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)
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.
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? • 3.75atm.
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 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.
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 250 C, what will the pressure be if I heat the container to 1500 C? 2.13 atm