The iodide ion reacts with hypochlorite ion (the active ingredient in chlorine bleaches) in the following way: $\mathrm{OCl}^{-}+\mathrm{I}^{-} \longrightarrow \mathrm{OI}^{-}+\mathrm{Cl}^{-} .$ This rapid reaction gives the following rate data: $$ \begin{array}{ccc} \hline\left[\mathrm{OCI}^{-}\right](M) & {\left[\mathrm{I}^{-}\right](M)} & \text { Initial Rate }(\mathrm{M} / \mathrm{s}) \\ \hline 1.5 \times 10^{-3} & 1.5 \times 10^{-3} & 1.36 \times 10^{-4} \\ 3.0 \times 10^{-3} & 1.5 \times 10^{-3} & 2.72 \times 10^{-4} \\ 1.5 \times 10^{-3} & 3.0 \times 10^{-3} & 2.72 \times 10^{-4} \\ \hline \end{array} $$ (a) Write the rate law for this reaction. (b) Calculate the rate constant with proper units. (c) Calculate the rate when $\left[\mathrm{OCl}^{-}\right]=2.0 \times 10^{-3} \mathrm{M}\( and \)\left[\mathrm{I}^{-}\right]=5.0 \times 10^{-4} \mathrm{M}$

To determine the rate law for the reaction, we want to find the orders of the reactants (OCl⁻ and I⁻). We can do this by examining how the initial concentrations affect the initial rate in the provided data. The rate law has the general form: Rate = k[OCl⁻]^m[I⁻]^n Where k is the rate constant, m and n are the orders of OCl⁻ and I⁻ respectively. Consider the two sets of initial concentrations: 1. [OCl⁻] = 1.5 x 10⁻³ M, [I⁻] = 1.5 x 10⁻³ M, Initial rate = 1.36 x 10⁻⁴ M/s 2. [OCl⁻] = 3.0 x 10⁻³ M, [I⁻] = 1.5 x 10⁻³ M, Initial rate = 2.72 x 10⁻⁴ M/s From these two sets of data, we can find the order m as follows: (2.72 x 10⁻⁴) / (1.36 x 10⁻⁴) = ([3.0 x 10⁻³]^m[I⁻]^n) / ([1.5 x 10⁻³]^m[I⁻]^n) 2 = (3.0 / 1.5)^m |_divide both sides by n as it cancels out_| 2 = 2^m Therefore, m = 1 Now, we look for the order n. Compare two other sets of initial concentrations: 1. [OCl⁻] = 1.5 x 10⁻³ M, [I⁻] = 1.5 x 10⁻³ M, Initial rate = 1.36 x 10⁻⁴ M/s 3. [OCl⁻] = 1.5 x 10⁻³ M, [I⁻] = 3.0 x 10⁻³ M, Initial rate = 2.72 x 10⁻⁴ M/s We find the order n as follows: (2.72 x 10⁻⁴) / (1.36 x 10⁻⁴) = ([OCl⁻]^m[3.0 x 10⁻³]^n) / ([OCl⁻]^m[1.5 x 10⁻³]^n) 2 = (3.0 / 1.5)^n |_divide both sides by m as it cancels out_| 2 = 2^n Therefore, n = 1 Now that we have determined the orders for both reactants, the rate law is: Rate = k[OCl⁻][I⁻]

To find the rate constant (k), we can use any set of initial concentrations and their corresponding initial rate from the given data. Let's use the first set: 1.36 x 10⁻⁴ M/s = k(1.5 x 10⁻³ M)(1.5 x 10⁻³ M) k = ((1.36 x 10⁻⁴) M/s) / ((1.5 x 10⁻³)^2 M²) k ≈ 6.08 x 10² M⁻¹s⁻¹ Therefore, the rate constant (k) is approximately 6.08 x 10² M⁻¹s⁻¹.

Now that we have the rate law and the rate constant, we can calculate the reaction rate for the given concentrations: [OCl⁻] = 2.0 x 10⁻³ M [I⁻] = 5.0 x 10⁻⁴ M Rate = k[OCl⁻][I⁻] Rate = (6.08 x 10² M⁻¹s⁻¹)(2.0 x 10⁻³ M)(5.0 x 10⁻⁴ M) Rate ≈ 6.08 x 10⁻⁵ M/s Therefore, the reaction rate when [OCl⁻] = 2.0 x 10⁻³ M and [I⁻] = 5.0 x 10⁻⁴ M is approximately 6.08 x 10⁻⁵ M/s.