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Wize University Chemistry Textbook > Gases and their Properties

Ideal Gas Law

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The Ideal Gas Law

The equation below describes ideal gases. Real gases act differently, but act most similarly to ideal gases at high temperatures and low pressures!

PV=nRT\boxed{PV=nRT}

P is pressure measured in kPa (or maybe atm Torr, mmHg...)
V is volume measured in L or m3
n is number of moles of the gas
R is the ideal gas constant (will be either 8.314J/mol K OR 0.082 L atm/mol K)
T is temperature measured in K

Wize Tip
Pressure=Force/unit area=N/m2=1 Pa

How to convert different units of pressure:

101 300 Pa=101.3 kPa=1 bar=1 atm=760 mmHg=760 torr\boxed{101\ 300 \ Pa=101.3\ kPa=1 \ bar=1 \ atm=760 \ mmHg =760 \ torr}

PAGE BREAK

We mentioned that R (the ideal gas constant) could be either 8.314J/mol K or 0.082 L atm/mol K. How do we know which value to use?

Watch Out!
Using the correct value for R is more important than you might think! Students often make the mistake of using the wrong value of R on an exam and they get the question wrong. Let's see how we can easily prevent that :)


The ideal gas constant appears frequently in chemistry, for this reason, it comes in many forms depending on the context of its use and the units involved:
Example:

Suppose the variables in the ideal gas law equation had the following units:

P(kPa)×V(L)=n(mol)×R(?)×T(K)P(kPa)\times V(L)=n(mol)\times R(?)\times T(K)
What should R be in this case? (These terms need to combine correctly to ensure that this equation makes sense!)
R must be 8.314 J/ mol K which is the same as 8.314 kPa L/mol K



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Example: Ideal Gas Law

1.1 mols of Argon are stored in a 2.0 L container kept at 10.0 °C. What is the pressure of this gas? (ans. in kPa)

n=1.1, V=2L, T=10°C P=?
Is everything in correct units??

Need to convert T from °C to K → °C + 273=K So 10°C + 273=283 K
PV=nRT
P=nRT/V
P=(1.1moles)(8.314kPa L/mol K)(283K)/2L
P=1294 kPa = 1300 kPa (sig figs)

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Example: Ideal Gas Law

a) A 4 L cylinder containing 3 moles of He(g) arrives from a chemical supply company. Given that the lab you are working in has a room temperature of 298 K, calculate the pressure inside the flask.

n=3 moln=3\ mol
V=4 LV = 4\ L
T=298 KT = 298\ K
PV=nRTPV=nRT
P=?P=?
P=nRTV=(3 mol)(0.08206 L atm K−1mol−1)(298 K)(4 L)=18.3 atmP=\dfrac{nRT}{V}=\dfrac{(3\ mol)(0.08206\ L\ atm\ K^{-1}mol^{-1})(298\ K)}{(4\ L)}=18.3\ atm

b) At what temperature will the cylinder have an internal pressure of 9 atm?

n=3 moln=3\ mol
V=4 LV=4\ L
P=9 atmP=9\ atm
T=?T=?
T=PVnR=(9 atm)(4 L)(3 mol)(0.08206 L atm K−1mol−1)=146 KT=\dfrac{PV}{nR}=\dfrac{(9\ atm)(4\ L)}{(3\ mol)(0.08206\ L\ atm\ K^{-1}mol^{-1})}=146\ K

c) Your lab mate steals some of the gas from your cylinder for a reaction he is doing. He fills a 1 L bulb with 1 atm of your gas at 298 K. If the cylinder is at room temperature, what is the internal pressure of the cylinder once the gas has been removed?


nstolen=PVRT=(1 atm)(1 L)(0.08206 L atm K−1mol−1)(298 K)=0.04 moln_{stolen}=\dfrac{PV}{RT}=\dfrac{(1\ atm)(1\ L)}{(0.08206\ L\ atm\ K^{-1}mol^{-1})(298\ K)}=0.04\ mol
Tank:
n=2.96 moln=2.96\ mol
T=298 KT=298\ K
V=4 LV=4\ L
P=nRTV=(2.96 mol)(0.08206 L atm K−1mol−1)(298K)(4 L)=18.1 atmP=\dfrac {nRT}{V}=\dfrac{(2.96\ mol)(0.08206\ L\ atm\ K^{-1} mol^{-1})(298K)}{(4\ L)}=18.1\ atm

Practice: Stoichiometry and the Ideal Gas Law

The combustion of methanol (CH3OH) is shown below. If 16 g of methanol is burned in oxygen, what volume of CO2 is produced if the pressure is 101.3 kPa, T = 25°C, and R = 8.314 kPa L/mol K? Round to the nearest whole number.

CH3OH + O2 → CO2 + H2O


Extra Practice
Ideal Gas Law: Kinetic Molecular Theory
The natural gas delivered to homes in Calgary is normally a mixture of methane (CH4), ethane (C2H6), propane (C3H8) and carbon dioxide (CO2).
(a) In the laboratory, a chemistry student has collected some Calgarian natural gas in a 2.00 L plastic bottle at 0.902 atm and 23°C. What is the concentration of gas in the bottle?
(b) The bottle was weighed before and after filling with gas to determine the exact composition of gases. The student found that in the mixture the mole fraction of C3H8(g) was 0.10 and the mole fraction of CH4(g) was 0.90. What was the total mass of the gas in the bottle?
Partial Pressure and Vapor Pressure
A sample of N2 gas was collected over water. The temperature of the vessel was 300.0 K and the volume of the sample was 18.0 L. The vapor pressure of water at 300.0 K is 3.53 kPa and the total pressure of the sample was 122.00 kPa. What is the mass of the N2 in this sample?
Practice: Kinetic Molecular Theory
The natural gas delivered to homes in Calgary is normally a mixture of methane (CH4), ethane (C2H6), propane (C3H8) and carbon dioxide (CO2).
(a) In the laboratory, a CHEM 203 student has collected some Calgarian natural gas in a 2.00 L plastic bottle at 0.902 atm and 23°C. What is the concentration of gas in the bottle?
(b) The bottle was weighed before and after filling with gas to determine the exact composition of gases. The student found that in the mixture the mole fraction of C3H8(g) was 0.10 and the mole fraction of CH4(g) was 0.90. What was the total mass of the gas in the bottle?
Ideal Gas Laws: Molar volume
Answer the following two questions based on the Ideal Gas Law:
Like Spring 2019 Exam 2
When 100 g of He and 100 g of Ne are placed in a container, the partial pressure of Ne is found to be 6 atm. What is the partial pressure of He?
Ideal Gas Law
If 10 g each of O2(g)\rm O_2(g) and HBr(g)\rm HBr(g) are in separate containers of equal volume and temperature, which one of the following statements is true?
Partial Pressure and Vapor Pressure
A sample of N2 gas was collected over water. The temperature of the vessel was 300.0 K and the volume of the sample was 18.0 L. The vapor pressure of water at 300.0 K is 3.53 kPa and the total pressure of the sample was 122.00 kPa. What is the mass of the N2 in this sample?
Ideal Gas Law
4 moles of O3(g) are trapped inside a sealed rigid vessel. The gas undergoes a reaction,
O3(g)→1.5 O2(g)\rm O_3(g) \rightarrow 1.5\ O_2(g)
Assuming all of the oxygen is consumed and the volume has remained constant, what was the effect on the pressure
A 10.0 L sample of Br2 gas is collected over water at 298 K. If the total pressure of the sample is 180.0 kPa, how many mols of Br2 are present in this sample? The vapor pressure of water at 298 K is 3.17 kPa. [Do NOT include units in your answers]
A mixture of 4.6 mols of H2 gas, 3.1 mols of N2 gas and 2.6 mols of He are stored in a 60.0 L canister at 298 K. What is the partial pressure of each compound?
P
H2
Find the new volume of 3.0 mols of an ideal gas initially at standard temperature and pressure after the pressure is changed to 40.0 kPa.
[Do Not include units in your answer]
Ideal vs real behaviour of gases
A sample of gas has a molar volume of 10.1 L at 745 Torr and −138 °C. Is the gas behaving ideally?
Gas Stoichiometry and Limiting Reagent
Consider the following equation:
4NH3(g) + 7O2(g) → 4NO2(g) + 6H2O(l)
3 L NH3 and 7 L O2 were reacted at 350 °C and 111 kPa. How much NO2 can be produced?
Partial Pressure
A mixture of H2(g) and CO(g) (total mass 4.50 g) occupies a volume of 3.76 L at 298 K and 108 kPa. What is the partial pressure of each gas in this mixture? Calculate the volume percent of H2?
Vapour Pressure
A sample of N2 gas was collected over water. The temperature of the vessel was 300.0 K and the volume of the sample was 18.0 L. The vapour pressure of water at 300.0 K is 3.53 kPa and the total pressure of the sample was 122.00 kPa. What is the mass of the N2 in this sample?
Gas Law
Consider the following two containers of gas that are at the same temperature. Which of the following statements comparing these two containers are false and which are true?
Gases: Vapor Pressure
A sample of N2 gas was collected over water. The temperature of the vessel was 300.0 K and the volume of the sample was 18.0 L. The vapour pressure of water at 300.0 K is 3.53 kPa and the total pressure of the sample was 122.00 kPa. What is the mass of the N2 in this sample?
Ideal Gas Law: Gas Mixtures
2. A mixture of 4.6 mols of H2 gas, 3.1 mols of N2 gas and 2.6 mols of He are stored in a 60.0 L canister at 255 K. What is the partial pressure of each compound?
P
H2
Ideal Gas Law: Gas Mixtures
3. A 10.0 L sample of Br2 gas is collected over water at 298 K. If the total pressure of the sample is 180.0 kPa, how many mols of Br2 are present in this sample? The vapor pressure of water at 298 K is 3.17 kPa.
Ideal Gas Law: Partial Pressures
Calculate the partial pressure of neon (in atm) in a mixture of 3.1 g of argon, 1.2 g of neon, and 2.4 g of krypton at 0oC in 1.5 L container.
Ideal Gas Law: Pressure
0.103 moles of Cl2 gas in a sealed cylinder with a piston has a volume of 3.25 L at a pressure of 0.780 atm. Assuming that the sample behaves as an ideal gas and the temperature remains constant, calculate the pressure (in atm) of the sample if the piston is moved and the volume of the cylinder is reduced to 1.82 L.
2 gases were mixed together in a 5 L vessel at 243 K to create a total pressure of 9.3 atm. If gas 1 has 2 moles, what is the partial pressure of gas 2? (R = 0.08206 L*atm/mole*K)
0.238 g of a gas were placed in a 250 mL vessel. If the gas is heated to 85 oC, the gas has a pressure of 7 atm. Which gas is in the vessel? (R = 0.08206 L*atm/mole*k)
Ideal Gas Law: Molecular mass calculation
The density of an unknown gas at 100oC and 746 torr is 1.994 g/L. What is the molecular mass (in g/mol) of this unknown gas?
A mixture of 4.6 moles of H2 gas, 3.1 moles of N2 gas and 2.6 moles of He are stored in a 60.0 L canister at 298 K. What is the partial pressure of each compound? (Write answer in format X.XX atm, i.e. 4.25 atm)
P
H2
3 moles of O2 gas at 100 K was released into a 2 L balloon. If O2 is a real gas, what is the pressure of the gas? (For O2, a = 0.0145 atm /L2, and b = 0.1711 L/mol, R = 0.08206 L*atm/mole*K).
An ideal gas at 30.0 C and pressure of 2 × 105 Pa is in a container having a volume of 1.40 L.
Determine the number of moles of gas in the container.
The gas pushes against a piston, expanding to twice its original volume, while the pressure falls to atmospheric pressure. Find the final temperature.
Ideal Gas Laws: Gas mixtures
2 gases were mixed together in a 5 L vessel at 243 K to create a total pressure of 9.3 atm. If gas 1 has 2 moles, what is the partial pressure of gas 2? (R = 0.08206 L*atm/mole*K)
Gas Laws: Van der Waals Equation
Find the difference between the ideal pressure and the Van der Waals pressure for 2 mol of CO2 in a 1L vessel at room temperature. CO2 (a = 3.640 L2atm/mol2; b = 0.04267 L/mol).
Ideal Gas Law
A sample of argon is loaded into a 3L sealed vessel and at room temperature the initial pressure is 2.6atm. The vessel is then loaded into an autoclave and heated to 580oC. What is the final pressure inside the vessel?
Ideal Gas Law
A 8.0 L sample of Br2 gas is collected over water at 298 K. If the total pressure of the sample is 168.0 kPa, how many moles of Br2 are present in this sample? The vapor pressure of water at 298 K is 3.17 kPa.
Ideal Gas Law: Partial Pressure
A mixture of 4.6 moles of H2 gas, 3.1 moles of N2 gas and 2.6 moles of He are stored in a 60.0 L canister at 255 K. What is the partial pressure of each compound?
P
H2
Ideal Gas Law: Mole fraction
A 10.0 L sample of Br2 gas is collected over water at 298 K. If the total pressure of the sample is 180.0 kPa, how many moles of Br2 are present in this sample? The vapor pressure of water at 298 K is 3.17 kPa.
Ideal Gas Law
A sample of a gaseous compound is distributed into two vessels, A and B, of equal volume held at the same temperature and pressure. Vessel A is heated to twice its initial temperature in Kelvin, followed by compression to one quarter of its initial volume. Vessel B is cooled to half of its initial temperature in K, followed by expansion to twice it’s original volume. What is the ratio of the pressure in vessel A to the pressure in vessel B after these transformations?
Ideal Gas Law: Volume as a function of pressure
Find the new volume of 3.0 moles of an ideal gas initially at standard temperature and pressure after the pressure is changed to 40.0 kPa.
Ideal Gas Law: Volume as a function of moles
What is the volume of 2.5 moles of Ne at 298 K and 1.0 atm? What is the new volume after 4.5 moles of Ne are added?
Ideal Gas Law: Gas mixtures
A mass of 0.4 g of hydrogen (H2) and 3.2 g of helium (He) are mixed in a rigid 500 mL container. What is the partial pressure of helium when the container is cooled to 77 K?
A 6.00 L flask is evacuated and weighed, 21.64g. The vessel is then filled with a gas at STP, after filling the vessel weighs 27.31g. What is the molecular weight of the gas?
Ideal Gas Law: Identify the Ideal Gas
A scientist has a series of tubes filled with different noble gases in her lab. She realizes one day that the labels have worn away and she can't remember which gas is which. She decides to determine the gasses identity using the ideal gas law. She finds that there is 4.314 g of gas and at room temperature (298 K) the pressure in the 2.75 L tube is 97.4 kPa. What is the identity of the gas?
Practice: Ideal Gas Law
3.0 moles of Argon are stored in a 2.0 L container kept at 10 °C. What is the pressure of this gas? Please calculate the pressure in kPa.
A sample of a gaseous compound is distributed into two vessels, A and B, of equal volume held at the same temperature and pressure. Vessel A is heated to twice its initial temperature in Kelvin, followed by compression to one quarter of its initial volume. Vessel B is cooled to half of its initial temperature in K, followed by expansion to twice it’s original volume. What is the ratio of the pressure in vessel A to the pressure in vessel B after these transformations?
A 15 L sample of N2 gas held at 328 K is compressed such that the pressure rises from 1.0 atm to 7.8 atm. What is the final volume of the gas?
For an ideal gas which variables in the following pairs are not directly proportional to each other (if all other factors remain constant)?
Find the new volume of 3.0 mols of an ideal gas initially at standard temperature and pressure after the pressure is dropped to 20.0 kPa.
When coal is burned, sulfur that is present within coal is converted to sulfur dioxide (SO2). This results in the acid rain phenomenon. If 3.75 kg of S are reacted with oxygen, calculate the volume of SO2 gas (in L) formed at 25.0 °C and 1.10 atm.
Ideal Gas Law: Stoichiometry
What volume of hydrogen (STP) is produced by dissolving one-half mole of aluminum in sulfuric acid?
2Al(s)+3H2SO4(aq)→Al2(SO4)3(aq)+3H2(g)2Al(s)+3H_2SO_4(aq)→Al_2(SO_4)_3(aq)+3H_2(g)
Ideal Gas Law: Molecular weight
At 150.°C and 1.00 atm, 500. mL of a vapor has a mass of 0.4183 g. What is the molecular weight of the compound?
Which of the following graphs is NOT consistent with the ideal gas law assuming that the other parameters are kept constant?
Ideal Gas Law: Practice
A small tank of compressed oxygen gas is left outside in the sun and its temperature increases. Assume that the amount of gas and the volume of the tank do not change.
Identify which of the four graphs below show how…
A. …the pressure (P) of the gas inside the tank changes as T increases.
Ideal Gas Law: Kinetic Molecular Theory
The natural gas delivered to homes in Calgary is normally a mixture of methane (CH4), ethane (C2H6), propane (C3H8) and carbon dioxide (CO2).
(a) In the laboratory, a chemistry student has collected some Calgarian natural gas in a 2.00 L plastic bottle at 0.902 atm and 23°C. What is the concentration of gas in the bottle?
(b) The bottle was weighed before and after filling with gas to determine the exact composition of gases. The student found that in the mixture the mole fraction of C3H8(g) was 0.10 and the mole fraction of CH4(g) was 0.90. What was the total mass of the gas in the bottle?
The enthalpy of combustion for ethanol (C2H5OH) is -1370.7 kJ/mol. Calculate q, w, ΔH and ΔU when 45g of ethanol are burned at 1atm and 298K.
Stoichiometry
The following gaseous reaction takes place at 473 K and 101.3 kPa:
N2(g)+O2(g)→NO2(g)N_{2(g)}+O_{2(g)}\to NO_{2(g)}
If 80.0 g of 02 are available to react, how many litres of N2 will be required to completely consume the oxygen supply?
Ideal Gas Laws
5. Find the new volume of 3.0 mols of an ideal gas initially at standard temperature and pressure after the pressure is changed to 40.0 kPa.
Ideal Gas Laws: Volume
6. What is the volume of 2.5 mols of Ne at 298 K and 1.0 atm? What is the new volume after 4.5 mols of Ne are added?
Worked Example
Four moles of an ideal gas originally at 323 oC and 7.3 atm underwent a complete expansion against a constant external pressure of 1 atm and did 8kJ of work. Calculate q, ΔE, ΔH.
Solve for the missing initial variable (Vi):
hint: rearrange PV=nRT to do this!
Ideal Gas law
Inflatable balloons are often used to gently lift a sunken ship from the ocean floor to the ocean surface. We want to fill two balloons (one for each side of the ship) that are approximately 100m long cylinders with a radius of 0.5m with nitrogen gas at a pressure of 1.1 atm. If we remember that the water temperature at the ocean floor is approximately 0 oC how much nitrogen will we need? Answer in moles. R=0.08206Latm/Kmol
Ideal Gas Law
1.1 mols of Argon are stored in a 2.0 L container kept at 10 °C. What is the pressure of this gas? (answer in kPa)
Practice Exam 2 (CHEM 2045 UF)
Consider two separate 1 L containers at 273 K, one filled with 2 g H2 and one filled with 2 g of O2. Which of the following will be true?
Like Spring 2019 Exam 2
At 100oC and 1.00 atm, what volume of nitrogen gas is required to react completely with 10.0 L of hydrogen gas to produce ammonia gas?
Ideal Gas Law
12 moles of Xenon are held inside a 15L flask at room temperature.
The flask is then cooled to – 100oC.The flask is then allowed to expand into a 23L but we need to keep the pressure constant. What temperature is required to keep the pressure constant as the gas expands into the new volume.
Ideal Gas Law
12 moles of Xenon are held inside a 15L flask at room temperature.
The flask is then cooled to – 100oC what is the pressure inside the flask at -100oC?
Ideal Gas Law
12 moles of Xenon are held inside a 15L flask at room temperature.
What is the initial pressure inside the flask?
Ideal Gas Law
Four grams of Helium (an ideal gas) is packed into a 500mL flask and heated in a boiling pot of water. What is the internal pressure of the flask? R=0.08206Latm/Kmol