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; 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 ( 0 C): 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 (0 0 C) and 1.00 atm. “Room temperature”: 298 K (25 0 C)

A whirlwind tour through the early gas laws:

Boyle’s Law: P 1 V 1 = P 2 V 2 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. Kinetic Molecular Theory

Examples If you heat a 1.25 L balloon from a temperature of 25 0 C to 40 0 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 25 0 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.

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):

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 25 0 C, what will the pressure be if I heat the container to C? 2.13 atm

Gas Worksheet