Questions: Balance the chemical equation below using the smallest possible whole number stoichiometric coefficients. H₂(g) + P₄(s) → PH₃(g)

Transcript text: Balance the chemical equation below using the smallest possible whole number stoichiometric coefficients. \[ \mathrm{H}_{2}(g)+\mathrm{P}_{4}(s) \rightarrow \mathrm{PH}_{3}(g) \]

Solution

Solution Steps

Step 1: Write the Unbalanced Equation

The given chemical equation is: \[ \mathrm{H}_{2}(g) + \mathrm{P}_{4}(s) \rightarrow \mathrm{PH}_{3}(g) \]

Step 2: Identify the Atoms to Balance

We need to balance the number of hydrogen (H) and phosphorus (P) atoms on both sides of the equation.

Step 3: Balance Phosphorus Atoms

There are 4 phosphorus atoms in \(\mathrm{P}_{4}\) on the reactant side. To balance the phosphorus atoms, we need 4 phosphorus atoms on the product side. Since each \(\mathrm{PH}_{3}\) molecule contains 1 phosphorus atom, we need 4 \(\mathrm{PH}_{3}\) molecules: \[ \mathrm{H}_{2}(g) + \mathrm{P}_{4}(s) \rightarrow 4\mathrm{PH}_{3}(g) \]

Step 4: Balance Hydrogen Atoms

Now, we have 4 \(\mathrm{PH}_{3}\) molecules on the product side, which means we have \(4 \times 3 = 12\) hydrogen atoms. To balance the hydrogen atoms, we need 6 \(\mathrm{H}_{2}\) molecules on the reactant side (since each \(\mathrm{H}_{2}\) molecule contains 2 hydrogen atoms): \[ 6\mathrm{H}_{2}(g) + \mathrm{P}_{4}(s) \rightarrow 4\mathrm{PH}_{3}(g) \]