Simple Gas Laws & The Ideal Gas Law

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

The Simple Gas Laws

Concept: Boyle's Law

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Video Transcript

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

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Video Transcript

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

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Video Transcript

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

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Video Transcript

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

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Video Transcript

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. 

Simple Gas Law Calculations

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?  

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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 0oC into a mechanized piston-cylinder engine. If the volume measures 7.18 cm3 what will the new temperature be at 12.3 mL? 

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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?

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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.

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Ideal Gas Law and Chemical Reactions

Concept: Ideal Gas Stoichiometry

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Video Transcript

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 25oC and 723 mmHg.

Mg (s) + 2 HCl (aq) → MgCl2 (aq) + H2 (g)

How many grams of magnesium reacted?

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When 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 (C2H2), an important fuel in wielding, is produced in the laboratory when calcium carbide (CaC2) reacts with water:

CaC2 (s) + 2 H2O (l) → C2H2 (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 21oC the vapor pressure of the water is 29 torr, how many grams of acetylene were produced? 

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Simple Gas Laws & The Ideal Gas Law Additional Practice Problems

In the synthesis of ammonia gas from nitrogen and hydrogen,

N2(g) + 3H2(g) → 2NH3(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

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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

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How many moles of O2 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

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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

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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 O2 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

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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.

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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

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Consider two cylinders of gas. One cylinder contains N2 at 2 atm and 25C. The other cylinder contains F2 at 1 atm and 50◦C. Which statements is/are true?

I) The N2 molecules and the F2 molecules have the same average kinetic energy.

II) Every molecule in the N2 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 N2 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

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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

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Consider the chemical reaction:

2 KClO3 (s) → 2 KCl (s) + 3 O2 (g)

If 245.1 grams of KClO3 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 KClO3 is 122.55 g/mol)

  1. 44.8 L
  2. 67.2 L
  3. 89.6 L
  4. 112 L
  5. 134 L
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Calculate the density of CO2(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

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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.

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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

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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

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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, C3H5(NO3)3 (Molar mass = 227.11 g). Nitroglycerin is a highly explosive compound and decomposes according to the following equation:

4 C3H5(NO3)3(s)  → 12 CO2 (g) + 10 H2O (g) + 6 N2 (g) + O2 (g)

Calculate the total volume of CO 2 gas collected at 1.2 atm and 27.0 oC 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

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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

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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

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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

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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. 

 

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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

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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

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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

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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 O2(g) → 2 ZnO(s) + 2 SO2(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 O2(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

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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 1018

b. 6.1 x 10 22

c. 8.6 x 1019

d. 1.4 x 1018

e. 2.7 x 10 20

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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

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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

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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

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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 O2. What is the partial pressure of H 2?

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