Explain the calculation of equilibrium concentrations given the value of the equilibrium constant.

(N/A) To calculate equilibrium concentrations when initial concentrations are known and the equilibrium constant $(K_c)$ is provided,follow these steps:
Step-$1$: Write the balanced chemical equation for the reaction.
Step-$2$: Create an $ICE$ (Initial,Change,Equilibrium) table under the balanced equation for each substance involved.
$(i)$ List the initial concentration.
$(ii)$ Define the change in concentration as $x$ (in $mol/L$) based on the stoichiometry of the reaction.
$(iii)$ Express the equilibrium concentration as the sum of the initial concentration and the change.
Step-$3$: Substitute these equilibrium concentrations into the equilibrium constant expression $(K_c)$ and solve the resulting algebraic equation for $x$. If a quadratic equation is obtained,select the root that is physically meaningful (i.e.,concentrations must be positive).
Step-$4$: Use the calculated value of $x$ to determine the actual equilibrium concentrations of all reactants and products.
Step-$5$: Verify the results by substituting the calculated equilibrium concentrations back into the $K_c$ expression to ensure they yield the given constant.