1.1 What is Chemistry?

http://www.ck12.org Chapter 14. The Properties of Gases

R=PT××Vn=((^1273 atmK)()( 122 mol.^4 L))= 0 .0821 L·atmK−^1 ·mol−^1

Using more precise measurements, the ideal gas constant is found to have a value of 0.08206 L•atm•K−^1 •mol−^1.

Example 14.7

Sulfur hexafluoride (SF 6 ) is a colorless, odorless, and very unreactive gas. Calculate the pressure (in atm) exerted
by 1.82 moles of the gas at 69.5°C when confined to a rigid steel vessel with a volume of 5.43 L.

Answer:

T 1 = 69. 5 ◦C+ 273 = 342 .5 K

P=

nRT

V

P=

( 1 .82 mol)( 0 .08206 L·atm·K−^1 ·mol−^1 )( 342 .5 K)

5 .43 L

P= 9 .42 atm

Note that, in order for all of the units to cancel correctly, the pressure must be expressed in atmospheres, the volume
must be in liters, the amount must be in moles, and the temperature must be in Kelvin. If different units were used,
the ideal gas constant would have a different value.

Lesson Summary

• Pressure and volume are inversely proportional at a constant temperature.


• Volume and temperature are directly proportional at a constant pressure.


• Pressure and temperature are directly proportional at a constant volume.


• Pressure, volume, and temperature are related by the combined gas law.


• The volume occupied by a gas at a given temperature and pressure is proportional to the number of gas
  molecules present.


• For any ideal gas, PV=nRT, where R is a constant with a value of 0.08206 L•atm•K−^1 •mol−^1.

Lesson Review Questions

1. A sample of a gas has a volume of 4.22 L at 27.8°C and 734 mmHg. What will its volume be at 24.6°C and
   755 mmHg?


2. How many molecules of nitrogen gas are in a 5.20 L vessel at 136°C and 0.43 atm?


3. A 34.8 L tank of Ar gas is connected to an evacuated 87.5 L tank. If the final pressure is 640 mmHg, what
   must have been the original gas pressure in the 34.8 L tank?


4. A 54.0 L cylinder contains 798 g of chlorine gas at 29°C. What mass of chlorine must be released to reduce
   the pressure to 0.78 atm?


5. A sample of gas at 1 atm has a temperature of 15°C and a volume of 2.58 L. The temperature is then raised to
   38°C at 1 atm.
   a. Does the volume of the gas increase or decrease?
   b. Calculate the new volume.


6. An automobile engine contains a vaporized sample of gasoline. The initial volume in the cylinder is 0.725
   L. After compression, the volume is reduced to 0.075 L. The fuel mixture initially exerts a pressure of 1.00