Gas Worksheet

UPDATED - DONE WITH ALL THE QUESTIONS :)

Ideal Gas Law (there are 8 Questions)

1.      Under what conditions does a gas behave as ideal?   When it has large volume and low pressure and/or high temperature.                                                                       

2.     Under what conditions does a gas not behave as ideal?          When gases tend to condense.                       

a.     Why does this occur?             Because the gas have high pressure or low lemperatures.                             

3.              How many moles of gas does it take to occupy 12 liters at a pressure of 20.3 kPa and a temperature of 398 K?

Given: V = 12 L ; P = 20.3 kPa ; T = 398 K

Required : n

Calculation:

n = PV/RT                                                                                                                                                      
n = 20.3 kPa x 12 L / 8.13 LkPa/Kmol x 398 K                                                                                                    
n = 243.6 LkPa / 315.78 Lkpa/mol                                                                                                                  
n = 0.77 mol

Paraphrase: 12 liters of gas wth a pressure 20.3 kPa and a temperature 298 K has 0.77 moles.                       

Analysis: The temperature is high, therefore the moles aren’t many.                                                                                      

4.              If I have a 5.5 liter container that holds 1.2 moles of gas at a temperature of 125⁰ C, what is the pressure inside the container?

Given: V = 5.5 L ; n = 1.2 mol ; T = 125oC + 273 = 398 K

Required: P

Calculation:

P = nRT/V                                                                                                                                                      
P = 1.2 mol x 8.31 LkPa/Kmol x 398 K / 5.5 L                                                                                       
P = 721.61 kPa                                                                                                           

Paraphrase: 5.5 liter container that holds 1.2 moles of gas at a temperature of 125^oC has a pressure of 721.61 kPa

Analysis: The temperature is quite high and the volume is quite small, therefore it makes sense that the pressure is quite high.                                                                                   

5.              It is not safe to put aerosol canisters in a campfire, because the pressure inside the canisters gets very high and they can explode.  If I have a 1.0 liter canister that holds 5 moles of gas, and the campfire temperature is 1200⁰ C, what is the pressure inside the canister?

Given: V = 1 L ; n = 5 mol ; T = 1200^oC + 273 = 1473 K

Required: P

Calculation:

P = nRT/V                                                                                          

P = 5 mol x 8.31 LkPa/Kmol x 1473 K / 1 L                                                                                      

P = 61203.15 kPa                                                                                                                               

Paraphrase: 1 L canister that holds 5 moles of gas in a temperature of 1200^oC has a 61203.15 kPa.

Analysis: The moles are quite many and the temperature is really high while the mass is small, therefore it’s reasonable that the pressure is high.                                                                                                      

6.              How many moles of gas are in a 25 liter scuba canister if the temperature of the canister is 330 K and the pressure is 2300 kPa? 

Given: V = 25 L ; T = 330 K ; 2300 kPa

Required: n

Calculation:

n = PV/RT                                                                                                                              

n = 2300 kPa x 25 L / 8.31 LkPa/Kmol x 330 K                                                                                            

n = 57500 LkPa / 2742.3 LkPa/mol                                                                                                   

n = 20.97 mol                                                                                                                                     

Paraphrase : 25 liert scuba caniseter has 20.97 moes if the temperature of the canister is 330 K and the pressure is 2300 kPa.                                                                                                                                               

Analysis: The pressure is really large, it makes sense how the moles are many.

7.              I have a balloon that can hold 103 liters of air.  If I blow up this balloon with 2 moles of oxygen gas at a pressure of 109 kPa, what is the temperature of the balloon?

Given: V = 103 L ; n = 2 mol ; P = 109 kPa

Required: T

Calculation

T = PV/nR                                                                  

T = 109 kPa x 103 L / 3 mol x 8.31 LkPa/Kmol                                                                                            

T = 11227 LkPa / 24.93 LkPa/K                                                                                                                    

T = 450.34 K                                                                                                                                      

Paraphrase : The balloon that hold 103 L of air that is blown with 2 moles at a pressure of 109 kPa has a temperature of      450.34 K.                                                                                                                   

Analysis: The mass is large, it makes sense that the temperature alse large.     

8.              I have a balloon that can hold 0.5 L of air.  If I blow up this balloon with 25 grams of oxygen gas at a pressure of 101.3 kPa, what is the temperature of the balloon?

Given: V = 0.5 L ; M = 2 g ; P = 101.3 K

Required: T

Calculation:

T = PV/nR                                                                  

nO₂ = 25 g O₂ x 1 mol/32 g O₂ = 0.78125 mol                                                                                                

T = 101.3 kPa x 0.5 L / 8.31 LkPa/Kmol x 1.78125 mol                                                                               

T = 50.65 LkPa / 14.80 LkPa/K                                                                                                                     

T = 3.42 K                                                                                                                                          

Paraphrase : The temperature of a balloon that can hold 0.5 L of air with 25 grams of oxygen at a pressure 101.3 kpa is 3.42 K.

Analysis: The mass is small, therefore it’s reasonable that the temperature is also small.

Partial pressures, effusion, and diffusion  (there are 7 questions)

1.      Compare and contrast diffusion and effusion:           Diffusion is the movement of molecules from higher concentration to lower concentration until the concentration is uniform throughout. Effusion is the escape of gas through a tiny hole in a container. Both are the movement of gas and molecules. Also, both diffusion and effusion is faster in gas with lower molar mass than in gases with higher molar mass.                                                                                                                                                                                   

2.     Do gases with higher or lower molar masses diffuse faster?              Lower.                                                

3.     Do gases diffuse from high to low concentration or from low to high concentration?           Gases diffuse from higher to lower concentration.                                                                                                                

4. A metal tank contains three gases:  oxygen, helium, and nitrogen.  If the partial pressures of the three gases in the tank are 35 atm of O₂, 5 atm of N₂, and 25 atm of He, what is the total pressure inside of the tank?

Given: P₁ = 35 atm x 101.3 = 3545.5 kPa ; P₂ = 5 atm x 101.3 = 506.5 kPa ; P₃ = 25 atm x 101.3 = 2532.5 kPa

Required: P_total

Calculation:

P_total = 3545.5 kPa + 506.5 kPa + 2532.5 kPa                                                                                   

P_total = 6584.5 kPa                                                                                                                  

Paraphrase : The total pressure inside the tank is 6584.5 kPa.

Analysis: The answer makes sense because the total pressure is bigger than the partial pressures.

5. Blast furnaces give off many unpleasant and unhealthy gases.  If the total air pressure is 0.99 atm, the partial pressure of carbon dioxide is 0.05 atm, and the partial pressure of hydrogen sulfide is 0.02 atm, what is the partial pressure of the remaining air?

Given: P_total = 0.99 atm x 101.3 = 100.287 kPa ; P₁ = 0.05 atm x 101.3 kPa = 5.065 kPa ; P₂ = 0.02 atm x 101.3 = 2.026 kPa

Required: P₃

Calculation:

(0.99 atm x 101.3) = (0.05 atm x 101.3) + (0.02 atm x 101.3) + P₃                                      

100.287 kPa = 5.065 kPa + 2.026 kPa + P₃

P₃ = 100.287 kPa – (5.065 + 2.026)kPa

P₃ = 93.196 kPa                                                         

Paraphrase: The pressure of remaining air is 93.196 kPa.

Analysis: The answer makes sense because the partial pressure of the remaining air is lowet than the total pressure.

Given: Ptotal = 0.99 atm x 101.3 = 100.287 kPa ; PO2 = 22%

Required: PO2

Calculation:

PO2 = 22/100 x 0.99 kPa = 0.2178 kPa                                                                                            

Paraphrase: The partial pressure of oxygen is 0.22 kPa

Analyis: It makes sense because the total pressure is near 100 kPa but lower and the partial pressure of oxygen is near 22 kPa but also lower.

7.     Compare the effusion rates of NH₃ gas and HCl gas. (Show your work!)

Given: molas mass NH₃ = 14 g + 3(1) g = 17 g ; molar mass HCl = 1 g + 34 g = 35 g

Required: effusion rate

Calculation:

NH₃/HCl = √(molar mass HCl/molar mass NH3)

NH₃/HCl = √(35g/17g)                                                                                                                       

NH₃/HCl = √2.05882                                                                                                                         

NH₃/HCl = 1.43                                                                                                         

Paraphrase: the effusion rate of NH3 and HCl is 1.43

BONUS
8. If I place 3 moles of N₂ and 4 moles of O₂ in a 27 L container at a temperature of 298 K, what will the pressure of the resulting mixture of gases be?

Given: nN2 = 3 mol ; nO2 = 4 mol ; V = 27 L ; T = 298 K

Required: P

Calculation:

P1 = (nN2)RT/V                                                                                                                                                  

P1 = (3 mol x 8.31 LkPa/Kmol x 298 K)/27 L                                                                                                     

P1 = 7429.14 LkPa/27 L                                                                                                                                      

P1 = 275.15 kPa                                                                                                                                                                                                                                                                                                                                

P2 = (nO2)RT/V                                                  

P2 = (4 mol x 8.31 LkPa x 298 K)/27 L

P2 = 9905.52 LkPa/27 L

P2 = 366.87 kPa

Ptotal = P1 + P2

Ptotal = (275.15 + 366.87)kPa

Ptotal = 642.02 kPa

Paraphrase: The pressure of the mixed gas is 642.02 kPa

Analysis: It makes sense that the pressure isn’t too high or too low, because the volume isn’t too big or too small. The temperature also isn’t too high or too low.