The rate of reaction:
`H_(2)O + 2S_(2)O_(4)^(2-)(aq) rarr 2HSO_(3)^(ɵ)(aq) + S_(2)O_(3)^(2-)(aq)`
was studied as follows. In an experiment, the concentration of `S_(2)O_(4)^(2-)(0.4 M)` half changed in `3.73 xx 10^(6) s`. In another experiment, `0.25 M S_(2)O_(4)^(2-)` half changed in `6.0 xx 10^(6) s`. Find the order of the reaction.

Explanation

To find the order of the reaction given the half-life data, we can follow these steps:

### Step 1: Understand the relationship between half-life and concentration
For a reaction, the half-life (t₁/₂) is related to the initial concentration (A₀) and the order of the reaction (n) by the following relationship:
- For a reaction of order n, the half-life is given by:
- t₁/₂ ∝ 1 / (A₀)^(n-1)

### Step 2: Write the equations for the two experiments
...