Given the following reaction, with Kp=1.05 at 250 degrees C what is Kc? The reaction is PCl5 to PCl3+Cl2
To find Kc from Kp, we need to use the relationship between the two equilibrium constants. The general 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 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 gas products minus the number of moles of gas reactants
For the given reaction: PCl5 ⇌ PCl3 + Cl2
Let's calculate Δn first:
Δn = (n_PCl3 + n_Cl2) - n_PCl5
Since there is one mole of PCl3 and one mole of Cl2 produced for every mole of PCl5 consumed, Δn = (1 + 1) - 1 = 1
Now, we can rearrange the equation mentioned earlier and solve for Kc:
Kc = Kp / (RT)^Δn
Given that Kp = 1.05 and the temperature is 250 degrees C (which is 523 K), and Δn = 1, we can substitute these values into the equation:
Kc = 1.05 / (0.0821 * 523)^1
Calculating the expression inside the parentheses:
(0.0821 * 523)^1 = 42.9463^(1) = 42.9463
Now, we can substitute this value back into the equation:
Kc = 1.05 / 42.9463 = 0.0244
Therefore, the value of Kc for the reaction PCl5 ⇌ PCl3 + Cl2, when Kp = 1.05 at 250 degrees C, is approximately 0.0244.