COMEDK 2023 Shift 1 Paper

To determine the equilibrium constant Kx for the given reaction, we will use the equilibrium constants for reactions (a), (b), and (c) provided and manipulate these to match the target reaction. The equilibrium constant for a reaction that is the reverse of a given reaction is the inverse of the original reaction's equilibrium constant, and when a reaction is multiplied by a coefficient, the equilibrium constant is raised to that coefficient. Combining reactions also combines the equilibrium constants by multiplication.
Let's see how we can derive the given reaction from the reactions provided:
GIVEN REACTIONS:
(a) N2+3H2=2NH3:K1
(b) N2+O2=2‌NO:K2
(c) 2H2+O2=2H2O:K3
TARGET REACTION:
4NH3+5O2=4‌NO+6H2O;Kx
STEP 1: Rewrite the given reactions to match parts of the target reaction.
To produce the target reaction from the given ones, notice how we must reverse reaction (a) to get NH3 as a reactant instead of a product and keep other reactions as they directly or indirectly give the desired products or reactants:
Reverse (a) (thereby inverting K1 ):
2NH3=N2+3H2;K1′=‌

1

K1

Multiply by 2 to match 4NH3 in the final reaction:
4NH3=2N2+6H2;K1′′=(‌

1

K1

)2
For reaction (b) to match the target reaction's 4‌NO, it must be multiplied by 2 :
2(N2+O2=2‌NO);K2′=(K2)2
Reaction (c) is already in a suitable form to form 6H2O when multiplied by 3 :
3(2H2+O2=2H2O);K3′=(K3)3
STEP 2: Combine the modified reactions.
Combining the modified forms of reactions (a), (b), and (c) and their equilibrium constants' manipulations, we aim to achieve the target reaction:
To get the target reaction, you need to combine the reversed and modified version of (a) with those of (b) and (c), taking into account that (a) provides the NH3 and through (b) and (c) we get NO and H2O, respectively, as products.
Kx=‌

K2′⋅K3′

K1′′

Substituting the modified equilibrium constants:
Kx=‌

(K2)2⋅(K3)3

(‌ 1 K1 )2

Therefore, simplifying gives:
Kx=K22K33∕K12
Hence, the correct option is A:
Kx=K22K33∕K12