Balance the following equations: $$ \begin{array}{l}{\text { (a) } \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)} \\ {\text { (b) } \mathrm{N}_{2} \mathrm{O}_{5}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{HNO}_{3}(a q)} \\ {\text { (c) } \mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(l)+\mathrm{HCl}(g)} \\ {\text { (d) } \mathrm{Zn}(\mathrm{OH})_{2}(s)+\mathrm{HNO}_{3}(a q) \longrightarrow \mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l)}\end{array} $$

1. Check the number of atoms for each element on both sides of the equation: 1 C atom, 2 O atoms on the left, and 1 C atom, 2 O atoms on the right. 2. Since the number of atoms for each element is already equal on both sides, this equation is already balanced: \(\mathrm{CO}(g) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)\)

1. Check the number of atoms for each element on both sides of the equation: 2 N atoms, 5 O atoms, and 2 H atoms on the left, and 1 N atom, 3 O atoms, and 1 H atom on the right. 2. Balance N atoms by adding a coefficient of 2 to HNO3(aq): \(\mathrm{N}_{2}\mathrm{O}_{5}(g)+\mathrm{H}_{2}\mathrm{O}(l) \longrightarrow 2\mathrm{HNO}_{3}(aq)\) 3. Now we have: 2 N atoms, 5 O atoms, and 2 H atoms on the left, and 2 N atoms, 6 O atoms, and 2 H atoms on the right. 4. Balance the O atoms by adding a coefficient of 2 to H2O(l): \(\mathrm{N}_{2}\mathrm{O}_{5}(g)+2\mathrm{H}_{2}\mathrm{O}(l) \longrightarrow 2\mathrm{HNO}_{3}(aq)\)

1. Check the number of atoms for each element on both sides of the equation: 1 C atom, 4 H atoms, and 2 Cl atoms on the left, and 1 C atom, 4 Cl atoms, and 1 H atom on the right. 2. Balance H atoms by adding a coefficient of 4 to HCl(g): \(\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(l)+4\mathrm{HCl}(g)\) 3. Now we have: 1 C atom, 4 H atoms, and 2 Cl atoms on the left, and 1 C atom, 4 H atoms, and 8 Cl atoms on the right. 4. Balance the Cl atoms by adding a coefficient of 4 to Cl2(g): \(\mathrm{CH}_{4}(g)+4\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(l)+4\mathrm{HCl}(g)\)

1. Check the number of atoms for each element on both sides of the equation: 1 Zn atom, 2 O atoms, 2 H atoms, 1 N atom on the left, and 1 Zn atom, 6 O atoms, 2 H atoms, 2 N atoms on the right. 2. Balance N atoms by adding a coefficient of 2 to HNO3(aq): \(\mathrm{Zn}(\mathrm{OH})_{2}(s)+2\mathrm{HNO}_{3}(a q) \longrightarrow \mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{H}_{2}\mathrm{O}(l)\) 3. Now we have: 1 Zn atom, 2 O atoms, 2 H atoms, 2 N atoms on the left, and 1 Zn atom, 6 O atoms, 2 H atoms, and 2 N atoms on the right. 4. Balance the O atoms by adding a coefficient of 2 to H2O(l): \(\mathrm{Zn}(\mathrm{OH})_{2}(s)+2\mathrm{HNO}_{3}(a q) \longrightarrow \mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}(a q)+2\mathrm{H}_{2}\mathrm{O}(l)\)