Electrolysis of water is a decomposition reaction. The sum of mole ratio of hydrogen and oxygen gases liberated during electrolysis of water is

Explanation

To solve the problem regarding the electrolysis of water and the sum of the mole ratio of hydrogen and oxygen gases liberated, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Electrolysis Reaction**:
The electrolysis of water can be represented by the following chemical equation:
\[ 2 \text{H}_2\text{O} \rightarrow 2 \text{H}_2 + \text{O}_2 \]
This indicates that 2 moles of water decompose to produce 2 moles of hydrogen gas and 1 mole of oxygen gas.

2. **Identify the Mole Ratio**:
From the balanced equation, we can see the mole ratio of hydrogen (H₂) to oxygen (O₂):
- Moles of hydrogen (H₂) = 2
- Moles of oxygen (O₂) = 1

3. **Calculate the Sum of the Mole Ratio**:
Now, we need to find the sum of the mole ratios:
\[ \text{Sum of mole ratio} = \text{Moles of H}_2 + \text{Moles of O}_2 = 2 + 1 \]

4. **Final Calculation**:
\[ \text{Sum of mole ratio} = 3 \]

### Conclusion:
The sum of the mole ratio of hydrogen and oxygen gases liberated during the electrolysis of water is **3**.