Question

For the reaction, ${\text{A}} + {\text{B}} \rightleftharpoons {\text{C}} + {\text{D}},{{\text{K}}_c} = 9.$ If A and B are taken in equal amounts, then amount of C at equilibrium is :-
(A) 1
(B) 0.75
(C) 0.25
(D) None of these

Answer 1

Chemical equilibrium is the condition of a chemical reaction in which all the reactants and products are present in quantities that have no further propensity to change over time, resulting in no detectable change in the system's properties.

Complete answer:
When a chemical compound in the solid state is in chemical equilibrium with a solution of that compound, it is called solubility equilibrium. The solid can dissolve in its entirety, through dissociation, or through chemical reaction with another solution component, such as acid or alkali. A temperature-dependent solubility substance, which acts as an equilibrium constant, characterises each solubility equilibrium. Solubility equilibria are essential in a variety of situations, including pharmaceuticals, the climate, and many others.
When the forward reaction and the reverse reaction each proceed at the same time, this condition occurs. The forward and backward reaction rates are usually not negligible, but they are roughly equivalent. As a result, there are no net improvements in the reactant and chemical concentrations. Dynamic equilibrium is the term for such a condition.
$A + B \to C + D$

| A| B| C| D
---|---|---|---|---
Initial| 1| 1| -| -
At equilibrium| 1 - x| 1 – x | x| x
$\dfrac{n}{v}$ | $\dfrac{{1 - x}}{1}$ | $\dfrac{{1 - x}}{1}$ | $\dfrac{x}{1}$ | $\dfrac{x}{1}$

Using Equilibrium Constant
${K_C} = \dfrac{{[C][D]}}{{[A][B]}}$
Given ${K_C} = 9$
\begin{array}{*{20}{l}} {{K_C} = \dfrac{{x \times x}}{{(1 - x) \times (1 - x)}} = {{\left( {\dfrac{x}{{1 - x}}} \right)}^2}} \\\ {9 = {{\left( {\dfrac{x}{{1 - x}}} \right)}^2}} \\\ {\dfrac{x}{{1 - x}} = |3|} \\\ {x = 0.75} \end{array}
When a chemical compound in the solid state is in chemical equilibrium with a solution containing the compound, it is called a solubility equilibrium. This kind of equilibrium is a complex equilibrium in which certain individual molecules move between the solid and solution phases at the same time, resulting in similar rates of dissolution and precipitation.

Note:
The solution is considered to be saturated as it has reached equilibrium. The solubility of a solute is its concentration in a saturated solution. Temperature affects solubility. A supersaturated solution is one that has a greater concentration of solute than its solubility.