(a) For the generic reaction A → B what quantity, when graphed versus time, will yield a straight line for a first-order reaction?

Consider the reaction of peroxydisulfate ion (S₂O₈^2-) with iodide ion (I^-) in aqueous solution:

S₂O₈^2-(aq) + 3 I^-(aq) → 2 SO₄^2-(aq) + I₃^-(aq)

 At a particular temperature, the initial rate of disappearance of S₂O₈^2- varies with reactant concentrations in the following manner:

Experiment [S₂O₈^2-] (M) [I^-] (M) Initial Rate (M/s)

1 0.018 0.036 2.6 × 10^-6

2 0.027 0.036 3.9 × 10^-6

3 0.036 0.054 7.8 × 10^-6

4 0.050 0.072 1.4 × 10^-5

(a) Determine the rate law for the reaction and state the units of the rate constant.

(a) The gas-phase decomposition of SO₂Cl₂, SO₂Cl₂(g) → SO₂(g) + Cl₂(g), is first order in SO₂Cl₂. At 600 K the half-life for this process is 2.3 × 10⁵ s. What is the rate constant at this temperature?

(b) At 320°C the rate constant is 2.2 × 10^-5 s^-1. What is the half-life at this temperature?

Consider the gas-phase reaction between nitric oxide and bromine at 273°C: 2 NO(g) + Br₂(g) → 2 NOBr(g). The following data for the initial rate of appearance of NOBr were obtained:

Experiment [NO] (M) [Br₂] (M) Initial Rate (M/s)

1 0.10 0.20 24

2 0.25 0.20 150

3 0.10 0.50 60

4 0.35 0.50 735 

(b) Calculate the average value of the rate constant for the appearance of NOBr from the four data sets.

(b) How can you calculate the rate constant for a first-order reaction from the graph you made in part (a)?