A mixture of 0.166 moles of C is reacted with 0.117 moles of O2 in a sealed, 10 L vessel at 500 K, producing a mixture of CO and CO2. The total pressure is 0.640 atm. What is the partial pressure of CO?
Please provide a step by step explanation with the answer so I can understand the process. I tried it but I didn't get it.
I tried working it out by finding the moles of CO and then dividing that over the total moles and multiplied by .640atm, but I didn't get the right answer.
Have you found a solution to this problem yet?
No, I haven't.
If we have a mixture of 0.33 moles of oxygen and 0.22 moles of carbon dioxide, the mole fraction of carbon dioxide is .
To find the partial pressure of CO in the mixture, we need to use the ideal gas law equation:
PV = nRT
Where:
P is the total pressure of the mixture (0.640 atm)
V is the volume of the vessel (10 L)
n is the number of moles of gas (unknown for CO)
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature in Kelvin (500 K)
First, let's calculate the total number of moles of gas in the mixture. Since we have 0.166 moles of C and 0.117 moles of O2, we can add these values together:
Total moles of gas = 0.166 moles of C + 0.117 moles of O2 = 0.283 moles
Next, we need to use the total number of moles to find the number of moles of CO. Since there is no information given about the reaction or any limiting reagents, we will assume that all of the C reacts to form CO and CO2. Therefore, the moles of CO will be equal to the moles of C:
Moles of CO = 0.166 moles
Now, we can rewrite the ideal gas law equation for CO:
P * V = n * R * T
Since we are looking for the partial pressure of CO, we can substitute the values we have:
n = 0.166 moles
P = unknown (partial pressure of CO)
V = 10 L
R = 0.0821 L·atm/(mol·K)
T = 500 K
Now, rearrange the equation to solve for P:
P = (n * R * T) / V
Substitute the values:
P = (0.166 moles * 0.0821 L·atm/(mol·K) * 500 K) / 10 L
Solving this equation will give you the partial pressure of CO.
P = 0.678 atm
Therefore, the partial pressure of CO in the mixture is 0.678 atm.