Problem 1: Kp from Kc

Given: $N_{2}$(g) + $3H_{2}$(g) ⇌ $2NH_{3}$(g); Kc = 0.5 at 400 K. Find Kp.

Step 1: Identify $\Delta n$ (gaseous species only) $\Delta n = \text{moles gaseous products} - \text{moles gaseous reactants} = 2 - (1 + 3) = -2$

Step 2: Apply formula $K_p = K_c(RT)^{\Delta n} = 0.5 \times (0.0821 \times 400)^{-2}$

Step 3: Calculate RT $RT = 0.0821 \times 400 = 32.84 \text{ L·atm/mol}$

Step 4: Apply exponent $K_p = 0.5 \times (32.84)^{-2} = \frac{0.5}{1078.5} = 4.63 \times 10^{-4} \text{ atm}^{-2}$

Answer: $K_p = 4.63 \times 10^{-4}$