Question

The water gas shift reaction involves the reaction of carbon monoxide with water vapor to form carbon dioxide and hydrogen gas:

CO(g) + H₂O(g) → CO₂(g) + H₂(g)

28.01 g CO and 9.01 g water vapor are combined in a reaction vessel. At the end of the reaction, a total pressure of 945.3 torr is found.

A.) Which gases are left at the end of the reaction?

B.) What are mole fractions of the gases left in the reaction vessel after the reaction? Clearly identify which mole fraction belongs to which gas, and report all mole fractions to three significant figures.

C.) What is the actual volume of the reaction vessel if the reaction from Question 1 occurred at 115.0^oC? Give your answer with the correct unit. Hint: you should be able to find the moles of all gases from the data given.

D.) If the volume of the reaction vessel is somehow changed to 55.3 L at constant temperature, what will the new total pressure of the gas mixture (after the reaction in Question 1) be? Give your answer to the correct number of significant figures and unit.

Answer 1

As per the reaction equation one mole of CO will react with one mole of water vapour

mass of CO = 28.01

Moles of CO = Mass / Molecular weight of CO = 28.01 / 28.01 = 1 moles

Mass of H2O = 9.01

Moles of H2O = Mass / Mol wt = 9.01 / 18.02 = 0.5 moles

so moles of CO reacted with H2O vapours = 0.5 moles

a) At the end of reaction the gases present = Carbon monoxide , CO2 and H2

b) The total moles of each gas will be

moles of CO left = 0.5 moles

Moles of H2 formed = 0.5moles

Moles of CO2 formed = 0.5 moles

Total moles of gases present = 0.5 + 0.5 + 0.5 = 1.5 moles

mole fraction of CO = Moles of CO / Total moles = 0.5 / 1.5 = 0.33

Mole fraction of CO2 = 0.5 / 1.5 = 0.33

Mole fraction of H2 = 0.5 /1.5 = 0.33

c) The temperature = 115 ⁰C = 273.15 +117 K = 388.15 K

pressure = 945.3 torr

Gas constant =R = 62.36 L Torr K⁻¹ mol⁻¹

total moles = 1.5 moles

we will use ideal gas equation

PV = nRT

Volume = nRT / Pressure = 1.5 X 62.36 X 388.15 / 945.3 = 38.41 Litres

d) The volume changed to 55.3 L at constant temperature,

we will use

P1V1 = P2V2

P1 = 945.3 Torr

V1 = 38.41 L

P2 = ?

V2 = 55.3 L

P2 = P1V1 / V2 = 945.3 X 38.41 / 55.3 = 656.58 Torr