A 200.0mL closed flask contains 2.000mol of carbon monoxide gas and 2.000mol of oxygen gas at the temperature of 300.0K. How many moles of oxygen have to react with carbon monoxide in order to decrease the overall pressure in the flask by 10%? Assume ideal gas behavior. The reaction of carbon monoxide and oxygen gas is described by the following equation.

2CO (g) + O2 (g) ⟶2CO2 (g)

There will react 0.400 moles of oxygen.

Explanation:

Step 1: Data given

Volume of the closed flask = 200.00 mL = 0.2 L

Number of moles of CO = 2.000 mol

Number of moles of O2 = 2.000 mol

Temperature = 300.0 K

Pressure decreases with 10%

Step 2: The balanced equation

2CO (g) + O2 (g) ⟶2CO2 (g)

Step 3: Calculate the initial pressure of the flask before the reaction

P = nRT/V

⇒ with n = the number of moles (2.000 moles CO + 2.000 moles O2 = 4.000 moles)

⇒ R is gas constant (0.08206 atm*L/mol*K)

⇒T = the temperature = 300.0K

⇒ V = the volume = 200.0 mL = 0.2 L

P = (4 * 0.08206*300) / 0.2

P = 492.36 atm

Step 4: When the pressure is 10 % decreased:

The final pressure = 492.36 - 49.236 = 443.124 atm

Step 5: Calculate the number of moles

n = PV/RT

⇒ with n = the number of moles

⇒ with P = the pressure = 443.124 atm

⇒ V = the volume = 200.0 mL = 0.2 L

⇒ R is gas constant (0.08206 atm*L/mol*K)

⇒T = the temperature = 300.0K

n = (443.124*0.2) / (0.08206*300)

n = 3.6 moles = total number of moles

Step 6: Calculate number of moles

For the reaction : 2CO (g) + O₂ (g) ⟶ 2CO₂ (g)

For each mole of O2 we have 2 moles of CO, to produce 2 moles of CO2

Moles CO = (2 - 2X) moles

Moles O2 = (2-X) moles

Moles CO2 = 2X

The total number of moles (4 - X) = 3.6 moles

Where X are moles that react

X = 0.400 moles

There will react 0.400 moles of oxygen.