take to raise the temperature of 15.7 g of the silver metal by 17.2 °C.

Watch Solution

A 1.00 g sample of NH _{4}NO_{3} is decomposed in a bomb calorimeter. The temperature increases by 6.12°C. What is the molar heat of decomposition for ammonium nitrate?

a) -602 kJ•mol^{-1}

b) -398 kJ•mol^{-1}

c) 7.53 kJ•mol^{-1}

d) 164 kJ•mol^{-1}

Watch Solution

When a 45.0 g sample of an alloy at 100.0 °C is dropped into 100.0 g of water at 25.0 °C, the final temperature is 37.0 °C. What is the specific heat of the alloy? The specific heat of water is 4.184 J•g^{-1}•°C^{-1}

a) 0.423 J•g^{-1}•°C^{-1}

b) 1.77 J•g^{-1}•°C^{-1}

c) 9.88 J•g^{-1}•°C^{-1}

d) 48.8 J•g^{-1}•°C^{-1}

Watch Solution

Three separate 3.5g blocks of Al, Cu, and Fe at 25 °C each absorb 0.505 kJ of heat. Which block reaches the highest temperature? The specific heats of Al, Cu, and Fe are 0.900 J/g•°C, 0.385J/g•°C, and 0.444 J/g•°C, respectively.

a) Fe

b) Fe and Cu

c) Al and Cu

d) Al

e) Cu

Watch Solution

A student mixes 100 mL of 0.50 M NaOH with 100 mL 0f 0.50 M HCl in a Styrofoam® cup and observes a temperature increase of ΔT_{1}. When she repeats this experiment using 200 mL of each solution, she observes a temperature change of ΔT_{2}. If no heat is lost to the surroundings or absorbed by the Styrofoam® cup, what is the relationship between ΔT_{1} and ΔT_{2}?

a) ΔT_{2} = 4 ΔT_{1}

b) ΔT_{2} = 2 ΔT_{1}

c) ΔT_{2 }= 0.5 ΔT_{1}

d) ΔT_{2 } = ΔT_{1}

Watch Solution

When 68.00 J of energy are added to a sample of Gallium that is initially at 25°C, the temperature rises to 38.0° C. What is the volume of the sample?

The specific heat of Gallium is 0.372 J•g ^{-1}•°C^{-1}.

Density of Gallium is 5.904 g•cm^{–3}.

a) 2.38 cm^{3}

b) 4.28 cm^{3}

c) 14.1 cm^{3}

d) 31.0 cm^{3}

Watch Solution

In a bomb calorimeter, reactions are carried out at:

(A) constant pressure

(B) constant volume

(C) 1 atm pressure and 25°C

(D) 1 atm pressure and 0°C

Watch Solution

How much energy is required to change the temperature of 21.5 g Cu from 27 to 88.1 °C? The specific heat capacity of copper is 0.385 J/gK.

- 223 J
- 506 J
- 641 J
- 729 J
- 3.41 x 10
^{3}

Watch Solution

If it takes 0.216 kJ of heat to raise the temperature of a 12.0 g piece of Al from 15.5 to 35.5 ^{o}C, what is the specific heat (J/g K) of Al?

Watch Solution

Adding water to a steel pan on a flame slows the rise in temerature of the pan, which of the following concepts does this represent?

A. Heat capacity is an intensive property

B. Heat capacity is an extensive property

C. The example does not relate to heat capacity

D. Temperature is a state function

Watch Solution

When a fresh breath of air is drawn into the lungs, it is heated by your body. Let’s assume it reaches thermal equilibrium with your body temperature of 37°C. Given the temperature, pressure, and the average molar mass of air, you could easily calculate that your breath of 0.48 L corresponds to 0.51 g of air. The specific heat of air is 1.0 J/g•°C.

I. Given that the temperature outside is 21°C, how much heat is required to take the air in your 0.48 L breath from 21°C to 37°C?

II. The heat calculated in the previous question is lost every time you exhale. Assuming 15 breaths per minute, how much heat would be lost in one day by exhaling? Furthermore, assuming a daily energy intake of 8400 kJ (corresponding to 2000 food Calories), what percent of your daily energy intake is lost as heat due to exhaling during a 24 hour period?

Watch Solution

Which substance (with specific heat capacity provided) would show the smallest temperature change upon gaining 200.0 J of heat?

a) 50.0 g Al, C_{Al} = 0.903 J/g°C

b) 50.0 g Cu, C_{Cu} = 0.385 J/g°C

c) 25.0 g granite, C_{granite} = 0.79 J/g°C

d) 25.0 g Au, C_{Au} = 0.128 J/g°C

e) 25.0 g Ag, C_{Ag} = 0.235 J/g°C

Watch Solution

Two aqueous solutions are both at room temperature and are then mixed in a coffee cup calorimeter. The reaction causes the teperature of the resulting solution to fall below room temperature. Which of the following statements is TRUE?

a) The products have a lower potential energy than the reactants.

b) This type of experiment will provide data to calculate ΔE _{rxn}.

c) The reaction is exothermic.

d) Energy is leaving the system during the reaction.

e) None of the above statements is true.

The same reaction in a bomb and coffee-cup calorimeter :

a) will give the same value for ΔH _{rxn }because it is the same reaction.

b) will give the same value for ΔH _{rxn} because both systems are identical.

c) will give the same values because both systems are at a constant pressure.

d) will give slightly different values because the coffee-cup calorimeter will do some PV work.

e) will give slightly different values because the bomb calorimeter will do some PV work.

Watch Solution

The specific heat of liquid ethanol, C_{2}H_{5}OH(*l*), is 2.46 J/g•°C and the heat of vaporization is 39.3 kJ/mol. The boiling point of ethanol is 78.3°C. The molecular weight of ethanol 46 g/mol. What amount of enthalpy is required to heat 50.0 g of liquid ethanol from 23.0°C to ethanol vapor at 78.3°C?

1) 42.7 kJ

2) 49.5 kJ

3) 179 kJ

4) 1970 kJ

5) 6840 kJ

Watch Solution

Assuming the heat released from the combustion of CH _{4} can be used with 100% efficiency, how much CH_{4} (in g) is required to be combusted in the presence of excess oxygen to warm 1.75 kg of water (C_{w}= 4.184 J/gK) from 25.0 to 98.0 °C? The enthalpy of combustion of CH_{4} is -802.3 kJ/mol.

A. 56.5 g

B. 46.2 g

C. 28.7 g

D. 10.7 g

E. 7.04 g

Watch Solution

A 0.500-L sample of 0.400 M Na_{2}CO_{3} (aq) is added to 0.500 L of 0.400 M Ba(NO _{3})_{2} (aq) in a calorimeter with a total heat capacity equal to 656 J•K ^{–1} at a constant pressure of one bar. The temperature change is +1.25 K. Use these data to calculate the value of ΔH°rxn for the equation:

Watch Solution

A 0.3423 g sample of pentane, C_{5}H_{12}, was burned in a bomb calorimeter. The temperature of the calorimeter and the 1.000 kg of water contained therein rose from 20.22ºC to 22.82ºC. The heat capacity of the calorimeter is 2.21 kJ/ºC. The heat capacity of water = 4.184 J/gºC. How much heat was given off during combustion of the sample of pentane?

1) 8.8 kJ

2) -8.8 kJ

3) 16.6 J

4) 16.6 kJ

5) 3.1415 kJ

Watch Solution

The change in enthalpy (∆H) is a measure of the heat of reaction at

1) Constant temperature.

2) Constant pressure.

3) Constant volume.

4) Constant internal energy.

5) Constant entropy.

Watch Solution

A 100.0 mL sample of 0.200 M aqueous hydrochloric acid is added to 100.0 mL of 0.200 M aqueous ammonia in a calorimeter whose heat capacity is negligible. The following reaction occurs when the two solutions are mixed.

Watch Solution

A 55.0-g piece of metal is heated in boiling water to 99.8 °C and then dropped into cool water in an insulated beaker containing 225 mL of water with an initial temperature of 21.0 °C. The final temperature of the metal and water is 23.1 °C, what is the specific heat capacity of the metal?

Watch Solution

What is the minimum mass of ice at 0 °C that must be added to the contents of a can of diet cola (340. mL) to cool the cola to 0 °C from room temperature (20.5 °C)? The heat of fusion for ice is 333 J/g. Assume the cola density is equivalent to water (1 g/mL).

Watch Solution

How much energy must be transferred to raise the temperature of a cup of coffee that is 250 mL from 20.5 °C to 368.8 K? Assume that water and coffee have the same density 1.00 g/mL and specific heat capacity (4.184 J/g•K).

Watch Solution

Which of the following substances (with specific heat capacity provided) would show the greatest temperature change upon absorbing 100.0 J of heat?

a) 10.0 g Ag, C_{Ag} = 0.235 J/g°C

b) 10.0 g H_{2}O, C_{H2O} = 4.18 J/g°C

c) 10.0 g ethanol, C_{ethanol} = 2.42 J/g°C

d) 10.0 g Fe, C_{Fe} = 0.449 J/g°C

e) 10.0 g Au, C_{Au} = 0.128 J/g°C

Watch Solution

The molar heat capacity of silver is 25.35 J/mol × ^{o}C . Calculate how much energy (in kJ) it would take to raise the temperature of 15.7 g of the silver metal by 17.2 ^{o}C.

Watch Solution

It takes 75.0 J to raise the temperature of an 19.3 g piece of unknown metal from 21.0^{o}C to 46.7^{o}C. What is the specific heat of for the metal?

Watch Solution

A total of 2.25 moles of a compound are allowed to react with water in a foam coffee cup and the reaction produces 83.1 g of solution. The addition of the compound caused the temperature of the solution to increase from 20.5 ^{o}C to 32.1 ^{o}C. What is the enthalpy of the reaction? Assume no heat is transferred or lost to the surroundings or to the foam coffee cup. The specific heat of the solution is 4.184 J/(g×^{o}C) .

Watch Solution

The same reaction in a bomb and coffee-cup calorimeter:

a. will give the same value of Hrxn because it is the same reaction.

b. will give the same value for Hrxn because both systems are identical.

c. will give the same values because both systems are at constant temperature.

d. will give slightly different values because the coffee-cup calorimeter will do some PV work.

e. will give slightly different values because the bomb calorimeter will do some PV work

Watch Solution

A sample of 1.67 grams of compound Y is burned completely in a bomb calorimeter which contains 2500 g of water. The temperature rises from 24.273ºC to 24.587ºC. What is ∆*U*_{rxn} for the combustion of compound Y? The hardware component of the calorimeter has a heat capacity of 3.29 kJ/ºC. The specific heat of water is 4.184 J/g·ºC, and the MW of Y is 117 g/mol.

1. -344.7

2. -615.4

3. -392.1

4. -322.0

5. -302.5

6. -185.4

7. -482.0

8. -652.5

9. -278.2

10. -424.3

Watch Solution

Which substance (with specific heat capacity provided) would show the smallest temperature change upon gaining 200.0 J of heat?

a. 50.0 g Al, C_{Al} = 0.903 J/g°C

b. 50.0 g Cu, C_{Cu} = 0.385 J/g°C

c. 25.0 g granite, C_{granite} = 0.79 J/g°C

d. 25.0 g Au, C_{Au} = 0.128 J/g°C

e. 25.0 g Ag, C_{Ag} – 0.235 J/g°C

Watch Solution

In constant-volume calorimetry, what is FALSE?

a. There is no work performed.

b. The total energy is measured by the change in pressure.

c. The total energy is determined only by heat.

d. The heat capacity of the calorimeter needs to be known in order to determine the heat.

e. All of the above are true.

Watch Solution

The specific heat of copper metal is 0.385 J/g K. How many joules of heat are necessary to raise the temperature of a 1.42-kg block of copper from 25.0 °C to 88.5 °C?

A) 3.47 x 10^{4} J

B) 34.7 J

C) 2.34 x 10^{5} J

D) 8.46 J

Watch Solution

If three samples of silver, one with a mass of 10.0 grams, another with a mass of 50.0 grams and a third with a mass of 100.0 grams each absorb 36.3 kJ of heat which sample will experience the greatest increase in temperature?

- The 10.0 gram sample
- The 50.0 gram sample
- The 100.0 gram sample
- Each will have the same increase in temperature
- Depends on the starting temperature of each

Watch Solution

A piece of iron (mass = 100.0 g) at 398 K is placed in a Styrofoam coffee cup calorimeter containing 25.0 mL of water 298 K. Assuming that no heat is lost to the cup, what will be the final temperature of the water? The specific heat capacity of iron = 0.449 J/gºC.

A. 308 K

B. 328 K

C. 338 K

D. 368 K

E. 388 K

Watch Solution

A bar of hot metal is placed in water in a insulated container and the two are allowed to reach thermal equilibrium. When 1.0 kg of metal at 100°C is placed in 2.0 gk of water, the temperature water bath raises from 20°C to 25°C. What is the specific heat capacity of the metal (J/g K)?

a) 0.5

b) 1.5

c) 0.22

d) 25

e) 0.025

Watch Solution

Ethanol (C_{2}H_{5}OH) melts at -114°C. The enthalpy of fusion is 5.02 kJ/mol. The specific heats of solid and liquid ethanol are 0.97 J/g•K and 2.3 J/g•K, respectively. How much heat (kJ) is needed to convert 25.0 g of solid ethanol at -135°C to liquid ethanol at -50°C?

A) 207.3 kJ

B) -12.7 kJ

C) 6.91 kJ

D) 4192 kJ

E) 9.21 kJ

Watch Solution