# Confusion about the SN1 and SN2 Mechanism

My book says, and I understand, that the $$\mathrm{S_N1}$$ mechanism is much faster for tertiary alkyl halides than primary. And the opposite for $$\mathrm{S_N2}.$$ This all makes sense. What I don't get is the conclusion it comes to next: hence, we predict that the primary alkyl halides will react primarily via $$\mathrm{S_N2},$$ and the tertiary via $$\mathrm{S_N1}.$$

The reason I get confused here is that nothing was said about the comparative rates for a primary alkyl halide via the $$\mathrm{S_N1}$$ or $$\mathrm{S_N2}$$ (they just compared primary and tertiary for $$\mathrm{S_N1}$$ and $$\mathrm{S_N2}$$). In my mind, which mechanism dominates for primary or tertiary should be dependent on the relative rates for that compound; not rates compared between primary and tertiary.

Is my argument sound? And if so, is there some literature you know of that explains this in such a manner?

• Just measure the absolute rate. Then you know all relative rates. – Zhe Mar 31 '19 at 12:40
• If your reactant and product are chiral, you can tell from the stereochemistry of the product which mechanism was at play. SN2 shows inversion of configuration, while SN1 scrambles it (racemic mixture as product). – Karsten Theis Mar 31 '19 at 13:35

Your reasoning is correct. It's the relative rates for a given alkyl halide that matter, and it's difficult to draw conclusions about those, because the relative rates are not fixed, as the $$\mathrm{S_N2}$$ rate is dependent also on the nucleophile concentration.
We can write the rate of the $$\mathrm{S_N1}$$ as $$k_1[\text{alkyl halide}]$$ and the rate of the $$\mathrm{S_N2}$$ as $$k_2[\text{alkyl halide}][\text{nucleophile}]$$, so the relative rate at a fixed concentration of the alkyl halide is given by
$$\frac{\mathrm{S_N2}}{\mathrm{S_N1}} = \frac{k_2[\text{nucleophile}]}{k_1}.$$
The identity of the nucleophile will be a factor as well, since that will affect $$k_2$$.