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Wize University Chemistry Textbook > Gases and their Properties

Other Applications of the Ideal Gas Law

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Applications of the Ideal Gas Law

Determining the Molecular Weight (M) of an Unknown Gas

PV=nRT plug in n=mMPV=nRT\ plug\ in\ n=\frac{m}{M}
PV=mMRTPV=\frac{m}{M}RT
where, m=mass (g) and M=molar mass (g/mol)

Rearrange the equation to solve for M (molecular weight) of the unknown gas:

M=mRTPVM=\frac{mRT}{PV}

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Finding the Density of a Gas

The equation for density (𝛿) is:
δ=mV\boxed{\delta=\frac{m}{V}}

We can rearrange the ideal gas law to find density:

PV=nRT plug in n=mMPV=nRT\ plug\ in\ n=\frac{m}{M}

PV=mRTMPV=\frac{mRT}{M}
Solve for density:
mV=δ=MPRT\frac{m}{V}=\delta=\frac{MP}{RT}


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Standard Molar Volume

Recall: we talked about Avogadro's law where P and T are kept constant.
PV=nRT
V/n=RT/P where RT/P=constant
V/n=constant

Based on this, imagine if we were looking at two different gases in two different containers, each with the same P, T, and number of moles of gas particles.

We have made n (moles) a constant too. If that is the case, then the volume for all the gases should be the same, and they are!

Wize Concept
Specifically at STP (P=1atm and T=0°C or 273K), 1 mol of any gas occupies 22.4L! **Memorize this!**
STP=Standard Temperature and Pressure

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Photo by OpenStax / CC BY


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Example: Standard Molar Volume

In the following reaction, if you start with 4L H2(g) and 1.5L N2(g) at STP, what would the volume of each of the 3 gases be when the reaction is complete?

3H2(g) + N2(g) -> 2NH3(g)

@STP: T=273 K, P=1 atm (constant), 1 mol=22.4 L

We can convert the volumes into moles using 1 mol=22.4 L:
H2(g):
4L x (1 mol)22.4L =0.1786 moles4L\ x\ \frac{\left(1\ mol\right)}{22.4L}\ =0.1786\ moles

N2(g):
1.5L x (1 mol)22.4L=0.06696 moles1.5L\ x\ \frac{\left(1\ mol\right)}{22.4L}=0.06696\ moles

Now that we have moles of each reagent, we need to determine the limiting reagent.
To do this, divide each number of moles by the stoichiometric coefficient in the balanced equation:
H2(g):

0.1786 moles3 moles =0.05953\frac{0.1786\ moles}{3\ moles\ }=0.05953

N2(g):

0.06696 moles1 mole=0.06696\frac{0.06696\ moles}{1\ mole}=0.06696

The smallest number is for H2(g) so it is the limiting reagent!

Solve for moles of NH3(g) produced:

0.1786 moles H2(g) x 2 moles NH3(g)3 moles of H2(g)=0.1191 moles NH3(g)0.1786\ moles\ H_2\left(g\right)\ x\ \frac{2\ moles\ NH_3\left(g\right)}{3\ moles\ of\ H_2\left(g\right)}=0.1191\ moles\ NH_3\left(g\right)

Calculate the volume of NH3(g) using 1 mol =22.4 L

0.1191 moles NH3(g) x 22.4 L1 mol=2.6671 L ≈2.67L0.1191\ moles\ NH_3\left(g\right)\ x\ \frac{22.4\ L}{1\ mol}=2.6671\ L \ \boxed{\approx2.67L}

How many L of H2(g) are leftover?

0L of H2(g) leftover since it was the limiting reagent\boxed{\text{{0L of H2(g) leftover since it was the limiting reagent}}}
H2 was the limiting reagent and got completely used up!

We just need to find the L of N2(g) that are leftover.

First let's determine the moles leftover.

0.1786 moles H2(g) x (1 mol N2(g))3 moles H2(g)=0.05953 moles N2(g) used0.1786\ moles\ H_2\left(g\right)\ x\ \frac{\left(1\ mol\ N_2\left(g\right)\right)}{3\ moles\ H_2\left(g\right)}=0.05953\ moles\ N_2\left(g\right)\ used

We started with 0.06696 moles of N2(g)

0.06696 moles-0.05953 moles= 0.00743 moles N2(g) left over

Finally convert this into volume to determine the volume of N2(g) leftover:

0.00743 moles x 22.4L1 mol=0.166432 L  ≈0.17 L0.00743\ moles\ x\ \frac{22.4L}{1\ mol}=0.166432\ L\ \ \boxed{\approx 0.17\ L}

Practice: Solving for Molar Mass of a Gas

The density of an unknown gas at 100oC and 746 torr is 1.994 g/L. What is the molecular mass of this unknown gas?

Practice: Determine the Gas

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?

Practice: Solve for Molecular Weight

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?
Extra Practice
Ideal Gas Law: Gas mixtures
When 100 g of Kr and 100 g of Xe are placed in a container, the partial pressure of Xe is found to be 4 atm. What is the partial pressure of Kr?
Ideal Gas Law: Gas mixtures
When 100 g of Kr and 100 g of Xe are placed in a container, the partial pressure of Xe is found to be 4 atm. What is the partial pressure of Kr?
Ideal Gas Law
If the following gases are used to fill balloons of a 1L volume at 1 atm and 298K, what is the correct ranking of the densities of the gases in the balloons. CH4\rm CH_4, C2H6\rm C_2H_6, C4H10\rm C_4H_{10}, Xe\rm Xe, N2\rm N_2, O2\rm O_2.
A 16.0 L gas vessel contains 40.0 kPa of He, 15.0 kPa of Ne and 25.0 kPa of Kr. What is the density of this mixture?
[Do NOT include units in your answers]
A mixture of gases containing 02, N2 and H2 contains 0.20 mols of N2 in a 12 L sealed vessel. If the total pressure is 188 kPa at 298 K, what is the partial pressure of nitrogen? What is the average molar mass of this mixture? The density of the mixture is 1.52g/L.
Ideal Gas Law
A 0.483 g sample of gas occupies a volume of 0.530 L at 130 °C and 109 kPa.
a. What is the molar mass of this gas?
b. Whats the density of this gas at STP?
Partial Pressure
300 mL H2 was collected over water at 21 ⁰C and 748 Torr. Vapour pressure of water at 21 ⁰C is 18.65 Torr.
a. How many moles of H2 and water vapour were present in the moist gas mixture?
b. Calculate the mass of the gas after being dried.
Vapor Pressure
A sample of H2 gas was collected over water. The temperature of the vessel was 273.15 K and the volume of the sample was 20.0 L. The vapour pressure of water at 300.0 K is 5.0atm and the total pressure of the sample was 15.5atm. What is the mass of the H2 in this sample?
What is the density of a sample of O2 with a pressure of 1255 kPa at 10 °C?
Ideal Gas Laws
1. A mixture of gases containing O2, N2 and H2 contains 0.20 mols of N2 in a 12 L sealed vessel. If the total pressure is 188 kPa at 298 K, what is the partial pressure of nitrogen? What is the average molar mass of this mixture? The density of the mixture is 1.52g/L.
Ideal Gas Laws
4. A 16.0 L gas vessel contains 40.0 kPa of He, 15.0 kPa of Ne and 25.0 kPa of Kr. What is the density of this mixture?
Ideal Gas Law
Calculate the density (in g/L) of HF gas at 35oC and 0.78 atm
Ideal Gas Law
Which of the following 5 gases has the lowest density at 50oC and 1.3 atm?
If the following gases are used to fill balloons of a 1L volume at 1 atm and 298K, what is the correct ranking of the densities of the gases in the balloons. CH4\rm CH_4, C2H6\rm C_2H_6, C4H10\rm C_4H_{10}, Xe\rm Xe, N2\rm N_2, O2\rm O_2.
Ideal Gas Law
7 moles of N2 gas at 372 K was released into a 9 L balloon. If N2 is a real gas, what is the pressure of the gas? (For N2, a = 0.0135 atm /L2, and b = 0.1937 L/mol, R = 0.08206 L*atm/mole*K).
Ideal Gas Law
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)
"The Periodic Table", image retrieved from Chemistry 2e (https://d3bxy9euw4e147.cloudfront.net/oscms-prodcms/media/documents/Chemistry2e-OP_QCzV58S.pdf) by Flowers, P et al., is licensed under CC BY
Ideal Gas Law: Density
A 16.0 L gas vessel contains 40.0 kPa of He, 15.0 kPa of Ne and 25.0 kPa of Kr. What is the density of this mixture?
Ideal Gas Law
Consider the following 5 gases. If an equal volume of each gas is placed into a separate balloon, which gas sample will have the greatest mass? Assume the balloons are all at the same temperature and pressure.
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?
What is the density of a sample of O2 with a pressure of 1255 kPa at 10 °C?
Molar Mass
A mixture of 5.5 mols of Ar, 3.5 mols of O2 and 1.0 mol of Xe is prepared. What is the density of this mixture if the total pressure is 2.0 atm at 25° C?
Ideal Gas Law
A student has two balloons held at ambient pressure and temperature (1 atm, 298 K), one is 3 L contains Helium, the other is 14 L and contains argon. The student transfers both gasses into a single balloon which is also held at ambient temperature and pressure. What is the density of the gas mixture in the final balloon?
A mixture of ideal gases containing O2, F2 and N2 contains 0.20 mols of N2 in a 12 L sealed vessel. If the density of this mixture is 1.52 g/L at room temperature under 188 kPa, of pressure. What is the average molar mass of this mixture?
Stoichiometry and Ideal Gas Law Practice
The combustion of methanol (CH3OH) is shown below. If 16g of methanol is burned in oxygen, what volume of CO2 is produced if the pressure is 101.3kPa, T=25C, and R=8.314kPaL/molK? Round to the nearest whole number.
CH3OH + O2 --> CO2 + H2O
Is the equation balanced?
No
A piece of zinc is allowed to react with an excess quantity of sulfuric acid, and the hydrogen gas produced is collected in a gas burette by displacement of water. Neglecting the effect of the vapor pressure of water on the system, calculate how many milligram (mg) of zinc would generate 92.0 mL of the gas at a temperature of 25.0 °C and a pressure of 1.00 atm.
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?
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?
Gas Laws: Practice
A student decides to do a more controlled version of the hydrogen balloon explosion. The unbalanced chemical equation for this reaction is shown below:
H2(g)+O2(g)→H2O(g)H_2(g)+O_2(g)→H_2O(g)
(a) Write the balanced chemical equation for this reaction.
Ideal Gas Law
A student adds 0.165 g of an unknown gas to a 125 mL flask. If the student finds the pressure to be 0.987 atm at 20.0 °C, is the gas likely to be methane, CH4, nitrogen, N2, oxygen, O2, neon, Ne , or argon, Ar?
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?