1. The Ideal Gas Law
PV = nRT

2. Definition
The ideal gas law is the mathematical relationship among:
Pressure (P)
Volume (V)
Temperature (T)
Amount of the Gas in Moles (n)
The law quantitatively describes the behavior of a gas sample for any combination of conditions:
If you know three of the conditions, you can solve for the fourth.
PV = nRT

3. Units of Measurement Volume must always be measured in liters (L).
1L = 1000mL = 0.001kL
Amount of the gas must always be measured in moles (mol).
If amount is given in grams, you must do a gram to mole conversion!
Temperature must always be measured in Kelvin (K).
K = ˚C ˚C = K - 273
Pressure must always be measured in atmospheres (atm).
1 atm = 760 mmHg = 760 torr = x 105 Pa = kPa

4. Standard Temperature and Pressure (STP)
Standard temperature is 273 K.
Standard pressure is 1 atm.
At STP, 1 mole of any ideal gas occupies 22.4 L.

5. PV = nRT The Ideal Gas Constant Represented as R in the ideal gas law.
R is a constant value that never changes.
The value for R is derived from the standard volume (22.4L) of 1 mole of a gas at STP.
PV = nRT can be arranged as R = PV/nT
R = (1 atm)(22.4 L)/(1 mol)(273 K) = L•atm/mol•K
PV = nRT

6. Solving Ideal Gas Law Problems
What is the pressure exerted by a mol sample of nitrogen gas in a 10.0L container at 25˚C?
1. Determine given values and unknown.
n= mol, V = 10.0 L, T = 25˚C , R = L•atm/mol•K
P = ?
2. Convert given values into proper units.
K = 25˚C = 298 K
3. Rearrange equation to solve for unknown. Plug in given values to solve for unknown.
P = nRT/V
P = (o.500 mol)( L•atm/mol•K)(298 K) / 10.0 L
P = 1.22 atm

7. Solving Ideal Gas Law Problems
What is the volume of an 8.00g sample of oxygen gas at 293 K and atm?
1. Determine given values and unknown.
n= 8.00g, T = 293 K , P = atm, R = L•atm/mol•K
V= ?
2. Convert given values into proper units.
8.oo g O2 x (1 mol O2 / g O2 ) = mol O2
3. Rearrange equation to solve for unknown. Plug in given values to solve for unknown.
V = nRT/P
V= (o.250 mol)( L•atm/mol•K)(293 K) / atm
V = 6.17 L