1. Basic Chemistry Chapter 11 Gases Chapter 11 Lecture
Fourth Edition
Chapter Gases
11.8 The Ideal Gas Law
Learning Goal Use the ideal gas law equation to solve for P, V, T, or n of a gas when given three of the four variables in the ideal gas law equation. Calculate density, molar mass, or volume of a gas in a chemical reaction.

2. The Ideal Gas Law PV = nRT
The ideal gas law is a combination of the four properties (P, V, n, and T), written as a single expression: PV = nRT.
Rearranging the ideal gas law equation shows that the four properties are equal to the gas law constant, R, equal to L atm per mol K.

3. The Ideal Gas Law
Using a different unit for pressure, 760 mmHg, gives us another value for R, 62.4 L mmHg, per mol K.

4. Guide to Using the Ideal Gas Law

5. Learning Check
How many moles of N2 gas are present if the sample occupies 215 mL at atm and
30.0 °C?

6. Step 1 State the given and needed quantities.
Solution
How many moles of N2 gas are present if the sample occupies 215 mL at atm and
30.0 °C?
Step 1 State the given and needed quantities. P V n R T
Given
0.813 atm
0.215 L
L atm
K mol
30.0 °C
+ 273
= 303 K
Need
? moles

7. Solution
How many moles of N2 gas are present if the sample occupies 215 mL at atm and
30.0 °C?
Step 2 Rearrange the ideal gas law equation to solve for the needed quantity.

8. Solution
How many moles of N2 gas are present if the sample occupies 215 mL at atm and
30.0 °C?
Step 3 Substitute the gas data into the equation and calculate the needed quantity.

9. Learning Check
Butane, C4H10, is used as fuel for barbeques and as an aerosol propellant. If you have 108 mL of butane at 715 mmHg and 25 °C, what is the mass, in grams, of butane?

10. Step 1 State the given and needed quantities.
Solution
Given 108 mL of butane, C4H10, at 715 mmHg and 25 °C, what is the mass, in grams, of C4H10?
Step 1 State the given and needed quantities. P V n R T
Given
715 mmHg
108 mL
(0.108 L)
62.4 L mmHg
K mol
25 °C
+ 273
= 298 K
Need
? moles

11. Solution
Given 108 mL of butane, C4H10, at 715 mmHg and 25 °C, what is the mass, in grams, of C4H10?
Step 2 Rearrange the ideal gas law equation to solve for the needed quantity.
Molar Mass
moles of C4H10
grams of C4H10

12. Solution
Given 108 mL of butane, C4H10, at 715 mmHg and 25 °C, what is the mass, in grams, of C4H10?
Step 3 Substitute the gas data into the equation and calculate the needed quantity.

13. Molar Mass of a Gas
Another use of the ideal gas law is to determine the molar mass of a gas. Dividing the mass of gas by the moles of gas gives the molar mass of the gas.
Given the mass, in grams, of gas, we can calculate the number of moles of the gas using the ideal gas law equation.

14. Guide to Calculating the Molar Mass of a Gas

15. Learning Check
What is the molar mass, in grams per mole, of a g sample of gas at atm and 45 °C, that occupies a volume of 2.05 liters?

16. What is the molar mass, in grams per mole, of a
Solution
What is the molar mass, in grams per mole, of a
3.16-g sample of gas at atm and 45 °C, that occupies a volume of 2.05 liters?
Step 1 State the given and needed quantities. P V n R T
Given
0.750 atm
2.05 L
mass
= 3.16 g
0.0821
L atm
K mol
45 °C
+ 273
= 318 K
Need
? moles

17. Solution
What is the molar mass, in grams per mole, of a g sample of gas at atm and 45 °C, that occupies a volume of 2.05 liters?
Step 2 Rearrange the ideal gas law equation to solve for the number of moles.

18. Solution
What is the molar mass, in grams per mole, of a
3.16-g sample of gas at atm and 45 °C, that occupies a volume of 2.05 liters?
Step 2 Rearrange the ideal gas law equation to solve for the number of moles.

19. Solution
What is the molar mass, in grams per mole, of a
3.16-g sample of gas at atm and 45 °C, that occupies a volume of 2.05 liters?
Step 3 Obtain the molar mass by dividing the given number of grams by the number of moles.