Question

The values of $K_{p}1$and $K_{P}2$ for the reactions
$X\leftrightharpoons Y+ZandA\leftrightharpoons 2B$ Are in the ratio of $9:1.$ If the degree of dissociation of $XandA$ be equal, then total pressure at equilibrium $\left(1\right)and\left(2\right)$ are in the ration

• A. 3:1
• B. 1:9
• C. 36:1
• D. 1:1

Answer 1

The correct option is C 36:1

Suppose total pressure at equilibrium for reactions 1 and 2 are $P_{1}and{P}_2$respectively

$\begin{array}{ccccc}& X\leftrightharpoons & Y+& Z& \\ Initialmoles& 1& 0& 0& \\ Atequilibrium& 1-x& x& x& \end{array}$

$Totalmoles=1+\alpha$
Partial pressure of $X=p_x=\frac{(1-x)XP1}{1+x}$
$P_y<=\frac{\left(x\right)XP1}{1+x}=P_z$
$(K_{P1}=P_Y{P}_Z/P_x=x^2{P}_1/(1-x^2)\approx x^2{P}_1$

$\begin{array}{ccc}& A\leftrightharpoons & 2B\\ hlineInitialmoles& 1& 0\\ Atequilibrium& 1-x& 2x\end{array}$

$Totalmoles=1+\alpha$

$P_A=\frac{(1-x)XP2}{1+x}{P}_B=\frac{\left(2x\right)XP2}{1+x}$

$K_{P2}=P_B^2/P_A=4x^2{P}_2/(1-x^2)\approx 4x^2{P}_2$
$K_{P}1/K_{P}2=x^2{P}_1/4x^2{P}_2=9/1$
$P_1/P_2=36/1$