Balance the following equations using the method outlined in Section 3.7 : (a) \(\mathrm{C}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}\) (b) \(\mathrm{CO}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}\) (c) \(\mathrm{H}_{2}+\mathrm{Br}_{2} \longrightarrow \mathrm{HBr}\) (d) \(\mathrm{K}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{KOH}+\mathrm{H}_{2}\) (e) \(\mathrm{Mg}+\mathrm{O}_{2} \longrightarrow \mathrm{MgO}\) (f) \(\mathrm{O}_{3} \longrightarrow \mathrm{O}_{2}\) (g) \(\mathrm{H}_{2} \mathrm{O}_{2} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}\) (h) \(\mathrm{N}_{2}+\mathrm{H}_{2} \longrightarrow \mathrm{NH}_{3}\) (i) \(\mathrm{Zn}+\mathrm{AgCl} \longrightarrow \mathrm{ZnCl}_{2}+\mathrm{Ag}\) (j) \(\mathrm{S}_{8}+\mathrm{O}_{2} \longrightarrow \mathrm{SO}_{2}\) (k) \(\mathrm{NaOH}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}+\mathrm{H}_{2} \mathrm{O}\) (l) \(\mathrm{Cl}_{2}+\mathrm{NaI} \longrightarrow \mathrm{NaCl}+\mathrm{I}_{2}\) \((\mathrm{m}) \mathrm{KOH}+\mathrm{H}_{3} \mathrm{PO}_{4} \longrightarrow \mathrm{K}_{3} \mathrm{PO}_{4}+\mathrm{H}_{2} \mathrm{O}\) (n) \(\mathrm{CH}_{4}+\mathrm{Br}_{2} \longrightarrow \mathrm{CBr}_{4}+\mathrm{HBr}\)

It's important to notice that each equation has different elements in the reactants and products, however, the basic principle of balancing remains the same - ensuring that the count of each element on both sides of the equation is equal.

Let's balance each equation individually, keeping in mind that we can only change the coefficients in front of the chemical compounds, not the subscripts within them. (a) \(2\mathrm{C}+ \mathrm{O}_{2} \longrightarrow 2\mathrm{CO}\) (b) \(\mathrm{CO}+ \frac{1}{2}\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}\) (c) \(\mathrm{H}_{2}+ \mathrm{Br}_{2} \longrightarrow 2\mathrm{HBr}\) (d) \(2\mathrm{K}+2\mathrm{H}_{2} \mathrm{O} \longrightarrow 2\mathrm{KOH}+ \mathrm{H}_{2}\) (e) \(2\mathrm{Mg}+ \mathrm{O}_{2} \longrightarrow 2\mathrm{MgO}\) (f) \(2\mathrm{O}_{3} \longrightarrow 3\mathrm{O}_{2}\) (g) \(2\mathrm{H}_{2} \mathrm{O}_{2} \longrightarrow 2\mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}\) (h) \(\mathrm{N}_{2}+3\mathrm{H}_{2} \longrightarrow 2\mathrm{NH}_{3}\) (i) \(\mathrm{Zn}+2\mathrm{AgCl} \longrightarrow \mathrm{ZnCl}_{2}+2\mathrm{Ag}\) (j) \(S_{8}+8\mathrm{O}_{2} \longrightarrow 8\mathrm{SO}_{2}\) (k) \(2\mathrm{NaOH}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}+2\mathrm{H}_{2} \mathrm{O}\) (l) \(\mathrm{Cl}_{2}+2\mathrm{NaI} \longrightarrow 2\mathrm{NaCl}+\mathrm{I}_{2}\) (m) \(\mathrm{KOH}+ \frac{1}{3}\mathrm{H}_{3} \mathrm{PO}_{4} \longrightarrow \frac{1}{3}\mathrm{K}_{3} \mathrm{PO}_{4}+\mathrm{H}_{2} \mathrm{O}\) (n) \(\mathrm{CH}_{4}+\mathrm{Br}_{2} \longrightarrow \mathrm{CBr}_{4}+4\mathrm{HBr}\)