Write a balanced half-reaction for the reduction of liquid water to gaseous hydrogen in basic aqueous solution. Be sure to add physical state symbols where appropriate.

2 H₂O(l) + 2 e⁻ ⇒ H₂(g) + 2 OH⁻(aq)

Explanation:

Let's consider the unbalanced half-reaction for the reduction of liquid water to gaseous hydrogen in basic aqueous solution.

H₂O(l) ⇒ H₂(g)

First, we will perform the mass balance. We will balance oxygen atoms by multiplying H₂O by 2 and adding 2 OH⁻ to the right side.

2 H₂O(l) ⇒ H₂(g) + 2 OH⁻(aq)

Then, we perform the charge balance by adding 2 electrons to the left side.

2 H₂O(l) + 2 e⁻ ⇒ H₂(g) + 2 OH⁻(aq)

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