For which of the following chemical equations would the value of K_p equal K_c(RT)? (Note: K_c is sometimes called K.)

• A. N_2(g) + 3H_2(g) ⇌ 2NH_3(g)
• B. H_2(g) + I_2(g) ⇌ 2HI(g)
• C. 2SO_2(g) + O_2(g) ⇌ 2SO_3(g)
• D. CO(g) + 2H_2(g) ⇌ CH_3OH(g)

Answer: (B)

Verified step by step guidance

1. Recall the relationship between the equilibrium constants K_p and K_c 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), \(R\) is the gas constant, and \(T\) is the temperature in Kelvin.
2. Calculate \(\Delta n\) for each reaction by subtracting the total moles of gaseous reactants from the total moles of gaseous products:
3. - For \(N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)\): \(\Delta n = 2 - (1 + 3) = 2 - 4 = -2\)
4. - For \(H_2(g) + I_2(g) \rightleftharpoons 2HI(g)\): \(\Delta n = 2 - (1 + 1) = 2 - 2 = 0\)
5. - For \$2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)\(: \)\Delta n = 2 - (2 + 1) = 2 - 3 = -1$
6. - For \(CO(g) + 2H_2(g) \rightleftharpoons CH_3OH(g)\): \(\Delta n = 1 - (1 + 2) = 1 - 3 = -2\)
7. Identify the reaction where \(\Delta n = 1\) because the problem asks for when \(K_p = K_c (RT)\), which means the exponent on \((RT)\) must be 1. None of the reactions have \(\Delta n = 1\), so check for \(\Delta n = 0\) which simplifies the relationship to \(K_p = K_c\) (no \((RT)\) factor).
8. Since \(\Delta n = 0\) for the reaction \(H_2(g) + I_2(g) \rightleftharpoons 2HI(g)\), the relationship becomes \(K_p = K_c (RT)^0 = K_c\), which means \(K_p\) equals \(K_c\) without any \((RT)\) factor. Therefore, none of the given reactions satisfy \(K_p = K_c (RT)\) exactly, but the one with \(\Delta n = 1\) would if it existed.
9. Conclude that the reaction with \(\Delta n = 1\) would satisfy \(K_p = K_c (RT)\), but since none have \(\Delta n = 1\), the problem's correct answer is the one with \(\Delta n = 0\), where \(K_p = K_c\), which is \(H_2(g) + I_2(g) \rightleftharpoons 2HI(g)\).