Gases

Pressure Pressure = the force of gas molecules as they hit the sides of a container Air pressure units = atmospheres (atm) “Normal” atmospheric pressure = 1 atm Kilopascal (kPa) 101.325 kPa = 1 atm

“Room temperature” = 298°K or 25°C Temperature = a measurement of the amount of energy found within molecules. “Room temperature” = 298°K or 25°C To convert degrees Celsius (°C) to Kelvin (°K), simply add 273 to your Celsius measurement. All temperatures within calculations involving gas must be in Kelvin units!

Volume Volume = the amount of space in which a fluid is enclosed. Volume unit = the liter (L)

STP STP stands for “standard temperature and pressure” which is considered to be 273°K (0°C) and 1.00 atm.

Boyle’s Law P1V1 = P2V2 Increasing the pressure on a gas makes its volume decrease; and, decreasing the pressure will increase its volume.

Practice time... P1V1 = P2V2 (2 atm) x (50L) = (4 atm) x (? L) If you have 50L of gas at a pressure of 2 atm and you double its pressure, what will the new volume of the gas be? P1V1 = P2V2 (2 atm) x (50L) = (4 atm) x (? L) 100 atm · L = (4 atm) x (? L) 100 atm · L = 25 L 4 atm

Charles’s law states that as you increase the temperature of a gas, its volume increases too! Remember! All temperatures within calculations involving gas must be in Kelvin units!

Convert to Kelvin: 25°C + 273 = 298°K If you heat a 2.5 L balloon from a temperature of 25°C to 50°C, what will the new volume of the balloon be?   Convert to Kelvin: 25°C + 273 = 298°K 50°C + 273 = 323°K (2.5 L) x (323°K) = (298°K) x ??? 807.5 L · °K = (298°K) x ??? 807.5 L · °K = 2.7 L 298 °K

The Gay-Lussac law states that as you increase the temperature of a gas, its pressure goes up too!

Convert to Kelvin: 25°C + 273 = 298°K If you have a can of soda at a pressure of 20 atm at room temperature and put it into the fireplace which has a temperature of 1200°C, what will the pressure inside the can just before it explodes? Convert to Kelvin: 25°C + 273 = 298°K 1200°C + 273 = 1473°K (20 atm) x (1473°K) = (298°K) x ??? 29460 atm · °K = (298°K) x ??? 29460 atm · °K = 98.9 atm 298 °K

If I have 30mL of a gas at a pressure of 3 If I have 30mL of a gas at a pressure of 3.0 atm and a temperature of 400°K, what will the pressure become if I raise the temperature to 450°K and decrease the volume to 15mL?   (3.0 atm)(30mL) = (???)(15mL) 400°K 450°K .225 = (???)(15mL) 450°K 101.25 = (???)(15mL) 6.75atm = P2

The Combined Gas Law This equation can be used even if you do not have all three of these variables mentioned inside your problem! Simply remove the P, V, or T from the equation and keep on working.

All three… If I have 30mL of a gas at a pressure of 3.0 atm and a temperature of 400°K, what will the pressure become if I raise the temperature to 450°K and decrease the volume to 15mL?   (3.0 atm)(0.03L) = (???)(0.015L) 400°K 450°K .225 = (???)(0.015L) 450°K 101.25 = (???)(0.015L) 6.75atm = P2

Boyle’s only… P1V1 = P2V2 (2 atm) x (50L) = (4 atm) x (? L) If you have 50L of gas at a pressure of 2 atm and you double its pressure, what will the new volume of the gas be? P1V1 = P2V2 (2 atm) x (50L) = (4 atm) x (? L) 100 atm · L = (4 atm) x (? L) 100 atm · L = 25 L 4 atm

Convert to Kelvin: 25°C + 273 = 298°K Charles’ only… If you heat a 2.5 L balloon from a temperature of 25°C to 50°C, what will the new volume of the balloon be?   Convert to Kelvin: 25°C + 273 = 298°K 50°C + 273 = 323°K (2.5 L) x (323°K) = (298°K) x ??? 807.5 L · °K = (298°K) x ??? 807.5 L · °K = 2.7 L 298 °K

Convert to Kelvin: 25°C + 273 = 298°K Gay-Lussac only… If you have a can of soda at a pressure of 20 atm at room temperature and put it into the fireplace which has a temperature of 1200°C, what will the pressure inside the can just before it explodes? Convert to Kelvin: 25°C + 273 = 298°K 1200°C + 273 = 1473°K (20 atm) x (1473°K) = (298°K) x ??? 29460 atm · °K = (298°K) x ??? 29460 atm · °K = 98.9 atm 298 °K

The Combined Gas Law …the number of gas particles? Very helpful. But what about... …the number of gas particles?

The Ideal Gas Law PV=nRT P = pressure (atm) V = volume (L) n = number of moles T = temperature (°K) R = ideal gas constant (0.08206 L · atm/mole · °K)

If you have a 2.0 liter canister which holds 4 moles of gas, and the temperature of the fire you place the can is 1400°C, what is the pressure inside the canister? PV=nRT P = ? V = 2.0 L n = 4 moles R = 0.08206 L · atm/mole · °K T = 1400°C (Remember to convert all temperatures to Kelvin! So... T = 1673°K)

(P)(2.0L) = (4 moles)(0.08206 L · atm/mole · K)(1673°K) PV=nRT (P)(2.0L) = (4 moles)(0.08206 L · atm/mole · K)(1673°K) (P)(2.0L) = 549.1 L · atm P = 274.6atm

“Ideal gases” do not exist – but it provides the most precise predictions Most of the gases we work with are a mixture of several compounds and each have different masses which can cause different amounts of pressure. So...

Dalton’s Law of Partial Pressures The total pressure of a mixture of gases equals the sum of its individual pressures. Ptotal = P1 + P2 + P3 + .......

Ptotal = 0.45 atm + 0.50 atm + 0.25 atm + 0.60 atm A container is filled with a mixture of four gases. The partial pressures of these gases are as follows: Carbon dioxide = 0.45 atm, Oxygen gas = 0.50 atm, Methane = 0.25 atm, and Nitrogen gas = 0.60 atm. What is the total pressure inside the container? Ptotal = 0.45 atm + 0.50 atm + 0.25 atm + 0.60 atm Ptotal = 1.8 atm

And now, the return of your old friend... Stoichiometry of gases

Liquids and gases are measured in liters (L) - not grams (g). Don’t Panic!!! Liquids and gases are measured in liters (L) - not grams (g). The only conversion factor you need to learn is when you are converting between liters and moles: 1 mole = 22.4 L

Follow this roadmap to solve for any stoichiometry problems involving liters of reagent or product

How many liters of water can be made from 30 liters of oxygen at STP from the following reaction? 2H2 + O2 → 2H2O Since both the product AND the reactant are measured in liters, you replace the molar masses with this new conversion factor.

How many liters of water can be made from 30 liters of oxygen at STP from the following reaction? 2H2 + O2 → 2H2O = 60 L H2O

If the reaction is NOT taking place at STP, you will need to use the Ideal Gas Law: PV=nRT

(1atm)(V)=(100moles)(0.08206)(308ºK) Using the same chemical formula for the production of water in the previous example, how many liters of water can be made from 200 grams of hydrogen at a temperature of 308ºK and at 1atm? 200grams H2 1 mole H2 2 moles H2O = 100 moles H2O 2.0 grams H2 2 moles H2 Now convert moles of water to liters of water: PV=nRT (1atm)(V)=(100moles)(0.08206)(308ºK) V= 2,527.4 L

Follow this roadmap to solve for any stoichiometry problems involving liters of reagent or product