For which of the following chemical equations would the value of K_c equal K_p at a given temperature?

• A. N_2(g) + O_2(g) ightarrow 2NO(g)
• B. H_2(g) + I_2(g) ightarrow 2HI(g)
• C. 2SO_2(g) + O_2(g) ightarrow 2SO_3(g)
• D. 2NO_2(g) ightarrow N_2O_4(g)

Answer: (B)

Verified step by step guidance

1. Recall the relationship between the equilibrium constants \(K_c\) and \(K_p\) for gaseous reactions: \(K_p = K_c (RT)^{\Delta n}\), where \(R\) is the gas constant, \(T\) is the temperature in Kelvin, and \(\Delta n\) is the change in moles of gas (moles of gaseous products minus moles of gaseous reactants).
2. Calculate \(\Delta n\) for each reaction by subtracting the total moles of gaseous reactants from the total moles of gaseous products.
3. For the reaction \(N_2(g) + O_2(g) \rightarrow 2NO(g)\), count the moles: reactants = 1 + 1 = 2, products = 2, so \(\Delta n = 2 - 2 = 0\).
4. For the reaction \(H_2(g) + I_2(g) \rightarrow 2HI(g)\), count the moles: reactants = 1 + 1 = 2, products = 2, so \(\Delta n = 2 - 2 = 0\).
5. For the reactions where \(\Delta n = 0\), the term \((RT)^{\Delta n} = (RT)^0 = 1\), so \(K_p = K_c\). Identify which reactions have \(\Delta n = 0\) to determine for which \(K_c\) equals \(K_p\).