Gases

Getting started with gas calculations:• Before we can start talking about how gases behave in

numerical terms, we need to define some of the quantitative properties that are characteristic of gases:

• Pressure (P): The force of gas molecules as they hit the sides of the container in which they are placed.▫ Common units of pressure:

atmospheres (atm): The average air pressure at sea level.

kilopascals (kPa): The SI unit for pressure; 101.325 kPa = 1 atm.

mm Hg (Torr): 760 Torr = 1 atm.

Common Units continued• Volume (V): The amount of space in which a

gas is enclosed.▫The only commonly used unit of volume is liters

(L).• Temperature (T): A measurement of the

amount of energy that molecules have. The higher the energy, the higher the temperature.▫Common units of temperature:

Kelvin (K): The only units that can be used when doing numerical problems with gases.

Degrees Celsius (0C): Must be converted to Kelvin before doing problems (by adding 273).

Other terms frequently used:

•STP: Stands for “standard temperature and pressure”, namely 273 K (00 C) and 1.00 atm.

•“Room temperature”: 298 K (250 C)

A whirlwind tour through the early gas laws:

Boyle’s Law: P1V1 = P2V2

•  For any gas, the product of the pressure and the volume before a change is equal to the product of the pressure and the volume after a change.

•In plain English, what this means is that ▫If you put pressure on a gas, it gets smaller.

▫If you decrease pressure on a gas, it gets

larger.

Balloon Demonstration

Sample problems:

•If I have 10 L of gas at a pressure of 1 atm and double the pressure, what will the new volume of the gas be? ▫5 L

•If 250 L of a gas is in a sealed container at a pressure of 1.5 atm and I decrease the volume of the container to 100 L, what will the gas pressure inside the container be? ▫3.75 atm.

Charles’s Law: • If you increase the temperature of a gas, the

volume also increases. ▫Note: The temperature must be in Kelvin, NOT

degrees centigrade or Celsius

•  Why? The KMT tells us that the amount of energy that a gas has is determined by the temperature of the gas. ▫The more energy a gas has, the faster the gas

molecules move away from each other, causing more space between the molecules and a larger overall volume.

2

2

1

1

T

V

T

V

Kinetic Molecular

Theory

Examples

•If you heat a 1.25 L balloon from a temperature of 250 C to 400 C, what will the new volume of the balloon be? ▫1.31 L

•What temperature will be required to raise the volume of a 1.0 L balloon to 1.25 L if the initial temperature is 250 C? ▫373 K

Gay-Lussac’s Law:

•When you increase the temperature of an enclosed gas, the pressure of the gas goes up.

•This is why it’s a bad idea to put a spray can into a campfire – eventually the pressure rises so much that the sides of the can split and the can explodes.

2

2

1

1

T

P

T

P

Example:

•If you have a spray can at a pressure of 20 atm at room temperature and put it into a campfire at a temperature of 1200° C, what will the pressure in the canister be right before it explodes?

98.9 atm

The combined gas law:•If we put the last three gas laws together,

we can devise another law that encompasses all three of them (making it unnecessary to memorize the three):

2

22

1

11

T

VP

T

VP

How to use this law:

•Whenever you have a problem in which you change the pressure, volume, and/or temperature, just plug the values into it

▫If one of the variables isn’t mentioned, we can assume that it’s kept constant and we can just cross it out of the equation.

Examples:•If I have 25 mL of a gas at a pressure of 2.1

atm and a temperature of 300 K, what will the pressure become if I raise the temperature to 400 K and decrease the volume to 10 mL?

7 atm•If I have a container with an internal pressure

of 1.5 atm and temperature of 250 C, what will the pressure be if I heat the container to 1500 C?

2.13 atm

•Gas Worksheet