To find the value of Kp for the reaction PCl3(g) + Cl2(g) ⇌ PCl5(g) at 500 K, given KC = 0.042, we need to use the relationship between Kp and KC, which is based on the ideal gas law.
The expression relating Kp and KC for a balanced chemical equation is:
Kp = KC * (RT)^Δn
Where: Kp is the equilibrium constant in terms of partial pressures. KC is the equilibrium constant in terms of molar concentrations. R is the 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 number of moles of gaseous reactants.
In this case, the reaction involves a change in the number of moles of gas. The balanced equation is:
PCl3(g) + Cl2(g) ⇌ PCl5(g)
The number of moles of gaseous products is 1, and the number of moles of gaseous reactants is 2. Therefore, Δn = 1 - 2 = -1.
Now, we can plug in the values into the equation:
Kp = KC * (RT)^Δn
Kp = 0.042 * (0.0821 L·atm/(mol·K))^(−1)
Kp = 0.042 * (1/(0.0821 L·atm/(mol·K)))
Kp = 0.042 / (0.0821 L·atm/(mol·K))
Calculating the value:
Kp ≈ 0.512
Therefore, the value of Kp for the given reaction at 500 K is approximately 0.512.