CHAPTER 14: GASES

Chapter 14 Objectives State Boyle’s Law and Charles’s Law Know the variables that influence the behavior of gases Apply the gas laws to problems involving pressure temperature and volume of a gas Compare the separate laws to the universal gas laws

Kinetic theory: You must remember the following about the kinetic theory. It assumes the following concepts are true about gases. 1. gas particles do not attract or repel each other 2. Gases particles are much smaller than the distances between them

Kinetic theory: 3. Gas particles are in constant random motion 4. No kinetic energy is lost when gas particles collide with each other or the walls of their container 5. all gases have the same average kinetic energy at a given temperature

All of these assumptions are based on four factors: the number of gas particles present, the temperature, the pressure and the volume of the gas sample. These four things work together to determine the behavior of gases. When one variable changes, it affects the other three.

Think about squeezing a balloon Think about squeezing a balloon. As the volume is decreased, its pressure is increased This interdependence of the variable is the basis for our gas laws.

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:

Getting started with gas calculations 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.

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.

Think about if you sit on balloons to demonstrate that decreasing the volume increases the pressure inside the balloon so much that it pops! Or, You can use a vacuum pump to decrease the pressure around a balloon – the balloon will get bigger (until it pops, probably).

Boyle’s Law As the pressure on a gas increases - the volume decreases 1 atm As the pressure on a gas increases - the volume decreases Pressure and volume are inversely related As the pressure on a gas increases 2 atm 4 Liters 2 Liters

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? 3.8 atm.

Charles’s Law:

Have you ever noticed on a cold day that your car tire might look like it is low on air? Then after driving the car for a while the tire looks less flat. What makes the difference? *Charles law relates the volume of a gas and temperature

If you increase the temperature of a gas, the volume also increases If you increase the temperature of a gas, the volume also increases. (Note: The temperature must be in Kelvin, NOT degrees centigrade)   Why? The Kinetic Molecular Theory, 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.

Charles’ Law V1 V2 = T1 T2 (Pressure is held constant) Timberlake, Chemistry 7th Edition, page 259 (Pressure is held constant)

Examples: Remember to change degree C to Kelvin If you heat a 1.25 L balloon from a temperature of 250 C to 40.0 C, what will the new volume of the balloon be? 1.3 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? 370 * watch sig figs

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 20.0 atm at room temperature and put it into a campfire at a temperature of 12000 C, what will the pressure in the canister be right before it explodes? 99 atm

14.2 The Combined Gas law and Avogadro’s Principle   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? 2.1 atm

Ideal Gases: Now that we know how gases behave when we manipulate P, V, and T, it’s time to start thinking about how to deal with things like moles and grams. After all, if we’re going to do chemical reactions with gases, we’ll need to know how to calculate these!

Avogadro’s principle: One mole of every gas has the same volume. This law assumes that all gases behave perfectly and identically according to the rules of the kinetic molecular theory. Though not precisely true, it gives us very good answers under most conditions.

Ideal gas: A gas that behaves according to the kinetic molecular theory. No intermolecular forces, infinitely small, etc.   There is no ideal gas in the real world, but some gases come closer than others:

The gas molecules are small. The gas molecules have very weak intermolecular forces. The gas molecules are very hot, so they move quickly around and don’t interact with each other much. The gas is at low pressure, so the molecules have a lot of space between them.

Remember the molar volume for a gas is the volume that one mole occupies at 0 C and 1 atm pressure. This is STP. Because the volume of one mole of a gas at STP is 22.4 L, you can use the conversion factor: 22.4 L/1 Mol

14.3 The Ideal Gas Law Ideal gas: A gas that behaves according to the kinetic molecular theory. No intermolecular forces, infinitely small, etc. There is no ideal gas in the real world, but some gases come closer than others:

The gas molecules are small. The gas molecules have very weak intermolecular forces. The gas molecules are very hot, so they move quickly around and don’t interact with each other much. The gas is at low pressure, so the molecules have a lot of space between them.

Assuming that all gases are ideal, we can use an equation to relate the number of moles to the pressure (P), volume (V), and temperature (T), giving us the…

Ideal gas law: PV = nRT P = pressure (in atm of kPa) V = volume (L) n = number of moles T = temperature (Kelvin) R = ideal gas constant (depends on the unit of pressure used) 8.314 L kPa/mol K 0.08206 L atm/mol K Add : 62.4L mmHG/mol K

Examples:   If I have 10 liters of a gas at a pressure of 1.5 atm and a temperature of 250 C, how many moles of gas do I have? 0.61 mol. If I have 3.5 moles of a gas at a pressure of 895 kPa and they take up a volume of 50 L, what’s the temperature? 1538 K

14.4 Gas Stoichiometry at STP, the conversion factor between liters and moles is 22.4 L = 1 mole.  What this means is that, whatever method of stoichiometry we use, we need only replace the molar masses of the gases with the number 22.4 – for compounds that are solids, we still use the molar mass.

Example: Using the equation 2 H2 + O2  2 H2O, how many liters of water can be made from 25 liters of oxygen at STP? Answer: 50 L