The Ideal Gas Law

Recall that at constant volume, the relationship between pressure and temperature(K) is a direct variation:

Since the relationship is linear, we can say that P/T = m_{1}.

The relationship between volume, *V*, and the number of
moles, *n*, is also linear, assuming constant pressure and volume.
(Avogadro's Hypothesis). If you double the number of particles or moles of
particles, you will double the volume.

*n *

Since the relationship is linear, we can say that V/n = m_{2}.

Multiply the above fractions: _{} Let m_{1}m_{2 }= a new
constant, R, and cross multiply:

PV = nRT.

To get the value of R, we can substitute familiar STP conditions into the expression for R:

_{}

Note, however, that the gas constant R applies to all conditions. If we increase P, then volume will decrease accordingly and still produce 8.31.

**Example 1** What is the volume occupied by 6.0 g of hydrogen(H_{2}) at 30 ^{o}C
if it was subjected to a pressure of 101.3 kPa?

6.0
g/(2.0 g/mole) = 3.0 moles of H_{2}.

PV = nRT, so

_{}

**Example 2** List three ways of increasing pressure.

Since
_{}, we
can

(1) increase the amount of gas while keeping T and V constant.

(2) increase temperature while keeping *n*
and V constant.

(3) decrease volume while keeping *n*
and T constant.

**Example 3** Calculate the molar mass of an unknown gas using the data
below:

Volume
of syringe: 0.100
L

Mass
of syringe + unknown gas 90.99
g

Mass of empty syringe 90.67 g

Temperature 30.0 C

Pressure 100 kPa

_{}

molar
mass = _{}