Equimolar mixture of two gases \( A_{2} \) and \( B_{2} \) is taken in a rigid vessel at temperature \( 300 K \). The gases reacts according to given equations :
\[
\begin{array}{ll}
A_{2}(g) \rightleftharpoons 2 A(g) & K_{P_{1}}=? \\
B_{2}(g) \rightleftharpoons & K_{P_{2}}=? \\
A_{2}(g)+B_{2}(g) & \rightleftharpoons 2 A B(g) & K_{P_{3}}=2
\end{array}
\]
If the initial pressure in the container was 2 atm and final pressure developed at equilibrium is \( 2.75 atm \). in which equilibrium partial pressure of gas \( A B \) was \( 0.5 atm \), calculate the ratio of \( \frac{ K _{ p _{2}}}{ K _{ p _{1}}} \).
[Given : Degree of dissociation of \( B_{2} \) is greateı than \( A _{2} \) ].
