At temperature ,T, a compound `AB_2(g)` dissociates according to the reaction `2AB_2 (g) ltimplies 2AB(g)+B_2(g)` with a degree of dissociation, x, which is small compared with unity.Deduce the expression for `K_P`, in terms of x and the total pressure , P.

Explanation

To derive the expression for \( K_P \) in terms of the degree of dissociation \( x \) and the total pressure \( P \) for the reaction:

\[ 2AB_2(g) \rightleftharpoons 2AB(g) + B_2(g) \]

we will follow these steps:

### Step 1: Initial Conditions
Assume that initially, the pressure of \( AB_2 \) is \( P_0 \) and there are no products present. Thus, at \( t = 0 \):
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