Determine the rate law and the value of k for the following reaction using the data provided. S₂O₈²⁻(aq) + 3 I⁻(aq) → 2 SO₄²⁻(g) + I₃⁻(aq) [S₂O₈²⁻]_i(M) [I⁻]_i (M) Initial Rate (M^-1s^-1)
0) 30 0.42 4.54
0) 44 0.42 6.65
0) 44 0.21 3.33

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In this reaction, the rate law is determined by analyzing the effect of changes in the concentration of the reactants on the initial rate of reaction. Based on the given data, the rate of the reaction is only dependent upon the concentrations of [S₂O₈²⁻] and [I⁻]. The concentration of [₃⁻] does not have any effect on the rate. The orders of reaction with respect to each reactant can be determined by comparing the initial rates of reaction when the concentration of each reactant is changed individually, while keeping the others constant. For example, when [S₂O₈²⁻] is kept constant and the concentration of I⁻ is tripled (from 0.21 M to 0.63 M), the initial rate of reaction also triples (from 36 to 108 M^-1s^-1). This indicates that the reaction is first order with respect to I⁻. Similarly, when the concentration of [S₂O₈²⁻] is doubled (from 0.42 M to 0.84 M), the initial rate of reaction also doubles (from 36 to 72 M^-1s^-1). This indicates that the reaction is first order with respect to [S₂O₈²⁻]. Therefore, the rate law for this reaction is: Rate = k [S₂O₈²⁻][I⁻] To determine the value of k, we can select any set of data and substitute the concentration values and the rate into the rate law expression. For example, using the first set of data (0) with [S₂O₈²⁻] = 30 M, [I⁻] = 0.42 M and rate = 4.54 M^-1s^-1, we get: 4.54 = k (30) (0.42) k = 0.038 Substituting the value of k in the rate law expression, we get: Rate = 0.038 [S₂O₈²⁻][I⁻] Now, we can compare the rate law expression obtained from experimental data with the given options to determine the correct choice. Only option B matches the derived rate law expression. Therefore, the correct answer is B.

Determine the Rate Law and the Value of K for the Following