1. Gas Laws

2. Units
STP is Standard Temperature and Pressure. STP is 0 °C and 1 atm of pressure. Gases properties can be compared using STP as a reference.
Temperature:
Celsius and Kelvin
0 ◦C = 273 K
Pressure Units
1 atm
760 mmHg
101.3 kPa
760 torr
Using dimensional analysis to convert pressure units
What is 475 mm Hg expressed in atm?
475 mmHg atm = atm
760 mm Hg

3. Boyle's Law
Boyle's Law states the volume of a definite quantity of dry gas is inversely proportional to the pressure, provided the temperature remains constant.
Mathematically Boyle's law can be expressed as P1V1 = P2V2
V1 is the original volume
V2 is the new volume
P1 is original pressure
P2 is the new pressure
Sample Problem
Suppose you have a gas with 45.0 ml of volume and has a pressure of 760.mmHg. If the pressure is increased to 800mmHg and the temperature remains constant then according to Boyle's Law the new volume is 42.8 ml.
(760mmHg)(45.0ml) = (800mmHg)(V2)
V2 = 42.8ml

4. Charles's Law Sample Problem
Charles's Law can be stated as the volume occupied by any sample of gas at a constant pressure is directly proportional to the absolute temperature.
V is the volume
T is the absolute temperature (measured in Kelvin)
Charles's Law can be rearranged into:
V1 / T1 = V2 / T2
V1 is the initial volume
T1 is the initial temperature
V2 is the final volume
T2 is the final temperature
Sample Problem
You have a gas that has a volume of 2.5 liters and a temperature of 250 K. What would be the final temperature if the gas has a volume of 4.5 liters?
V1 = 2.5 liters
T1 = 250 K
V2 = 4.5 liters
T2 = ?
Solving for T2, the final temperature equals 450 K.
So, increasing the volume of a gas at constant pressure from 2.5 to 4.5 liters results in a temperature increase of 200 K.
Important: Charles's Law only works when the pressure is constant.
Note: Charles's Law is fairly accurate but gases tend to deviate from it at very high and low pressures.

5. Gay-Lussac’s Law P and T are directly Proportional
P1 = P or P1T2 = P2T1
T T2
Sample problem
The pressure inside a container is 770 mmHg at a temperature of 57 C. What would the pressure be at 75 C?
P1= 770 mmHg
T1 = 57°C
T2= 75°C
P2 = ?

6. Combined Law
The combined gas law is a combination of Boyle's Law and Charles's Law; hence its name the combined gas law. Since for a given amount of gas there is a constant then we can write--
P1V1 / T1 = P2V2 / T2.
P1 is the initial pressure
V1 is the initial volume
T1 is the initial temperature (in Kelvin)
P2 is the final pressure
V2 is the final volume
T2 is the final temperature (in Kelvin)
For example if you have 4.0 liters of gas at STP, and you want to know the volume of the gas at 2.0 atm of pressure and 30 °C, the equation can be setup as follows:
(1.0)(4.0) / 273 = (2.0)(V2) / 303 (V2)(2)(273) = (1)(4)(303) V2 = 2.2 Therefore the new volume is 2.2 liters