Questions: Calculate Kp for the reaction 2 NOCl(g) ⇌ 2 NO(g) + Cl2(g) at 400 °C if KC at 400 °C for this reaction is 2.1 × 10^-2 (R=0.08206 L · atm / K · mol)

Solution Steps

The relationship between \(K_c\) and \(K_p\) is given by the equation:

\[ K_p = K_c \left(RT\right)^{\Delta n} \]

where:

• \(R = 0.08206 \, \text{L} \cdot \text{atm} / \text{K} \cdot \text{mol}\)
• \(T\) is the temperature in Kelvin
• \(\Delta n\) is the change in moles of gas

For the reaction:

\[ 2 \text{NOCl}(g) \rightleftharpoons 2 \text{NO}(g) + \text{Cl}_2(g) \]

\(\Delta n = (\text{moles of products}) - (\text{moles of reactants}) = (2 + 1) - 2 = 1\).

The temperature is given as \(400^\circ \text{C}\). Convert this to Kelvin:

\[ T = 400 + 273.15 = 673.15 \, \text{K} \]

Substitute the values into the equation:

\[ K_p = K_c \left(RT\right)^{\Delta n} = (2.1 \times 10^{-2}) \left(0.08206 \times 673.15\right)^1 \]

Calculate \(RT\):

\[ RT = 0.08206 \times 673.15 = 55.224 \]

Now calculate \(K_p\):

\[ K_p = 2.1 \times 10^{-2} \times 55.224 = 1.1597 \approx 1.2 \]

Final Answer