Question

balance the arsenous acid half-reaction.
h₃aso₃ → h₃aso₄
how many electrons are required to
balance the half-reaction?

Explanation:

Step1: Balance O and H (in acidic/basic, here acidic-like as H present)

First, balance O by adding \( H_2O \). On left: 3 O, right: 4 O. So add 1 \( H_2O \) to left? Wait, no: \( H_3AsO_3 + H_2O
ightarrow H_3AsO_4 \). Now O: 3 + 1 = 4 (left), 4 (right). Now balance H: Left has \( 3H + 2H = 5H \), right has 3H. So add \( 2H^+ \) to right: \( H_3AsO_3 + H_2O
ightarrow H_3AsO_4 + 2H^+ \).

Step2: Balance charge (oxidation state change)

Find oxidation state of As: In \( H_3AsO_3 \), H is +1, O is -2. Let As be x: \( 3(+1) + x + 3(-2) = 0
ightarrow 3 + x -6 = 0
ightarrow x = +3 \). In \( H_3AsO_4 \): \( 3(+1) + x + 4(-2) = 0
ightarrow 3 + x -8 = 0
ightarrow x = +5 \). So As goes from +3 to +5, losing 2 electrons (oxidation, so electrons are products? Wait, half-reaction: oxidation (losing e⁻) or reduction? Here, As is oxidized (oxidation state increases), so the half-reaction is oxidation: \( H_3AsO_3
ightarrow H_3AsO_4 + 2e^- \) (after balancing charge: left charge: 0 (molecule), right: \( H_3AsO_4 \) is neutral, \( 2H^+ \) is +2, so total right charge is +2. So to balance charge, we need to add 2 electrons to right (since oxidation loses e⁻, which are negative, so \( 0 = +2 - 2 \) (charge from electrons: each e⁻ is -1, 2e⁻ is -2; +2 (from \( 2H^+ \)) + (-2) (from 2e⁻) = 0, same as left). Wait, let's redo charge balance:

After balancing O and H: \( H_3AsO_3 + H_2O
ightarrow H_3AsO_4 + 2H^+ \)

Left charge: 0 (molecule)
Right charge: \( H_3AsO_4 \) (0) + \( 2H^+ \) (+2) = +2

So to balance charge, we need to add 2 electrons (each -1) to the right: \( H_3AsO_3 + H_2O
ightarrow H_3AsO_4 + 2H^+ + 2e^- \)

Now check oxidation state: As goes from +3 to +5, change of +2, so 2 electrons lost (since oxidation is loss of e⁻), which matches the 2 electrons on the product side. So the number of electrons required to balance (i.e., the number of electrons transferred, which is 2) is 2.

Answer:

2