In which of the following reactions will K_c = K_p?

• A. H_2(g) + Cl_2(g) ightarrow 2HCl(g)
• B. 2NO_2(g) ightarrow 2NO(g) + O_2(g)
• C. N_2(g) + O_2(g) ightarrow 2NO(g)
• D. 2SO_2(g) + O_2(g) ightarrow 2SO_3(g)

Answer: (A)

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 \(\Delta n\) 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 \(\mathrm{H_2(g) + Cl_2(g) \rightarrow 2HCl(g)}\), the number of moles of gaseous reactants is 1 + 1 = 2, and the number of moles of gaseous products is 2, so \(\Delta n = 2 - 2 = 0\).
4. For the other reactions, compute \(\Delta n\) similarly and check if it equals zero. If \(\Delta n = 0\), then \(K_c = K_p\) because \((RT)^0 = 1\).
5. Identify the reaction(s) where \(\Delta n = 0\); in those cases, \(K_c\) equals \(K_p\).