Question 17.3: Converting Between Kc and Kp Problem Ammonium hydrosulfide d......

Plan We know K_p (0.19), so to convert between K_p and K_c, we must first determine Δn_{\text{gas}} from the balanced equation. Then we rearrange Equation 17.8. If we assume that pressure is measured in atmospheres, R = 0.0821 atm⋅L/mol⋅K; the given temperature must be converted to kelvins.

           K_p  =  K_c(RT)^{Δn_{\text{gas}}}          (17.8)

Solution Determining Δn_{\text{gas}}: There are 2 moles of gaseous product (1 mol NH_3 and 1 mol H_2S) and no gaseous reactant, so Δn_{\text{gas}} = 2 − 0 = 2. (Note that only moles of gaseous reactants and products are used to determine Δn_{\text{gas}}.)

Converting T from °C to K:           T (K) = 218°C + 273.15 = 491 K
Rearranging Equation 17.8 and calculating K_c:

            K_p  =  K_c(RT)^{Δn_{\text{gas}}}          or        K_p  =  K_c(RT)^2

so

                      K_c  =  K_p(RT)^{−2}  =  (0.19)(0.0821×491)^{−2}
                      =  1.2×10^{−4}

Check Rounding gives
                      (0.2)(0.1×500)^{−2}  =  (0.2)(4×10^{−4})  =  0.8×10^{−4}