Use each of the following reaction quotients to write the balanced equation:

(a) $\mathbf{Q}\mathbf{=}\frac{{\left[{\mathbf{CO}}_2\right]}^2{\left[{\mathbf{H}}_2\mathbf{O}\right]}^2}{\left[{\mathbf{C}}_2{\mathbf{H}}_4\right]{\left[{\mathbf{O}}_2\right]}^3}$

(b)$\mathbf{Q}\mathbf{=}\frac{{\left[{\mathbf{NH}}_3\right]}^4{\left[{\mathbf{O}}_2\right]}^7}{{\left[{\mathbf{NO}}_2\right]}^4{\left[{\mathbf{H}}_2\mathbf{O}\right]}^6}$

At a given point in time, a measure of the activity or concentrations of the chemical species involved in a chemical reaction.

a)
In this problem, we are tasked to write the balanced equation of a reaction based on its given reaction quotient.

$Q=\frac{{\left[{\text{CO}}_2\right]}^2{\left[{\text{H}}_2\text{O}\right]}^2}{\left[{\text{C}}_2{\text{H}}_4\right]{\left[{\text{O}}_2\right]}^3}$

We know that reaction quotient $Q=\frac{\left[\text{products}\right]}{\left[\text{reactants}\right]}$.

Each reaction component in the reaction quotient expression is also raised to their coefficient.

Therefore, the equation is written below.

${\text{C}}_2{\text{H}}_4+3{\text{O}}_2\rightleftharpoons 2{\text{CO}}_2+2{\text{H}}_2\text{O}$

b)
In this problem, we are tasked to write the balanced equation of a reaction based on its given reaction quotient.

$Q=\frac{{\left[{\text{NH}}_3\right]}^4{\left[{\text{O}}_2\right]}^7}{{\left[{\text{NO}}_2\right]}^4{\left[{\text{H}}_2\text{O}\right]}^6}$

We know that reaction quotient$Q=\frac{\left[\text{products}\right]}{\left[\text{reactants}\right]}$

Each reaction component in the reaction quotient expression is also raised to their coefficient.

Therefore, the equation is written below.

$4{\text{NO}}_2+6{\text{H}}_2\text{O}\rightleftharpoons 4{\text{NH}}_3+7{\text{O}}_2$