If C(s) + CO2(g) <-> CO(g), when equilibrium is established at 1000K, the total pressure in the system is 4.70 atm.
A. If kp= 1.72, what are the partial pressures of CO and CO2?
B. What is Kc of the reaction?
To find the partial pressures of CO and CO2, and the value of Kc for the reaction, we need to use the equilibrium expression and the given information.
The equilibrium expression for the reaction is given as:
Kc = ([CO] / [CO2])
A. To find the partial pressures of CO and CO2 when Kp = 1.72, we need to use the relationship between Kc and Kp. The relationship is given by the equation:
Kp = Kc * (RT)^(Δn)
Where:
- Kp is the equilibrium constant in terms of partial pressures.
- Kc is the equilibrium constant in terms of concentrations.
- R is the ideal gas constant (0.0821 L·atm/(mol·K)).
- T is the temperature in Kelvin.
- Δn is the change in the number of moles of gaseous products minus the change in the number of moles of gaseous reactants.
Since the given reaction has Δn = 0 (there is no change in the number of moles), we can rewrite the equation as:
Kp = Kc * (RT)^(0)
Kp = Kc
Therefore, Kp and Kc have the same value.
Now, we are given that Kp = 1.72, so we can conclude that Kc = 1.72.
B. To find the partial pressures of CO and CO2, we can use the equilibrium expression and the value of Kc. We know that at equilibrium, the partial pressures of CO and CO2 can be represented by the variables x and y, respectively. Thus, we can write the equation as:
Kc = ([CO] / [CO2])
1.72 = (x / y)
Given that the total pressure in the system is 4.70 atm, we can also write the equation as:
4.70 = x + y
Now, we have a system of two equations with two variables. We can solve these equations simultaneously to find the values of x (partial pressure of CO) and y (partial pressure of CO2).
1.72 = (x / y) ---> Equation 1
4.70 = x + y ---> Equation 2
To solve this system of equations, we can rearrange Equation 1 to isolate x:
x = 1.72 * y
Substitute this expression for x into Equation 2:
4.70 = (1.72 * y) + y
4.70 = 2.72 * y
Divide both sides by 2.72:
y = 4.70 / 2.72
y ≈ 1.72 atm
Now, substitute this value of y back into Equation 2 to find the value of x:
4.70 = x + 1.72
x = 4.70 - 1.72
x ≈ 2.98 atm
Therefore, the partial pressure of CO (x) is approximately 2.98 atm, and the partial pressure of CO2 (y) is approximately 1.72 atm.