Azomethane, [tex](CH_3)_2N_2[/tex], decomposes with a first-order rate. The chemical reaction is:

[tex](CH_3)_2N_2 (g) \rightarrow N_2(g) + 2CH_3(g)[/tex].

The following data were obtained for the decomposition in a 200-mL flask at 300°C:

| Time (min) | Total Pressure (torr) |
|------------|-----------------------|
| 0 | 36.2 |
| 15 | 42.4 |
| 30 | 46.5 |
| 48 | 53.1 |
| 75 | 59.3 |

Calculate the rate constant and the half-life for this reaction.

The rate constant and half-life for the first-order decomposition of azomethane can be calculated using the provided pressure data and the first-order rate equation, with half-life determined by the formula t1/2 = 0.693/k, applicable to first-order reactions.

Explanation:

To calculate the rate constant for a first-order reaction, we can use the first-order rate equation, which is ln([A]0/[A]t) = kt, where [A]0 is the initial concentration, [A]t is the concentration at time t, and k is the rate constant. Given the pressure data in a fixed-volume flask for the decomposition of azomethane to nitrogen and methane, we can assume that pressure is proportional to concentration and use the pressures at different times to calculate the rate constant. The half-life of a first-order reaction is given by t1/2 = 0.693/k.

To determine how to calculate these from your pressure data, please refer to the similar process used for other reactions. For example, the rate of the reaction for the decomposition of dinitrogen pentoxide at 45 °C and 0.40 M concentration, given a rate constant of 6.2 × 10-4 min⁻¹, is found by simply multiplying the concentration by the rate constant, as the rate of a first-order reaction is given by rate = k[N2O5].