In the chemical equation provided:
\[ 2K + 2H_2O \rightarrow 2KOH + \text{some amount of } H_2 \]
On the reactant side, the \(2H_2O\) contains 4 hydrogen atoms (since each water molecule \(H_2O\) has 2 hydrogen atoms, and there are 2 water molecules: \(2 \times 2 = 4\)).
Now, let's analyze the product side:
- The \(2KOH\) contains 2 hydrogen atoms (since each potassium hydroxide \(KOH\) has 1 hydrogen atom, and there are 2 \(KOH\): \(2 \times 1 = 2\)).
- The hydrogen gas \(H_2\) contributes an additional 2 hydrogen atoms.
So to balance the hydrogen atoms on the product side:
- From \(2KOH\) we have 2 hydrogen atoms.
- From \(H_2\) we have 2 hydrogen atoms.
Adding these together gives us: \[ 2 \text{ (from } KOH\text{)} + 2 \text{ (from } H_2\text{)} = 4 \text{ hydrogen atoms on the product side.} \]
Thus, the total number of hydrogen atoms on the product side must also be 4.