Q. \[ 2\mathrm{H}_2 + \mathrm{O}_2 \]

Step 1. Identify reactants and product. The given reactants are \(2\mathrm{H}_2\) and \(\mathrm{O}_2\). When hydrogen reacts with oxygen it forms water, with formula \(\mathrm{H}_2\mathrm{O}\). The unbalanced skeletal equation is \(2\mathrm{H}_2 + \mathrm{O}_2 = \mathrm{H}_2\mathrm{O}\).

Step 2. Count atoms on each side. Count hydrogen atoms and oxygen atoms separately.

Hydrogen atoms in the reactants: each \(\mathrm{H}_2\) molecule contains 2 hydrogen atoms. There are 2 molecules of \(\mathrm{H}_2\) given, so the total hydrogen atoms on the reactant side is \(2 \times 2 = 4\).

Oxygen atoms in the reactants: the \(\mathrm{O}_2\) molecule contains 2 oxygen atoms, so the reactant side has \(2\) oxygen atoms.

Hydrogen atoms in the product as written: each \(\mathrm{H}_2\mathrm{O}\) molecule contains 2 hydrogen atoms, so with coefficient \(1\) the product side has \(2\) hydrogen atoms. Oxygen atoms in the product as written: each \(\mathrm{H}_2\mathrm{O}\) molecule contains 1 oxygen atom, so with coefficient \(1\) the product side has \(1\) oxygen atom.

Step 3. Compare counts and adjust coefficients to balance. Reactant hydrogen count is \(4\) while product hydrogen count is \(2\). To balance hydrogen, place coefficient \(2\) in front of \(\mathrm{H}_2\mathrm{O}\). That gives product hydrogen atoms \(2 \times 2 = 4\), matching the reactants. With that coefficient the product oxygen atoms become \(2 \times 1 = 2\), which matches the \(2\) oxygen atoms from \(\mathrm{O}_2\) on the reactant side.

Step 4. Write the balanced equation using the smallest whole number coefficients. The balanced equation is

\[ 2\mathrm{H}_2 + \mathrm{O}_2 = 2\mathrm{H}_2\mathrm{O} \]

Step 5. Verify final atom counts. Reactant side: hydrogen \(2 \times 2 = 4\), oxygen \(2\). Product side: hydrogen \(2 \times 2 = 4\), oxygen \(2 \times 1 = 2\). All atoms balance. The coefficients \(2,1,2\) are the smallest whole numbers that balance the equation.