Consider the heterogeneous equilibrium process shown below.
C(s) + CO2(g) 2 CO(g)
At 700.°C, the total pressure of the system is found to be 3.87 atm. If the equilibrium constant KP is 1.52, calculate the equilibrium partial pressures of CO2 and CO.
I assume that at equilibrium Ptotal = 3.87 atm.
.........C(s) + CO2(g) ==> 2CO(g)
E...............3.87-p......p..
If Ptotal = 3.87, if we call CO p then CO2 is 3.87-p. Substitute into Kp expression and solve.
Well, it seems like we're dealing with a chemistry question here. But don't worry, I'll try to make it as fun as possible!
Alright, let's start with the equilibrium constant KP. Now, we know that CO2 is a gas, so its partial pressure will be represented by P(CO2). Similarly, the partial pressure of CO will be represented by P(CO).
According to the equation, it says that C(s) + CO2(g) gives 2 CO(g). So, if we assume that the initial partial pressure of CO2 is x, then the initial partial pressure of CO will be 2x.
Now, let's use the KP expression for this reaction:
KP = (P(CO))^2 / P(CO2)
We know that KP is given as 1.52. So, we can write the equation like this:
1.52 = (2x)^2 / x
Alright, let's solve this equation and find the value of x. After solving it, we get x = 0.77.
So, the equilibrium partial pressure of CO2 will be 0.77 atm, and the equilibrium partial pressure of CO will be 2(0.77) = 1.54 atm.
Hope that brings a smile to your face!
To solve this problem, we need to use the equilibrium constant expression and the given total pressure to determine the equilibrium partial pressures of CO2 and CO.
The equilibrium constant expression for the reaction is as follows:
KP = (PCO) ^2 / (PCO2 x PC)
Where:
PCO = partial pressure of CO
PCO2 = partial pressure of CO2
C = concentration of solid carbon (s)
Given:
Total pressure (PTotal) = 3.87 atm
KP = 1.52
Let's assume the equilibrium partial pressures of CO2 and CO are PCO2 and PCO respectively.
We know that in the balanced equation, the coefficients of CO2, CO, and C are 1, 2, and 1, respectively. This means that the change in the number of moles of the gases will be as follows:
Change in moles of CO2 = -x
Change in moles of CO = 2x
Since the total pressure is the sum of the partial pressures:
PTotal = PCO2 + PCO
Substituting the values into the equilibrium constant expression, we have:
1.52 = (PCO)^2 / (PCO2 x C)
Using the relationship between the moles and the partial pressures (PV = nRT), we can rewrite the equation as follows:
1.52 = (PCO)^2 / ((PTotal - PCO) x C)
Substituting the given PTotal value, we get:
1.52 = (PCO)^2 / ((3.87 atm - PCO) x C)
Simplifying the equation, we have:
1.52 = (PCO)^2 / ((3.87 - PCO) x C)
To solve for PCO, we can assume a value for x and calculate the corresponding values for PCO2 and PCO using the given equation. Then we can compare the sum of the calculated partial pressures with the given PTotal. Repeat this until we find the correct value of x.
Let's assume x = 0.1 atm for now.
PCO2 = (3.87 - 2 * 0.1) atm = 3.67 atm (calculated using the equation)
PCO = 2 * 0.1 atm = 0.2 atm (calculated using the equation)
PTotal_calculated = PCO2 + PCO = 3.67 atm + 0.2 atm = 3.87 atm
Since the calculated PTotal matches the given PTotal, the assumed value of x = 0.1 atm is correct.
Therefore, at equilibrium:
PCO2 = 3.67 atm
PCO = 0.2 atm
So the equilibrium partial pressures of CO2 and CO are 3.67 atm and 0.2 atm, respectively.
To calculate the equilibrium partial pressures of CO2 and CO, we can use the equation relating the equilibrium constant (KP) to the partial pressures of the reactants and products.
The equation is as follows:
KP = (P(CO)^2) / (P(CO2) * P(C))
Where KP is the equilibrium constant, P(CO) is the partial pressure of CO, P(CO2) is the partial pressure of CO2, and P(C) is the partial pressure of C(s).
We are given the following information:
KP = 1.52
Total pressure of the system = 3.87 atm
First, we need to calculate the partial pressure of C(s). Since the solid C(s) does not contribute to the pressure, its partial pressure is zero.
Next, let's assume the partial pressure of CO2 is x atm and the partial pressure of CO is y atm.
Now, we can substitute the partial pressures into the equilibrium constant equation:
1.52 = (y^2) / (x * 0)
Since x * 0 = 0, the equation simplifies to:
1.52 = y^2 / 0
This tells us that the partial pressure of CO2 is zero. However, this is not physically possible, as CO2 must have a nonzero partial pressure in the system.
This means that the reaction does not occur in the forward direction, and the equilibrium lies towards the reactants (C(s) and CO2).
Therefore, at equilibrium, the partial pressure of CO2 is 0 atm and the partial pressure of CO is y atm.
In summary:
Partial Pressure of CO2 (P(CO2)) = 0 atm
Partial Pressure of CO (P(CO)) = y atm
Note: It is important to note that at 700°C, the reaction may not have reached equilibrium. The given equilibrium constant KP might be at a different temperature.