Question

Connie and Dewayne know that solid potassium reacts very strongly with water, producing a chemical called potassium hydroxide along with hydrogen gas. They know the chemical equation looks like this.
2K + 2H 2 O → 2KOH + some amount of H 2

There are 4 atoms of hydrogen shown on the reactant side. How many total atoms of hydrogen must be on the product side?

Answer 1

In the given chemical equation:

\[ 2K + 2H_2O → 2KOH + \text{some amount of } H_2 \]

Let's break down the number of hydrogen atoms.

On the reactant side, the water molecules (H₂O) contribute hydrogen atoms as follows:
- Each water molecule (H₂O) has 2 hydrogen atoms.
- Since there are 2 water molecules, the total number of hydrogen atoms from water is:
\[
2 \text{ (H₂O)} \times 2 \text{ (H per H₂O)} = 4 \text{ hydrogen atoms}
\]

Now, looking at the product side, we need to account for:

1. The potassium hydroxide (KOH):
- Each KOH has 1 hydrogen atom.
- Since there are 2 KOH produced, the total contribution from KOH is:
\[
2 \text{ (KOH)} \times 1 \text{ (H per KOH)} = 2 \text{ hydrogen atoms}
\]

2. The hydrogen gas (H₂):
- Hydrogen gas (H₂) has 2 hydrogen atoms per molecule.
- The amount of hydrogen gas produced must make up the remaining hydrogen atoms needed to balance the equation.

We can set up the equation to find how many H₂ molecules we need:
- Total hydrogen on the product side must equal the total hydrogen on the reactant side.
- We have the total on the reactant side as 4 hydrogen atoms and we accounted for 2 hydrogen atoms from the KOH:
\[
4 \text{ (reactants)} = 2 \text{ (from KOH)} + n \times 2 \text{ (from H₂)}
\]
where \( n \) is the number of H₂ molecules produced.

Solving for \( n \):
\[
4 = 2 + n \times 2
\]
\[
4 - 2 = n \times 2
\]
\[
2 = n \times 2
\]
\[
n = 1
\]

This means there is 1 molecule of H₂ produced. Now we calculate the total hydrogen atoms on the product side:
- From KOH: 2 hydrogen atoms
- From H₂: \( 1 \times 2 = 2 \) hydrogen atoms

Total hydrogen on the product side:
\[
2 \text{ (from KOH)} + 2 \text{ (from H₂)} = 4 \text{ hydrogen atoms}
\]

Thus, the total number of hydrogen atoms on both sides confirms that they balance at **4 hydrogen atoms**.

**Final answer:** 4 total atoms of hydrogen must be on the product side.