Chemical and Ionic Equilibrium - Result Question 52

Answer:

Correct Answer: 52. $(1.86)$

Solution:

52. $A_2(g)+B_2(g) \rightleftharpoons 2 A B(g)\quad\quad\quad$ $\Delta n=0$

$ \begin{aligned} & K=\dfrac{[A B]^2}{\left[A_2\right]\left[B_2\right]}=\dfrac{\left(n_{A B}\right)^2}{n_{A_2} \cdot n_{B_2}}=\dfrac{(2 x)^2}{(1-x)(2-x)} \\ & \Rightarrow \quad 50=\dfrac{4 x^2}{x^2-3 x+2} \Rightarrow 23 x^2-75 x+50=0 \\ & \Rightarrow \quad x=\dfrac{75 \pm \sqrt{75^2-4 \times 23 \times 50}}{46}=0.93,2.32 \\ \end{aligned} $

$2.32$ is not acceptable because $x$ cannot be greater than $1$ .

Mole of $A B=2 x=2 \times 0.93=1.86$