Kp for the reaction CO2(g) + C(s) 2CO(g) is 1.47 at 727°C. Calculate Kc at this temperature
To calculate Kc at a given temperature, we need to convert Kp to Kc using the ideal gas law. The ideal gas law equation is:
PV = nRT
Where:
P is the pressure,
V is the volume,
n is the number of moles,
R is the ideal gas constant (0.0821 L atm / mol K),
T is the temperature.
For the reaction CO2(g) + C(s) ⇌ 2CO(g), we need to convert the pressures of CO2, C, and CO into concentrations, which is expressed in moles per liter (mol/L).
Step 1: Convert Kp to Kc using the ideal gas law equation.
Since the given Kp, 1.47, is the ratio of the partial pressures of products to reactants, we can express it as follows:
Kp = (P(CO)^2) / (P(CO2) * P(C))
Where P(CO2), P(C), and P(CO) are the partial pressures of CO2, C, and CO, respectively.
Step 2: Calculate the concentrations of CO2, C, and CO based on the ideal gas law.
Rearranging the ideal gas law equation, we have:
P = nRT / V
We can substitute P and solve for n/V to get the concentration (C):
C = n / V = P / (RT)
Given that T = 727°C, we need to convert it to Kelvin (as the ideal gas law requires temperature in Kelvin):
T(K) = T(°C) + 273.15
Converting 727°C to Kelvin:
T(K) = 727 + 273.15 = 1000.15 K
Step 3: Substitute the concentrations into the Kp expression and solve for Kc.
Since Kp = (P(CO)^2) / (P(CO2) * P(C)), we can rewrite the expression using concentrations:
Kp = [(C(CO))^2] / (C(CO2) * C(C))
To convert Kp to Kc, we need to substitute concentrations for partial pressures:
Kc = [(C(CO))^2] / (C(CO2) * C(C))
Finally, substitute the concentrations in terms of the partial pressures into the expression and solve for Kc.
Note: The concentration of C(s) is constant, represented by [C], since it's a pure solid and does not change its concentration.
Therefore, Kc = [(P(CO))^2] / (P(CO2) * [C])
Substituting P(CO), P(CO2) and [C] into the expression, we can calculate Kc at the given temperature.