Question

Ammonium hydrogen sulfide dissociates as follows:
$N{{H}_{4}}HS(s)\rightleftharpoons N{{H}_{3}}(g)+{{H}_{2}}S(g)$
If solid $N{{H}_{4}}HS$ is placed in an evacuated flask at a certain temperature it will dissociate until the total is 600 torr.
(a)- Calculate the value of equilibrium constant for the dissociation reaction.
(b)- Additional $N{{H}_{3}}$ is until introduced into the equilibrium mixture without changing the temperature until partial pressure of $N{{H}_{3}}$ is 750 torr. What is the partial pressure of ${{H}_{2}}S$ under these conditions? What is the total partial pressure in the flask?

Answer 1

The equilibrium constant can be calculated by taking the ratio of the product of the pressure of the products by the product of the pressure of the reactants and the values are only taken for the gases. The formula of the equilibrium constant will be:
${{K}_{p}}={{p}_{N{{H}_{3}}}}\text{ x }{{p}_{{{H}_{2}}S}}$

Complete step by step solution: The given reaction is:
$N{{H}_{4}}HS(s)\rightleftharpoons N{{H}_{3}}(g)+{{H}_{2}}S(g)$
As we can see that there are two products and each product each is 1 mole. So, after equilibrium both the products will have P pressure.
$N{{H}_{4}}HS(s)\rightleftharpoons \underset{P}{\mathop N{{H}_{3}}}\,(g)+\underset{P}{\mathop {{H}_{2}}S}\,(g)$
(a)- So, we are given the total pressure as 600 torrs. There are two products, therefore, the value of pressure of each component is 300 torr. The equilibrium constant can be calculated by taking the ratio of the product of the pressure of the products by the product of the pressure of the reactants and the values are only taken for the gases. The formula of the equilibrium constant will be:
${{K}_{p}}={{p}_{N{{H}_{3}}}}\text{ x }{{p}_{{{H}_{2}}S}}$
Putting the value, we get:
${{K}_{p}}=300\text{ x 300 = 9 x 1}{{\text{0}}^{4}}$
So, the equilibrium constant will be $9\text{ x 1}{{\text{0}}^{4}}$

(b)- We are given the pressure of $N{{H}_{3}}$ is 750 torr, and the equilibrium constant is $9\text{ x 1}{{\text{0}}^{4}}$, so we can calculate the pressure of ${{H}_{2}}S$ as:
${{K}_{p}}=9\text{ x 1}{{\text{0}}^{4}}={{p}_{N{{H}_{3}}}}\text{ x }{{\text{p}}_{{{H}_{2}}S}}$
${{K}_{p}}=9\text{ x 1}{{\text{0}}^{4}}=750\text{ x }{{\text{p}}_{{{H}_{2}}S}}$
${{\text{p}}_{{{H}_{2}}S}}=120\text{ torr}$
Now, we can calculate the total pressure as:
${{P}_{total}}=750+120=870$
Therefore, the total pressure is 870 torr.

Note: For finding the equilibrium constant in pressure or concentration then the physical state of the compound should be mentioned, because only the value of gases is taken in the formula, not solid, liquid, or aqueous.