Carbon monoxide and molecular oxygen react to form carbon dioxide. A 50.0 L reactor at 25.0 oC is charged with

Question

Carbon monoxide and molecular oxygen react to form carbon dioxide. A 50.0 L reactor at 25.0 oC is charged with 1.00 atm of CO. The gas is then pressurized with O2 to give a total pressure of 3.03 atm. The reactor is sealed, heated to 350 oC to drive the reaction to completion, and cooled back to 25.0 oC. Compute the final partial pressure of each gas (in atm).

What is the final pressure of CO?
What is the final pressure of CO2?
What is the final pressure of O2?

Answer 1

Go from the initial conditions:
T = 25.0°C = 298 K
V = 50.0 L
pPCO = 1.00 atm
pPO2 = 2.03 atm
R = 0.082057 L atm / mol K

Use the ideal gas law to solve for the number of moles:
PV=nRT
1.00 atm * 50.0 L = n * 0.082057 L atm / mol K * 298 K
n = 50 / (0.082057 * 298) = 2.045 mol of CO

Same thing for O2:
n = 100.06 / (0.082057 * 298) = 4.092 mol of O2

The reaction is 2 CO + O2 --> 2 CO2

So, you will need 1 mol of O2 for every 2 mol of CO. Since there is less CO than O2, CO is the limiting reactant. All of the CO will react, and it will use up 2.045 mol CO * 1 mol O2 / 2 mol CO = 1.022 mol O2.

So, the final concentrations will be:
CO: 0 mol
O2: 3.070 mol
CO2: 2.045 mol

Reverse the ideal gas law step:
PV = nRT
n for CO is 0, so pCO = 0 atm

pCO2 * V = nRT
pCO2 = nRT/V = 2.045 mol * .082057 L atm / mol K * 298 K / 50 L = 1.00 atm

pPO2 = 3.070 * .082057 atm * 298 / 50
pPO2 = 1.50 atm


Of course, this could have been done more simply:
2 atm CO + 1 atm O2 --> 2 atm CO2
So, the 1 atm of CO will consume 0.5 atm of O2 and produce 1 atm of CO2
CO: 1atm - 1atm = 0 atm
CO2: 0 atm + 1 atm = 1 atm
O2: 2 atm - 0.5 atm = 1.5 atm

This simple reaction is only applicable because the starting and finishing temperatures were the same. The 350°C temperature was just put in to throw you off: it has no appliciblity unless you were trying to find out the reaction kinetics (what percent yield you got), but since the question specified that the reaction went to completion, it does not matter.

Good luck!

Answer 2

2 moles of CO reacts with one mole of O2. So the 2.4 atm of CO will react with 1.2 atm of O2 giving 2.4 atm CO2 from the 4.5 atm of O2 4.5-1.2 =3.3atm are not used . So, the final pressure would be 1.2+3.3 =4.5 atm Remark : When you have a reaction it is not the atm which react but a number of moles. Care to units !