Final answer:
To convert the value of Kp (41) to Kc for the given reaction at 400 K, the equation Kp = Kc(RT)^Δn is used, where R is the gas constant, T is the temperature in Kelvin, and Δn is the change in the number of moles of gas. For this reaction, Δn is -2.
Step-by-step explanation:
The student has asked about converting the value of Kp to Kc for the reaction N₂(g) + 3 H₂(g) ⇌ 2 NH₃(g) at 400 K. The Kp value given is 41.
To convert Kp to Kc, we use the equation:
Kp = Kc(RT)^Δn
Where:
- R is the gas constant (0.0821 L·atm/K·mol)
- T is the temperature in Kelvin
- Δn is the change in the number of moles of gas
In this reaction, Δn = (2 - (1 + 3)) = -2 because 2 moles of NH₃ gas are produced from 1 mole of N₂ and 3 moles of H₂ gas.
Therefore, solving for Kc we get:
Kc = Kp / (RT)^Δn
Inserting the values (with T = 400 K and Δn = -2):
Kc = 41 / (0.0821 * 400)^-2
When you compute this, you'll find the value of Kc.