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Question: The equilibrium constant \(K_p\) (in atm) for the reaction is 9 at 7 atm and 300K \({A_2}(g) \rightl...

The equilibrium constant KpK_p (in atm) for the reaction is 9 at 7 atm and 300K A2(g)⇌B2(g)+C2{A_2}(g) \rightleftharpoons {B_2}(g) + {C_2} . Calculate the average molar mass(in g/molg/mol) of an equilibrium mixture: Given Molar of A2{A_2}, B2{B_2} and C2{C_2} are 7070, 4949 & 2121 gm/molgm/mol respectively.
A.5050
B.4545
C.4040
D.37.5

Explanation

Solution

KC{K_C} and KP{K_P} are equilibrium constants of gaseous mixtures. However, the difference between the two constants is that KC{K_C} is defined by molar concentrations, while KP{K_P} is defined by the partial pressures of gases inside a closed system.

Complete step by step answer:
-The equilibrium constant of a chemical reaction is the value of its reaction quotient at the chemical equilibrium, which has been approached after a sufficient time has been passed by a dynamic chemical system with no measurable tendency for further changes in its composition.
For a given set of reaction conditions, equilibrium is constant from initial analytical concentrations of reactants and product species in the mixture.
The partial pressure of one of the gases in the mixture is the pressure that it alone occupies the entire container. The partial pressure of gas A is often given the symbol Pa{P_a} . The partial pressure of gas B will be Pb{P_b} - and so on. There are two important relationships with partial pressure. The first is again quite clear. The total pressure of a mixture of gases is equal to the sum of partial pressures.
KP=KC(RT)Δn{K_P} = {K_C}{(RT)^{\Delta n}}
Since, Δn=1\Delta n = 1 , then Kc(RT){K_c}(RT)
9=KC×0.0821×300 KC=0.3654  9 = {K_C} \times 0.0821 \times 300 \\\ {K_C} = 0.3654 \\\
As, KC=[A][B][C]=X21=0.3654 x=0.6044  {K_C} = \frac{{[A][B]}}{{[C]}} = \frac{{{X^2}}}{1} = 0.3654 \\\ x = 0.6044 \\\
Average molecular weight =70×0.455+49×0.27+21×0.27=50 = 70 \times 0.455 + 49 \times 0.27 + 21 \times 0.27 = 50

So, the correct answer is “Option A”.

Note:
KP{K_P} is the equilibrium constant calculated from the partial pressures of an equilibrium equation. It is used to express the relationship between product pressures and reactive pressures. It is a unit less number, although it is related to pressures.