Ideal Gas Law

• An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces. One can visualize it as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other..

• An ideal gas can be characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T).

• The relationship between them may be deduced from kinetic theory and is called the Ideal Gas Law

• Real Gases deviate from ideal behavior at low temperatures and high pressure.

• PV= nRT• n = number of moles• R = universal gas constant = 8.314 L•kPa

K•mol

Universal Gas Constant (R )

• In kPa 8.314 L•kPa K•mol

• In Atmospheres 0.0821 L•atm K•mol

• How many moles of air molecules are contained in a 2.00 L flask at 98.8 kPa and 25.0 C?

• PV = nRT so…• (98.8 kPa)(2.00 L) = n (8.314 L•kPa)

(298K) K•mol Solving for n= (98.8 kPa)(2.00 L) (8.314 L•kPa)(298K) K•mol n= .0798 mol

Density of a Gas

Calculate the density in g/L of O2 gas at STP. From STP, we know the P and T.

P = 1.00 atm T = 273 K

Rearrange the ideal gas equation for moles/L

PV = nRT PV = nRT P = n

RTV RTV RT V

Substitute

(1.00 atm ) mol-K = 0.0446 mol O2/L

(0.0821 L-atm) (273 K)

Change moles/L to g/L

0.0446 mol O2 x 32.0 g O2 = 1.43 g/L

1 L 1 mol O2

Therefore the density of O2 gas at STP is

1.43 grams per liter

Molar Mass of a Gas

What is the molar mass of a gas if 0.250 g of the gas occupy .215 L at 0.813 atm and 30.0°C?

Molar mass = dRT d = m/v PMolar mass = (0.250 g/.215L)(.0821L•atm)(303K) K•mol

0.813 atm= 35.6 g/mol

A gas consisting of only carbon and hydrogen has an empirical formula of CH2. The gas has a density of 1.65 g/L at 27 C and .966 atm. Determine the molar mass and molecular formula of the gas.

Molar mass = dRT/P so…(1.65g/L)(.0821L•atm/K•mol)(300K)

.966 atm

= 42.1 g/mol 42.1g/mol = 3 so.. 3(CH2) or C3H6

14.03 g/mol