Write the equilibrium constant expression for these reactions: (a) \(2 \mathrm{NO}_{2}(g)+7 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\) (b) \(\mathrm{H}_{2} \mathrm{CO}_{3}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{HCO}_{3}^{-}(a q)\) (c) \(2 \mathrm{COF}_{2}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{CF}_{4}(g)\)

In every chemical reaction, there's a point where the rate of the forward reaction equals the rate of the backward reaction. This state is called chemical equilibrium. At equilibrium, the concentrations of reactants and products remain constant over time.
It’s important to note that these concentrations are not necessarily equal; they simply don’t change anymore.
This dynamic balance is crucial in understanding how and why reactions behave as they do. It's also essential for calculating the equilibrium constant, a vital concept in chemistry.

The equilibrium constant, denoted as K, is a measure of the ratio of the concentrations of products to reactants at chemical equilibrium.
For any given chemical reaction at equilibrium, this ratio is constant and depends only on the temperature.
To calculate the equilibrium constant, we use the balanced chemical equation. The general form for a reaction \( aA + bB \rightleftharpoons cC + dD \) is:
\( K = \ \frac{[C]^c [D]^d} { [A]^a [B]^b} \)
Here, [A], [B], [C], and [D] are molar concentrations of the chemicals, and a, b, c, and d are their coefficients from the balanced equation. This expression allows us to predict the direction of the reaction and the position of equilibrium.

Balancing a chemical equation is the process of ensuring the number of each type of atom on the reactants side is equal to the number on the products side.
This is crucial because it reflects the law of conservation of mass, stating mass cannot be created or destroyed in a chemical reaction.
For instance, in the reaction \( 2 \mathrm{COF}_{2}(g) \rightleftharpoons \mathrm{CO}_{2}(g) + \mathrm{CF}_{4}(g) \), the equation is balanced with 2 COF₂ on the reactant side and 1 CO₂ and 1 CF₄ on the product side, ensuring the number of each atom (C, O, F) is the same on both sides.
Balancing is fundamental for writing correct equilibrium constant expressions.

In equilibrium constant expressions, we use concentration ratios, also called activities, of reactants and products.
These ratios are represented by the molarity (M) of each substance involved. For gases, partial pressures can be used instead.
For example, in the reaction \( \mathrm{H}_{2}CO_{3}(aq) \rightleftharpoons \mathrm{H}^{+}(aq) + \mathrm{HCO}_{3}^{-}(aq) \), the equilibrium constant expression is:
\( K = \[\frac{[\mathrm{H}^{+}][\mathrm{HCO}_{3}^{-}]}{[\mathrm{H}_{2}\mathrm{CO}_{3}]}\] \)
This shows the relationship between the product of the concentrations of H⁺ and HCO₃^- to the concentration of H₂CO₃.
Understanding these ratios helps predict how changes in concentrations affect the position of equilibrium.