Molecular Composition of Gases

The Ideal Gas Law

Objectives:1. State the ideal gas equation.

2. Derive the ideal gas constant and state its units.

3. Use the ideal gas equation to calculate the amount of gas at any condition of temperature and pressure.

4. Use the ideal gas equation to calculate the molar mass of a gas given its density.

5. Reduce the ideal gas law to Boyle’s, Charles’, Gay-Lussac’s, or Avogadro’s Law.

The Ideal Gas Law

•Mathematical relationship between pressure, volume, temperature, and the number of moles of gas.

Ideal Gas LawCalculate the value of R for 1 mole of gas at STP.

• The value of “R” depends on the units used for P, V, and T.

• The ideal gas law can be reduced to any of the previously studied gas laws when certain variables are held constant.

Kmol

atmL

Kmole

Latm

*

*0821.0

)273)(1(

)4.22)(1(

Sample Problems1. A 2.07 L cylinder contains 2.88 mol of helium gas at

22oC. What is the pressure in atmospheres of the gas in the cylinder?

2. A tank of hydrogen gas has a volume of 22.9 L and holds 14.0 mol of the gas at 12oC. What is the reading on the pressure gauge in atmospheres?

3. A reaction yields 0.00856 mol of O2 gas. What volume will this occupy if it is collected at 43oC and 0.926 atm pressure?

4. What mass of ethene gas, C2H4 is contained in a 15.0 L tank that has a pressure of 4.40 atm at a temperature of 305 K?

Ideal Gas Law and Molar Mass

A chemist determines the mass of a sample of gas to be 3.17 g. Its volume is 942 mL at a temperature of 14oC and a pressure of 1.09 atm. What is the molar mass of the gas.

)27314)(0821.0(1000

194209.1

C

Kmol

atomLn

mL

LmLatm o

molesn 0436.0

molg

mol

g

moles

massM 7.72

0436.0

17.3

Ideal Gas Law and Molar Mass

massMolar

massnSince ""

....orRTM

mPV

PV

mRTM

Ideal Gas Law and Density

Knowing that density is mass/volume, what is the density of a sample of ammonia, if the pressure is 0.928 atm and the temperature is 63.0oC?

Lmol

CKmol

atmL

atm

RT

P

V

n

o

0336.0

2730.630821.0

928.0

Lg

mol

gL

mol 572.01

0305.17)0336.0(

Ideal Gas Law and Density

P

DRT

PV

mRTM

RT

MPDor ...