- Ch.1 - Intro to General Chemistry
- Ch.2 - Atoms & Elements
- Ch.3 - Chemical Reactions
- BONUS: Lab Techniques and Procedures
- BONUS: Mathematical Operations and Functions
- Ch.4 - Chemical Quantities & Aqueous Reactions
- Ch.5 - Gases
- Ch.6 - Thermochemistry
- Ch.7 - Quantum Mechanics
- Ch.8 - Periodic Properties of the Elements
- Ch.9 - Bonding & Molecular Structure
- Ch.10 - Molecular Shapes & Valence Bond Theory
- Ch.11 - Liquids, Solids & Intermolecular Forces
- Ch.12 - Solutions
- Ch.13 - Chemical Kinetics
- Ch.14 - Chemical Equilibrium
- Ch.15 - Acid and Base Equilibrium
- Ch.16 - Aqueous Equilibrium
- Ch. 17 - Chemical Thermodynamics
- Ch.18 - Electrochemistry
- Ch.19 - Nuclear Chemistry
- Ch.20 - Organic Chemistry
- Ch.22 - Chemistry of the Nonmetals
- Ch.23 - Transition Metals and Coordination Compounds

The **Simple Gas Laws** study the effect of changing **pressure, temperature and moles** have on the variable of **volume**. Together all three Simple Gas Laws combine to give the **Ideal Gas Law**.

**Concept:** Boyle's Law

Welcome back guys. In this new video, we get to take a look at the simple gas laws. Let's start it out. We're going to say that the first gas law states that at constant temperature, the volume occupied by a gas in a container is inversely proportional to its external pressure. What the heck does that mean?

Inversely proportional just means that they're opposite of each other. What this is really saying is volume and pressure are opposites, meaning if one goes up, let's say our volume goes up, that means that our pressure goes down. If our volume goes down, then our pressure goes up. That's all inversely proportional means.

We're going to say that the simple gas law that tells us this is Boyle's Law. If you want to see this visually, think of it like this. We have a container. Inside this container, we have this piston that pushes down. This piston represents pressure. Here we're going to say that the piston is not very low because there's not much pressure. We're going to say here pressure is very low, so pressure low. Now, all this space in here, all this free room in there is our volume. Because the pressure is low, our volume is very high. There's a lot of room.

But let's say that I decide that I want to push down on this piston. I come in, wrap my hand around it and push down. Now the pressure increases because I'm pushing down on it. As a result, look at the volume now. Pressure here would be high, as a result, volume would be very low. Pressure and volume being opposite of each other, that's Boyle's Law.

It's going to be important for you to remember these simple gas laws because professors can ask calculated questions on using Boyle's Law or they could just simply ask you a theory question, which simple gas law states that volume and pressure are opposites of each other, that they're inversely proportional. That would be an easy question to get correct, so just remember what it means. It means that pressure and volume are opposites of each other.

**Boyle’s Law** states that **pressure** and **volume** are **inversely proportionally,** which basically means they are opposites, at constant moles and temperature.

**Concept:** Charles Law

The next simple gas law states that at constant pressure, the volume occupied by a gas in a container is directly proportional to its absolute Kelvin temperature. All this means is volume and your Kelvin temperature are directly related. If your volume increases, then your temperature is increasing. If your volume is decreasing, well, your temperature must be decreasing. We're going to say that this is known as Charles' Law.

If we looked at a picture of this, so let's say we have a container. Here's the volume in the container. There's no heat being supplied to this container and as a result, the volume is low and the temperature is low. But let's say I take that same container and all of the sudden I light a match underneath it and heat it up. What happens here is there are gas particles here the whole time. When I heat them up, the gas particles are going to absorb this thermal energy from the match that I let. They absorb this thermal energy and use it as fuel to make the move, so they convert thermal energy to kinetic energy. So they have more energy so they're able to bounce off things faster and harder.

They absorb this energy and they hit the top of this piston with more force, thereby pushing it up, so the piston slides up because the gases are hitting it harder. As a result, because I increase the temperature, I increase the kinetic energy of my gas particles which then increased the volume. That's how it works. That's Charles' Law. So I increased the temperature, so the temperature now is high, so volume becomes high.

Remember the connection for this is because the gas particles absorb that thermal energy and change it to kinetic energy and use it to push the piston up, thereby increasing the volume.

**Charles Law** states that **volume** and **temperature** are **directly proportionally** if pressure and moles are constant. So if one is high then the other is high and vice versa.

**Concept:** Avogadro's Law

The next simple gas law states that at constant temperature and pressure, the volume of a gas is directly proportional to the amount moles of gas. Remember the SI unit for the amount of a substance is the mole. This law basically says that if my volume is increasing, it's because my moles are increasing. If my volume is decreasing, it's because my moles are decreasing. This is known as Avogadro's Law. Same guy from Avogadro's number.

This makes sense. Let's say we had only three gas particles in here. There's not that many of them, so we don't need that much room. But let's say I started pumping in way more gas particles, naturally, if I have more gas particles, I need room for them because you can't squeeze all of them into that small little space. So what do I do? I just increase the volume to fit more people in there.

**Avogadro’s Law** states that **volume** and **moles **are **directly proportionally **at constant pressure and temperature. So if one is high then the other is high and vice versa.

**Concept:** Understanding PV = nRT, the Ideal Gas Law

We're going to say that Boyle's Law, Charles' Law and Avogadro's Law, each of the gas laws focuses on the effects that changes in one variable can have on the volume of a gas. So these three guys are looking to see the effects that all of these changes have on the volume of a container. We're going to say altogether they combine to give us the Ideal Gas Law. This equation is going to be essential for our calculations dealing with gases.

The Ideal Gas Law is PV = nRT. We're going to say that P here equals pressure in atmospheres. We're going to say V equals volume in liters. We're going to say that n equals our moles of the gas. T equals temperature in Kelvin. R equals our gas constant. From the name gas constant it means that it's a constant number, so it's going to be up to you guys to remember what that constant number is. R equals 0.08206. The units are liters times atmospheres over moles times K.

What you should realize is the units in R are what is telling us the other units for everyone else. The units we find in R dictate the units found in all the other units. Because R has liters, volume has to be in liters. Because R has atmospheres, pressure is in atmospheres. Moles, moles. And Kelvin, that's why temperature has to be in Kelvin. The units of R dictate the units of all the other variables.

**Concept:** Gay-Lussac's Law

Usually, professors kind of skip this other gas law because it doesn't talk about the influences that we have on volume. It relates our pressure to our temperature, which is different. We're going to say in lab is where you usually see this simple gas law. Just make reference to this. You usually see this simple gas law in lab. Just remember what this one is because it could help you in lab when you're doing calculations or have to write a report.

Here, this last gas law states that at constant volume and moles, the pressure exerted by a gas is directly proportional to the internal temperature of the container. Basically, what it's saying here, pressure and temperature, they're saying that if your pressure is increasing, it's because your temperature is increasing. If your pressure is decreasing, it's because your temperature is decreasing.

Now, why is that? Let's think about it. Here we don't have any temperature at all and we have these three gas particles. The temperature is low, so the pressure is low. But I introduce a flame. We're saying that the volume stays constant, so the volume is not going to increase. The volume stays the same. We keep the volume the same. I increase the heat. The gas particles are going to absorb that thermal energy and use it as kinetic energy. They absorb that energy, they move faster. If they're moving faster, they're going to be hitting the walls of the container harder.

Remember we said, back in the beginning, that pressure is force per area. If the gases are moving faster and hitting the walls harder, then the pressure is going to naturally increase. It can naturally increase because we're keeping the volume the same. This simple gas law is called the Gay-Lussac's Law.

Remember this one. It's different from the first three. The first three are talking about the changes that we do to the other variables and the effects they have on the volume of a gas. Here we're talking about the influences of temperature on the pressures found in the container. Different. It's still important to know because your teachers may put it on the exam or you may be asked it in lab. Definitely in lab, so it's important to remember this last one here

**Gay-Lussac’s Law** states that **pressure** and **temperature **are **directly proportionally **at constant volume and moles. So if one is high then the other is high and vice versa.

Sometimes we will be given two of the same variables such as volume, temperature, pressure or moles. In these cases, you will have to learn to manipulate the Ideal Gas Law to isolate the equation you need.

**Example:** A sample of neon gas occupies 112 mL at 0.567atm. If the temperature remains constant, what is the volume (in L) at 1165 mmHg?

When manipulating the Ideal Gas Law you want your common set of variables on one side of your equation.

**Example:** An engineer pumps air at 0** ^{o}**C into a mechanized piston-cylinder engine. If the volume measures 7.18 cm

Manipulating the Ideal Gas Law can help us solve questions beyond our understanding of the Simple Gas Laws.

**Problem:** A large plastic container holds 47.1 g of water vapor at a pressure of 1.12 atm. What is the new pressure if 12.1 g of water vapor is removed at constant temperature?

A

0.832 atm

B

0.288 atm

C

0.575 atm

D

0.416 atm

% of students got this right

If we are not given two of the same variables such as volume, temperature, pressure or moles then we just use the** Ideal Gas Law**.

**Problem:** A steel tank has a volume of 592 L and is filled with 0.638 kg of hydrogen gas. Calculate the pressure of the gas if the temperature is 82 degrees Celsius.

A

15.5 atm

B

3.75 atm

C

31.0 atm

D

7.75 atm

% of students got this right

**Concept:** Ideal Gas Stoichiometry

Welcome back guys. In this new video, we're going to attempt to relate the Ideal Gas Law to our old friend, stoichiometry.

Let's take a look here at this first part. We say in the previous chapters, we encountered reactions that involved gases. So we might be talking about gases in greater detail now, but there have been times when we dealt with gases. The first time was when we had oxygen gas as a reactant. Remember, when did we see this? We saw this in combustion.

Example we have CH4 reacting with O2 gas. That creates, remember combustion creates carbon dioxide as a gas plus water vapor. All we have to remember to do here is just balance out the equation. That would be an example where we dealt with gases in combustion.

The second time when we dealt with gases in hydrogen displacement. Hydrogen displacement we have basically a metal reacting with an acid, HCl, HBr, or HI. The metal physically kicks out the hydrogen and hydrogen exists by itself as H2 gas. An example we have magnesium solid reacting with HCl aqueous. Magnesium comes in and kicks out the hydrogen.

Remember, magnesium is going to connect with the chlorine. That's going to form an ionic compound because we're going to have a metal connected to a nonmetal. Remember for ionic compounds, we have to remember the charges. Magnesium is in group 2A, so it's plus two. Chlorine is in group 7A, so it's minus one. The two from here would come here, the one from here would move over here. We'd have MgCl2 aqueous plus, remember the hydrogen got kicked out and it can't exist by itself, so it exists as H2 gas. We just have to balance it by putting a two here and we're done.

So this is hydrogen displacement. A metal physically kicks out hydrogen from a halogen. This could also happen with HBr, HI. They also would do hydrogen displacement.

Now it's time for us to connect our Ideal Gas Law concepts that we've covered thus far plus the older concepts we learned about stoichiometry.

We’ve dealt with gases on previous topics such as stoichiometry, where the gas was either a reactant or product. Now we can relate Stoichiometry to the Ideal Gas Law.

For a stoichiometric question dealing with the Ideal Gas Law just focus on the KNOWN quantities and determine which portion of the ideal Gas Law you need to isolate.

**Example:** Magnesium reacts with excess hydrochloric acid to form aqueous magnesium chloride and 26.7 mL of hydrogen gas at 25** ^{o}**C and 723 mmHg.

Mg (s) + **2** HCl (aq) → MgCl_{2} (aq) + H_{2} (g)

How many grams of magnesium reacted?

6mWhen a gas is collected over water the total pressure is the partial pressures of the gas and of water vapor. To determine the correct answer you need to find the partial pressure of only the gas.

**Example:** Acetylene (C_{2}H_{2}), an important fuel in wielding, is produced in the laboratory when calcium carbide (CaC_{2}) reacts with water:

CaC_{2} (s) + 2 H_{2}O (l) → C_{2}H_{2} (g) + Ca(OH)_{2} (aq)

The pressure of acetylene collected over water is 729 torr while the volume was measured as 629 mL. If at 21** ^{o}**C the vapor pressure of the water is 29 torr, how many grams of acetylene were produced?

A sealed container holding 0.0255 L of an ideal gas at 0.993 atm and 73oC is placed into a refrigerator and cooled to 43 oC with no change in volume. Calculate the final pressure of the gas.

Watch Solution

What is the volume occupied by 18.6 g of argon gas at a pressure of 1.19 atm and a temperature of 394 K? Express your answer with the appropriate units.

Compare the volume of 18.6 g of helium to 18.6 g of argon gas (under identical conditions).

The volume would be greater for helium gas.

The volume would be the same for helium gas.

The volume would be lower for helium gas.

Watch Solution

Use Equation to derive all the gas laws.

Watch Solution

Name five elements and five compounds that exist as gases at room temperature.

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If an ideal gas has a pressure of 6.07 atm, a temperature of 10.42 °C, and has a volume of 69.83 L how many moles of gas are in the sample?

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A sample of an ideal gas has a volume of 3.60 Lat 14.40 C and 1.80 atm. What is the volume of the gas at °C and 0.988 atm?

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If 3.63 moles of an ideal gas has a pressure of 1.25 atm, and a volume of 77.29 L. What is the temperature of the sample in degrees Celsius?

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A sample of carbon dioxide is contained in a 125.0 mL flask at 0.943 atm 17.4 degree C. How many molecules of gas are in the sample?

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The reaction for the combustion of propane is shown below. kcal

C3H8(g) + 5 O2 (g) ---> 3 CO2 (g) + 4 H2O (l) ΔH = -526.3 kcal/mol

How much heat is kcal released when 71.7 g of propane is burned?

If 1.65 moles of an ideal gas has a pressure of 2.56 atm and a volume of 81.95 L, what is the temperature of the sample?

Watch Solution

What pressure (in atm) will 0.44 moles of CO_{2} exert in a 2.6 L container at 25^{o}C?

Watch Solution

Which gas sample has the greatest volume at STP?

a. 20g of Ne

b. 2g of H_{2}

c. 8g of He

d. 20 g of N_{2}

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What volume will a balloon occupy at 1.0 atm, if the balloon has a volume of 7.6 L at 2888 mmHg?

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What volume will a balloon occupy at 1.0 atm, If the balloon has a volume of 8.8 L at 4.4 atm?

a. 2.0 L

b. 44 L

c. 0.50 L

d. 39 L

Watch Solution

A quantity of CO gas occupies a volume of 0.34L at 1.9atm and 309K . The pressure of the gas is lowered and its temperature is raised until its volume is 2.0L . Find the density of CO under the new conditions.

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Oxygen used in respiratory therapy is stored at room temperature under a pressure of 150 atm in a gas cylinder with a volume of 60.0 L. What volume would the oxygen occupy at 0.730 atm? Assume no temperature change; and if the oxygen flow to the patient is adjusted to 6.00 L/min at room temperature and 0.730 atm , how long will the tank of gas last?

Watch Solution

A sample of gas in a balloon has an initial temperature of 9°C and a volume of 1200L . If the temperature changes to 85°C , and there is no change of pressure or amount of gas, what is the new volume, V_{2}, of the gas? What Celsius temperature, T_{2}, is required to change the volume of the gas sample in Part A (T_{1} = 9°C , V_{1}= 1200L ) to a volume of 2400L ? Assume no change in pressure or the amount of gas in the balloon.

Watch Solution

A sample of ideal gas at room temperature occupies a volume of 34.0 L at a pressure of 782 torr . If the pressure changes to 3910 torr , with no change in the temperature or moles of gas, what is the new volume, V_{2}; and If the volume of the original sample in Part A (P_{1} = 782 torr , V_{1} = 34.0 L ) changes to 65.0L , without a change in the temperature or moles of gas molecules, what is the new pressure, P_{2}.

Watch Solution

A 1.00 L flask is filled with 1.00 g of argon at 25°C. A sample of ethane vapor is added to the same flask until the total pressure is 1.250atm .

**Part A**

What is the partial pressure of argon, *P*Ar, in the flask? Express your answer to three significant figures and include the appropriate units.

*P*Ar = _________________

**PART B**

What is the partial pressure of ethane, *P*ethane, in the flask? Express your answer to three significant figures and include the appropriate UNITS.

*P*ethane =_________________

Watch Solution

At 25.0°C, a sample of Xe gas occupies 106.5 mL in a piston-cylider apparatus when the external pressure is 644.4 torr. At what pressure (torr) will its volume become 215.2 mL if the temperature does not change? Enter your answer with two decimal places and no units.

Watch Solution

A sample of oxygen gas has its absolute temperature halved while the pressure of the gas remained constant. If the initial volume is 400 mL, what is the final volume?

Watch Solution

In the synthesis of ammonia gas from nitrogen and hydrogen,

N_{2}(g) + 3H_{2}(g) → 2NH_{3}(g)

what is the maximum volume, in liters, of NH _{3} that can be formed from 15.0 L of H _{2}.

a. 7.50

b. 10.0

c. 15.0

d. 22.5

e. 30.0

Watch Solution

Deviations from the ideal gas law are less at:

a. high temperatures and high pressures

b. high temperatures and low pressures

c. low temperatures and high pressures

d. low temperatures and low pressures

Watch Solution

How many moles of O_{2} will be present in a 3.00 L sample of the gas collected at 25°C and 0.900 atm?

1. 0.110 mol

2. 0.134 mol

3. 83.9 mol

4. 9.06 mol

5. 1.32 mol

Watch Solution

A certain quantity of a gas occupies 61.3 mL at 68°C. If the pressure remains constant, what would the volume of the gas be at 17°C?

1. 72 mL

2. 92 mL

3. 32 mL

4. 52 mL

Watch Solution

The volume of a gas is proportional to the temperature of a gas is known as

A) Avogadro's Law

B) Ideal Gas Law

C) Charles's Law

D) Boyle's Law

E) Dalton's Law

Watch Solution

A mixture of He and O _{2} is placed in a 4.00 L flask at 32°C. The partial pressure of the He is 2.7 atm and the partial pressure of the O_{2} is 1.4atm. What is the mole fraction of O _{2}?

a. 0.224

b. 0.341

c. 0.481

d. 0.518

e. 0.659

Watch Solution

A gas is collected and found to fill a volume of 2.85 L at 25.0°C. What will be its volume at standard temperature?

a. 1.3 L

b. 2.6 L

c. 4.5 L

d. 2.8 L

e. 1.3 L

Watch Solution

A sample of carbon dioxide gas as 125 ^{o}C and 248 torr occupies a volume of 275 L. What will the gas pressure be if the volume is increased to 321 L at 125 ^{o}C?

a. 441 torr

b. 289 torr

c. 356 torr

d. 359 torr

e. 212 torr

Watch Solution

Under which conditions will a gas behave most ideally?

1. high T and low P

2. low V and low P

3. high P and low V

4. high T and low V

5. low n and high P

6. high T and high n

7. high n and high P

8. high V and low T

9. high n and high V

Watch Solution

In the ideal gas law P V = n R T, P and V are

1. related, but not important.

2. independent of each other.

3. inversely proportional.

4. lovers.

5. never related mathematically.

Watch Solution

A fuel cell car is powered by electrons harvested from the flameless, low-temperature reaction

How many liters of oxygen is needed to react with 42.0 L of hydrogen at STP?

1. 21.0 L

2. 32.0 L

3. 63.0 L

4. 84.0 L

5. 22.4 L

6. 672 L

7. 42.0 L

8. 2.02 L

Watch Solution

Consider two cylinders of gas. One cylinder contains N_{2} at 2 atm and 25^{◦}C. The other cylinder contains F_{2} at 1 atm and 50◦C. Which statements is/are true?

I) The N_{2} molecules and the F_{2} molecules have the same average kinetic energy.

II) Every molecule in the N_{2} sample has the exact same speed.

III) If the pressure of N2 was increased without a change in n or V, the temperature would have to increase.

IV) The N_{2} gas would behave less ideally if the pressure was increased.

Which of these statements is true?

1. III and IV only

2. I and II only

3. II and III only

4. II and IV only

5. I and IV only

Watch Solution

A 40.2 L constant volume cylinder containing 2.21 mol He is heated until the pressure reaches 4.20 atm. What is the final temperature?

A) 658 K

B) 1074 K

C) 804 K

D) 931 K

E) 258 K

Watch Solution

A 55.0 L gas cylinder containing NO and 3.238 mol of N _{2} has a total pressure of 2.14 atm at 303 K. What is the mole fraction of NO?

A) 4.729

B) 0.683

C) 0.0467

D) 1.491

E) 0.316

Watch Solution

Consider the chemical reaction:

**2 KClO _{3} (s) → 2 KCl (s) + 3 O_{2} (g)**.

If 245.1 grams of KClO_{3} reacts completely in a container that is at constant pressure of 1.00 atm and constant temperature of 273 Celsius, what __volume of gas__ in liters is produced? (The molar mass of KClO_{3} is 122.55 g/mol)

- 44.8 L
- 67.2 L
- 89.6 L
- 112 L
- 134 L

Watch Solution

Calculate the density of CO_{2}(g) at 100°C and 10.0 atm pressure.

A) 1.44 g/L

B) 134 g/L

C) 44.0 g/L

D) 53.6 g/L

E) 14.4 g/L

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Under what conditions is a gas most likely to deviate from ideal behavior?

1. high temperatures

2. when considering noble gases

3. low density

4. high pressure

Watch Solution

A gas is showing a considerable amount of attractive forces. What is the likely value for the compressibility factor?

1. It will be slightly above one.

2. It will be slightly below one.

3. It will be equal to one.

Watch Solution

What pressure will 14.0 g of CO exert in a 3.5 L container at 75°C?

A) 1.1 atm

B) 2.3 atm

C) 4.1 atm

D) 6.4 atm

E) 5.0 atm

Watch Solution

Calculate the volume occupied by 0.845 mol of nitrogen gas at a pressure of 1.37 atm and a temperature of 315 K.

Given: n = 0.845 mol, P = 1.37 atm, T = 315 K

Find: V

Watch Solution

In the figures below, if shaded and unshaded spheres represent atoms of different elements, which of the above drawings most likely represents a molecular compound at room temperature and a pressure of 1 atm?

A) drawing (a)

B) drawing (b)

C) drawing (c)

D) drawing (d)

Watch Solution

Baggage handlers at airports routinely screen luggage for the presence of nitroglycerin, C_{3}H_{5}(NO_{3})_{3} (Molar mass = 227.11 g). Nitroglycerin is a highly explosive compound and decomposes according to the following equation:

4 C_{3}H_{5}(NO_{3})_{3}(*s*) → 12 CO_{2} (*g*) + 10 H_{2}O (g) + 6 N_{2} (*g*) + O_{2} (*g*)

Calculate the total volume of CO _{2} gas collected at 1.2 atm and 27.0 ^{o}C from 42.5 grams of nitroglycerin.

a. 12.6 L

b. 0.346 L

c. 1.04 L

d. 3.84 L

e. 11.5 L

Watch Solution

Calculate the mass, in grams, of 2.74 L of CO gas measured at 33°C and 945 mmHg (R = 0.08206 L•atm•K^{-1}•mol^{-1}, 1 atm = 760 mmHg).

a. 0.263 g

b. 35.2 g

c. 2.46 g

d. 3.80 g

e. 206 g

Watch Solution

Hydrogen and oxygen gas are mixed in a 7.75 L flask at 65°C and contains 0.482 g of hydrogen and 4.98 g of oxyen. What is the partial pressure of oxygen in the flask?

a. 33.5 atm

b. 0.557 atm

c. 67 atm

d. 1.11 atm

e. 0.043 atm

Watch Solution

Consider a gas in a container with an initial pressure, temperature and volume. What will happen to the pressure of the gas if the number of moles are quadrupled, the volume is tripled and the temperature is increased 5 times?

A. the pressure will increase by 12 times

B. the pressure will increase by 6.7 times

C. the pressure will remain inchanged

D. the pressure will increase by 2.4 times

E. the pressure will increase by 3.8 times

Watch Solution

A sample of carbon dioxide gas at 125°C and 248 torr occupies a volume of 275 L. What will the gas pressure be if the volume is increased to 321 L at 125°C?

a. 441 torr

b. 289 torr

c. 356 torr

d. 359 torr

e. 212 torr

Watch Solution

A particular balloon can be stretched to a maximum surface area of 1257 cm ^{2}. The balloon is filled with 3.0 L of helium gas at a pressure of 755 torr and a temperature of 298 K. The balloon is then allowed to rise in the atmosphere. If the atmospheric temperature is 273 K, at what pressure will the balloon burst? (Assume the balloon to be in the shape of a sphere.)

Watch Solution

An 11.5-mL sample of liquid butane (density = 0.573 g/ mL) is evaporated in an otherwise empty container at a temperature of 28.5 °C. The pressure in the container following evaporation is 892 torr. What is the volume of the container?

Watch Solution

In a common classroom demonstration, a balloon is filled with air and submerged in liquid nitrogen. The balloon contracts as the gases within the balloon cool. Suppose the balloon initially contains 2.95 L of air at a temperature of 25.0 °C and a pressure of 0.998 atm. Calculate the expected volume of the balloon upon cooling to -196 °C (the boiling point of liquid nitrogen). When the demonstration is carried out, the actual volume ofthe balloon decreases to 0.61 L. How does the observed volume of the balloon compare to your calculated value? Can you explain the difference?

Watch Solution

When hydrochloric acid is poured over potassium sulfide, 42.9 mL of hydrogen sulfide gas is produced at a pressure of 752 torr and 25.8 °C. Write an equation for the gas-evolution reaction and determine how much potassium sulfide (in grams) reacted.

Watch Solution

Consider the chemical reaction:

C(s) + H_{2}O(g) → CO(g) + H_{2}(g)

How many liters of hydrogen gas are formed from the complete reaction of 15.7 g C? Assume that the hydrogen gas is collected at a pressure of 1.0 atm and a temperature of 355 K.

Watch Solution

What is the mole fraction of oxygen gas in air (see Table 5.3)? What volume of air contains 10.0 g of oxygen gas at 273 K and 1.00 atm?

Watch Solution

A sample of nitrogen gas in a 1.75-L container exerts a pressure of 1.35 atm at 25 °C. What is the pressure if the volume of the container is maintained constant and the temperature is raised to 355 °C?

Watch Solution

A weather balloon is inflated to a volume of 28.5 L at a pressure of 748 mmHg and a temperature of 28.0 °C. The balloon rises in the atmosphere to an altitude of approximately 25,000 feet, where the pressure is 385 mmHg and the temperature is -15.0 °C. Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude.

Watch Solution

What is the temperature of 0.52 mol of gas at a pressure of 1.3 atm and a volume of 11.8 L?

Watch Solution

What is the pressure in a 15.0-L cylinder filled with 32.7 g of oxygen gas at a temperature of 302 K?

Watch Solution

What is the volume occupied by 12.5 g of argon gas at a pressure of 1.05 atm and a temperature of 322 K? Would the volume be different if the sample were 12.5 g of helium (under identical conditions)?

Watch Solution

A syringe containing 1.55 mL of oxygen gas is cooled from 95.3 octo 0.0 °C. What is the final volume of oxygen gas?

Watch Solution

A sample of gas has an initial volume of 13.9 L at a pressure of 1.22 atm. If the sample is compressed to a volume of 10.3 L, what is its pressure?

Watch Solution

What is the molar mass of an ideal gas if a 0.622 g sample of this gas occupies a volume of 300. mL at 35°C and 789 mm Hg?

a) 44.8 g•mol ^{–1}

b) 48.9 g•mol ^{–1}

c) 50.5 g•mol ^{–1}

d) 54.5 g•mol ^{–1 }

Watch Solution

For each of the items written below, state why it is wrong and write a version that is correct.

What’s wrong?

Write a correct version.

Watch Solution

A 355 mL container holds 0.146 g of Ne gas and an unknown amount of Ar gas at 35°C, and a total pressure of 626 mmHg. Calculate the number of moles of Ar gas present.

a) 7.24 x 10 ^{–3} mol Ar

b) 4.34 x 10 ^{–3} mol Ar

c) 4.27 x 10 ^{−3} mol Ar

d) 1.00 x 10 ^{−2} mol Ar

e) 5.79 x 10 ^{−3} mol Ar

Watch Solution

Calcium carbide (CaC_{2}) reacts with water to produce acetylene (C _{2}H_{2}) according to the equation

CaC_{2(s)} + H_{2}O_{(l)} → Ca(OH)_{(s) }+ C_{2}H_{2(g)}

A certain mass of CaC_{2} reacts completely with water to give 64.5 L of C _{2}H_{2} at 50.0°C and P = 1.00 atm. If the same mass of CaC_{2} reacts completely at 400.0°C and P= 2.00 atm, what volume of C_{2}H_{2} (in L) can be collected at the higher temperature and pressure?

a) none of the given answers

b) 516

c) 0.015

d) 67.2

e) 258

Watch Solution

The gas in a gas thermometer that has been placed in an oven, has a volume that is 3.68 times larger than the volume that it occupied at 86°C. Determine the temperature in the oven (in degrees Celsius)

a) 1048

b) 316

c) 3850

d) 25.9

e) 1321

Watch Solution

What is the pressure in atm exerted by a mixture of 1.00 g H _{2} and 5.00 g He when the mixture is contained in a volume of 5.00 L at 20.0°C?

a) 8.4

b) 7.84

c) 28.8

d) 0.574

e) 7.71

What is the partial pressure in atm exerted by the H _{2} in the gaseous mixture described in the previous question?

a) no given answer is close

b) 0.115

c) 2.4

d) 5.76

e) 1.54

Watch Solution

What is the final pressure in atmosphere if 100.0 L of gas at 150.0°C and 1.00 atm pressure is compressed to 5.00 L at 642°C? Zincblende, ZnS, is the most important zinc ore. Roasting (strong heating) of ZaS is the first step in the commercial production of zinc.

2 ZnS_{(s)} + 3 O_{2(g)} → 2 ZnO_{(s) }+ 2 SO_{2(g)}

a) no given answer is close

b) 57.1

c) 43.3

d) 128.4

e) 85.6

In the previous question, what volume (in liters) of SO _{2(g) }forms per liter of O_{2(g)} consumed? Both gases are measured at 25.0°C and 745 mm Hg.

a) no given answer is close

b) 1.45

c) 1.67

d) 1.33

e) 0.667

Watch Solution

The gas in a gas thermometer that has been placed in an oven has a volume that is 3.68 times larger than the volume that it occupies at 158°C. Determine the temperature in the oven (in degress Celsius).

a) 1313

b) 1586

c) 581

d) 43

e) 117

Watch Solution

If the pressure exerted by ozone, O _{3}, in the stratosphere is 3.0 x 10 ^{-3} atm and the temperature is 255 K, how many ozone molecules are in one liter?

a. 6.0 x 10^{18}

b. 6.1 x 10^{ }^{22}

c. 8.6 x 10^{19}

d. 1.4 x 10^{18 }

e. 2.7 x 10^{ }^{20}

Watch Solution

The density of the vapor of allicin, a component of garlic, is 1.14 g. L^{-1} at 125ºC and 175 torr. What is the molar mass of allicin?

1. 21.6 g · mol ^{-1 }

2. 50.8 g · mol ^{-1 }

3. 273 g · mol ^{-1 }

4. 869 g · mol ^{-1 }

5. 162 g · mol ^{-1}

Watch Solution

A sample of sodium azide (NaN _{3}), a compound used in automobile air bags was thermally decomposed and 15.3 mL of nitrogen gas was collected at 25°C and 755 torr. How many grams of nitrogen were collected?

a. 16.85

b. 12.8

c. 0.0174

d. 0.0168

e. 6.21 x 10 ^{-4}

Watch Solution

An oxygen tank of 500 L is 80 atm in a room 25°C and 1.0 atm is used for supplying oxygen to a patient. If the flow rate of oxygen coming out from the tank is set to me 1.00 L/s, about how long will this tank last for this purpose?

a. 11 hr

b. 5.5 hr

c. 2.3 hr

d. 16 min

e. 8.3 min

Watch Solution

Into a 500.0 L container at 18°C are placed 0.40 g of H _{2}, 20.0 g CO _{2} and 14.0 g of O_{2}. What is the partial pressure of H _{2}?

Watch Solution

The Simple Gas Laws represent theories and equations that try to relate together pressure, temperature, volume and the amount of a gas when discussing their chemical properties and behaviors.

**Boyle’s Law**

Boyle’s Law, also known as Mariotte’s Law, the Boyle-Mariotte Law or Pressure-Volume Law, states that pressure (P) and volume (V) are inversely proportionally, which basically means they are opposites of one another, at constant moles (n) and temperature (T).

This pressure-volume relationship is commonly displayed in the following example of a closed container. Pressure represents the downward force applied to the container while volume represents the free space within it.

When plotting this inverse pressure-volume relationship onto a chart you obtain the following:

The inverse relationship between pressure and volume at a constant mass for a gas at a fixed temperature is illustrated by the expression:

**Boyle’s Law Formula**

The Ideal Gas Law is presented as:

If moles (n) and temperature (T) are held constant then the formula simplifies into:

When dealing with two sets of data (2 pressures and 2 volumes) the Boyle’s Law formula becomes:

Now let’s use it in a practice problem.

**PRACTICE: **If an unknown gas were confined within a 5.15 L container at 3.20 atm, what would be the pressure if the volume were expanded to 11.23 L?

**STEP 1:** Identify the variables given.

**STEP 2:** Isolate the missing variable for the second pressure (P_{2}).

**Charles’ Law**

Charles Law, also known as the Temperature-Volume Law, states that volume (V) and temperature (T) are directly proportionally as long as pressure (P) and moles (n) are held constant. This temperature-volume relationship is commonly displayed by the application and removal of heat from a closed container with a moveable piston.

Being directly proportional means that as the temperature increases then the volume would also increase. This direct temperature-volume relationship can be plotted onto a chart and provide the following:

The direct relationship between temperature and volume at constant moles and pressure is illustrated by the expression:

**Charles’ Law Formula**

By rearranging the Ideal Gas Law we can isolate V and T:

If moles (n) and pressure (P) are held constant then the formula simplifies into:

Incorporating the two sets of data (2 volumes, 2 temperatures) produces the Charles’ Law formula as:

**PRACTICE: **If a 2.2 L container filled with gas at a temperature of 18.0 °C is heated to a temperature of 38.0 °C, what is the new volume of the container (in liters)?

**STEP 1:** Identify the variables given.

**STEP 2:** Gas behavior is examined under absolute temperature conditions and so we must convert all temperatures from Celsius to Kelvin.

**STEP 3:** Plug the given values into Charles’ Law formula.

**STEP 4:** Perform cross-multiplication between the two ratios.

**STEP 5:** Isolate the missing variable for the second volume (V_{2}).

**Avogadro’s Law**

Avogadro’s Law, also known as the Mole-Volume Law or Volume Amount Law, states that volume (V) and moles (n) are directly proportional as long as pressure (P) and temperature (T) are held constant. This mole-volume relationship is depicted with the addition or removal of gas molecules from a closed container with a moveable piston.

As more and more gas molecules are pumped into the container they push up against the moveable piston and thereby increase the volume inside the container. This direct mole-volume relationship can be plotted onto a chart and provide the following:

The direct relationship between the number of moles and volume at constant temperature and pressure is illustrated by the expression:

**Avogadro’s Law Formula**

By rearranging the Ideal Gas Law we can isolate V and n:

If temperature (T) and pressure (P) are held constant then the formula simplifies into:

Incorporating the two sets of data (2 volumes, 2 moles) produces the Avogadro’s Law formula as:

**PRACTICE: **How many moles will a sample of F_{2} gas occupy in a 2.50 L container, if 3.21 moles of F_{2} have a volume of 53.2 L?

**STEP 1:** Identify the variables given.

**STEP 2:** Plug the given values into Avogadro’s Law formula.

**STEP 3:** Perform cross-multiplication between the two ratios.

**STEP 4:** Isolate the missing variable for the second moles (n_{2}).

**Gay-Lussac’s Law**

This sometimes overlooked simple gas law, because it doesn’t involve a changing volume like the previous 3, states that pressure (P) and temperature (T) are directly proportional as long as volume (V) and moles (n) are held constant. This pressure-temperature relationship is depicted with the addition or removal of heat from a rigid, non-flexible container.

By increasing the temperature of a container the gas molecules will absorb the excess thermal energy and convert it into kinetic energy. With higher kinetic energies, the gas molecules will move faster and hit the walls of the container more frequently and with harder force. This in term leads to a higher overall pressure within the container.

This direct pressure-temperature relationship can be plotted onto a chart and provide the following:

The direct relationship between the pressure and temperature at constant volume and moles of gas is illustrated by the expression:

**Gay-Lussac’s Law Formula**

By rearranging the Ideal Gas Law we can isolate P and T:

If volume (V) and moles of gas (n) are held constant then the formula simplifies into:

Incorporating the two sets of data (2 pressures, 2 temperatures) produces the Gay-Lussac’s Law formula as:

**PRACTICE: **If an unknown gas possesses a pressure of 800 mmHg when the temperature is 20^{ }°C, what would be its pressure (in mmHg) when the temperature is increased to 110^{ }°C?

**STEP 1:** Identify the variables given.

**STEP 2: **Convert the Celsius values into Kelvin.

**STEP 3: **Plug the given variables into the Gay-Lussac’s Law Formula.

**STEP 4:** Perform cross-multiplication between the two ratios.

**STEP 5:** Isolate the missing variable for the second pressure (P_{2}).

By combining the Simple Gas Laws we are able to create the Ideal Gas Law and the Combined Gas Law. Through these equations we can examine gas behaviors as well as their properties dealing with molar mass, partial pressure, density, effusion, speed and velocity.

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