# X Y_{2} dissociates as X Y_{2}(g) rightleftharpoons X Y(g) + Y(g) when the initial pressure of X Y_{2} is 600 mm of Hg. The total equilibrium pressure is 800 mm of Hg. Find the value of the equilibrium constant for the reaction, assuming that the volume of the system remains unchanged. A) 50 mm Hg B) 100 mm Hg C) 166.6 mm Hg D) 400 mm Hg

## Question

$X Y_{2}$ dissociates as $X Y_{2}(g) \rightleftharpoons X Y(g) + Y(g)$ when the initial pressure of $X Y_{2}$ is $600 , \mathrm{mm}$ of $\mathrm{Hg}$. The total equilibrium pressure is $800 , \mathrm{mm}$ of $\mathrm{Hg}$. Find the value of the equilibrium constant for the reaction, assuming that the volume of the system remains unchanged.

A) $50 , \mathrm{mm} , \mathrm{Hg}$

B) $100 , \mathrm{mm} , \mathrm{Hg}$

C) $166.6 , \mathrm{mm} , \mathrm{Hg}$

D) $400 , \mathrm{mm} , \mathrm{Hg}$

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## Answer

### Solution

The correct option is **B) $100 , \mathrm{mm} , \mathrm{Hg}$**.

The dissociation reaction can be represented as: $$ XY_{2}(g) \rightleftharpoons XY(g) + Y(g) $$

Given:

- Initial pressure of $XY_{2}$: $600 , \mathrm{mm, Hg}$
- Total equilibrium pressure: $800 , \mathrm{mm, Hg}$

Let $x , \mathrm{mm, Hg}$ be the amount of $XY_{2}$ that dissociates. This also creates $x , \mathrm{mm, Hg}$ each of $XY$ and $Y$. Therefore, the remaining pressure of $XY_{2}$ is $(600 - x) , \mathrm{mm, Hg}$.

The total pressure at equilibrium, considering the contributions from all species, is: $$ P_{total} = (600 - x) + x + x = 600 + x , \mathrm{mm, Hg} $$

Setting the total pressure equation to the equilibrium pressure: $$ 600 + x = 800 \quad \Rightarrow \quad x = 200 , \mathrm{mm, Hg} $$

At equilibrium, the pressures for the various components are:

- $P_{XY_{2}} = 600 - x = 400 , \mathrm{mm, Hg}$
- $P_{XY} = x = 200 , \mathrm{mm, Hg}$
- $P_{Y} = x = 200 , \mathrm{mm, Hg}$

The equilibrium constant $K_p$ is defined as: $$ K_p = \frac{P_{XY} \cdot P_{Y}}{P_{XY_{2}}} $$

Calculating $K_p$: $$ K_p = \frac{200 \times 200}{400} = 100 , \mathrm{mm, Hg} $$

Thus, the value of the equilibrium constant **$K_p$ is $100 , \mathrm{mm, Hg}$**.