Question

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 10.00%? Assume ideal gas behavior. The reaction of carbon monoxide and oxygen gas is described by the following equation. 2CO(g)+O2(g)⟶2CO2(g)

Answer 1

Answer: 0.4000 mol

Step-by-step explanation:

In a closed flask with fixed volume, the number of moles of ideal gas is proportional to the pressure.

P∝n

To decrease the overall pressure by 10.00%, the number of moles should be decreased by 10.00% as well. Therefore, the number of moles must be decreased by

4.000 mol × 0.1000 = 0.4000 mol

Consider the equation for this reaction.

2CO(g)+O2(g)⟶2CO2(g)

In the balanced equation, 2 mol of carbon monoxide gas (CO) reacts with 1mol of oxygen gas to form 2 mol of carbon dioxide CO2. Notice that the change in the total number of moles is equal to the number of moles of oxygen that react. Therefore, if the total amount of gas decreases by 0.4000 mol, then 0.4000 mol of oxygen gas must react with carbon monoxide. In this case, 0.8000 mol of carbon monoxide is consumed and 0.8000 mol of carbon dioxide is produced.

Answer 2

0,400 moles of Oxygen

Step-by-step explanation:

Using PV = nRT it is possible to obtain the initial pressure of the flask before the reaction thus:

P = nRT/V

Where:

n are moles (4,000 moles, 2,000 of CO and 2,000 moles of H₂O)

R is gas constant (0,082atmL/molK)

T is temperature (300,0K)

V is volume (0,2000L)

Replacing, P = 492,0 atm

If you want to decrease the pressure in 10,00%, the final pressure must be:

492,0atm - 49,2 atm = 442,8 atm

Solving under the same conditions with this pressure, moles must be:

n = PV/RT

n = 3,600 total moles

In the reaction:

2CO(g) + O₂(g) ⟶ 2CO₂(g)

The moles you will have are:

CO: 2,000 moles - 2X

O₂: 2,000 moles - X

CO₂: 2X

Where X are moles that react

Thus, total moles are:

4,000moles - X = 3,600 moles

X = 0,400 moles

That means that moles of oxygen that have to react are 0,400 moles of Oxygen

I hope it helps!