Consider the general reaction given below at 400 K x ~A ( ~g ) y ~B ( ~g ) The values of K _ p and K _ c are studied under the same condition of temperature but variation in x and y. (i) K _ p =85.87 and K _ c =2.586 appropriate units (ii) K _ p =0.862 and K _ c =28.62 appropriate units. The values of x and y in (i) and (ii) respectively are:
D. \( array c (i) & (ii) \\ 1,2 & 2,1 array \)
The relationship between K_p and K_c is given by K_p = K_c(RT)^ n_g , where n_g = y - x. Given T = 400 K and R = 0.0821 L atm K^ -1 mol^ -1 . The value of RT = 0.0821 400 = 32.84. For case (i): K_p = 85.87 and K_c = 2.586. K_p K_c = 85.87 2.586 33.2. Since 33.2 32.84^1, we have n_g = y - x = 1. Checking options for (i): (1) y-x = 3-1 = 2 (2) y-x = 1-4 = -3 (3) y-x = 1-3 = -2 (4) y-x = 2-1 = 1. This matches. For case (ii): K_p = 0.862 and K_c = 28.62. K_p K_c = 0.862 28.62 0.0301. Since 0.0301 1 32.84 = 32.84^ -1 , we have n_g = y - x = -1. Checking option (4) for (ii): y-x = 1-2 = -1. This also matches. Thus, for (i) x=1, y=2 and for (ii) x=2, y=1.
Related: Chemistry — Chemical Equilibrium · All PYQ Banks