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