The data below were determined for the reaction shown below. s2o82 - + 3i - (aq) → 2so42 - + i3 - expt. # [s2o82-] (m) [i - ] (m) initial rate 1 0.038 0.060 1.4 * 10 - 5 m/s 2 0.076 0.060 2.8 * 10 - 5 m/s 3 0.076 0.030 1.4 * 10 - 5 m/s the rate law for this reaction must be:

The rate law for this reaction must be = k[S₂O₈⁻][I⁻].

Explanation:

To solve this problem, I will rewrite the data for clarification:

Exp. [S₂O₈⁻], M [I⁻], M initial rate

1 0.038 0.060 1.4 x 10⁻⁵ M/s

2 0.076 0.060 2.8 x 10⁻⁵ M/s

3 0.076 0.030 1.4 x 10⁻⁵ M/s

The initial rate method to determine the order of the reaction is one of the most accurate methods to determine the order. The rate law for this reaction = k[S₂O₈⁻]ᵃ[I⁻]ᵇ,

where, k is the rate constant of the reaction,

a is the order of the reaction with respect to [S₂O₈⁻].

b is the order of the reaction with respect to [I⁻].

From Exp 1 and 2,

The concentration of [S₂O₈⁻] changes while [I⁻] is constant, the initial rate of the reaction changes. So, the rate of the reaction depends on [S₂O₈⁻].

(initial rate) ₁ = k[S₂O₈⁻]₁ᵃ[I⁻]₁ᵇ (1)

(initial rate) ₂ = k[S₂O₈⁻]₂ᵃ[I⁻]₂ᵇ (2)

By dividing (1) over (2)

∴ (initial rate) ₁ / (initial rate) ₂ = [k[S₂O₈⁻]₁ᵃ[I⁻]₁ᵇ] / [k[S₂O₈⁻]₂ᵃ[I⁻]₂ᵇ]

∴ (1.4 x 10⁻⁵ M/s) / (2.8 x 10⁻⁵ M/s) = [k[0.038]ᵃ[0.06]ᵇ] / [k[0.076]ᵃ[0.06]ᵇ]

∴ (0.5) = [0.038]ᵃ / [0.076]ᵃ = [0.5]ᵃ

Taking log for the both sides,

log (0.5) = a log (0.5)

∴ a = 1.

∴ the reaction is first order reaction with respect to [S₂O₈⁻].

From Exp. 2 and 3,

The concentration of [S₂O₈⁻] is constant while [I⁻] changes, the initial rate of the reaction changes. So, the rate of the reaction depends on [I⁻].

(initial rate) ₂ = k[S₂O₈⁻]₂ᵃ[I⁻]₂ᵇ (3)

(initial rate) ₃ = k[S₂O₈⁻]₃ᵃ[I⁻]₃ᵇ (4)

By dividing (3) over (4)

∴ (initial rate) ₂ / (initial rate) ₃ = [k[S₂O₈⁻]₂ᵃ[I⁻]₂ᵇ] / [k[S₂O₈⁻]₃ᵃ[I⁻]₃ᵇ]

∴ (2.8 x 10⁻⁵ M/s) / (1.4 x 10⁻⁵ M/s) = [k[0.076]ᵃ[0.06]ᵇ] / [k[0.076]ᵃ[0.03]ᵇ]

∴ (2.0) = [0.06]ᵇ / [0.03]ᵇ = [2.0]ᵇ

Taking log for the both sides,

log (2.0) = a log (2.0)

∴ b = 1.

∴ the reaction is first order reaction with respect to [I⁻].

∴ the rate law for this reaction must be = k[S₂O₈⁻][I⁻].