Answer:
k[S₂O₈⁻][I⁻].
Step-by-step 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⁻].