SN1 and SN2 rate laws

You will write the rate laws of the two substitution mechanisms and the half-life of a first-order reaction. Then you will test what changes when concentrations change.

The idea. An $S_{\text{N}}2$ rate depends on the haloalkane and the nucleophile. An $S_{\text{N}}1$ rate depends on the haloalkane only. A first-order reaction has a half-life of $\ln 2 / k$.

Your tasks.

1. Complete sn2_rate(k, rx, nu).
2. Complete sn1_rate(k, rx).
3. Complete half_life(k) for a first-order reaction.