What alkyl halide or product will I get if I mix 2,4-dimethyl-3-pentanol with NaBr and sulfuric acid, and what substitution mechanism, SN1 or SN2 will that reaction undergo? Thanks in advance.

What if I mix 1-propanol with NaBr and sulfuric acid, what mechanism would that be?

What if I mix 2-pentanol with NaBr and sulfuric acid, what mechanism would that be?

You need to look at the stability of the + ion formed. There is a good description on the wikipedia pages:

http://en.wikipedia.org/wiki/SN2_reaction

http://en.wikipedia.org/wiki/SN1_reaction

for 1-propanol with NaBr and sulfuric acid, can I assume the mechanism is SN2 because the alcohol is on a primary carbon? I"m confused because when I write out the reaction, there will be a primary carbocation, and I'll have to do a shift right? I thought the product would be bromopropane but with the shift it will be 2-bromopropane?

for 2-pentanol, since the alcohol is on a secondary carbon, it can be either SN1 or SN2. I'm still confused

To determine the alkyl halide or product formed and the substitution mechanism of a reaction, you need to consider the functional group involved, the nature of the alkyl group, and the reaction conditions.

For the reaction of 2,4-dimethyl-3-pentanol with NaBr and sulfuric acid:

Step 1: Protonation of the alcohol group
Sulfuric acid (H2SO4) is a strong acid, and in this case, it serves to protonate the hydroxyl group (-OH) of the 2,4-dimethyl-3-pentanol, forming a water molecule and generating a more reactive carbocation intermediate.

Step 2: Nucleophilic attack by bromide ion
The bromide ion (Br-) provided by NaBr acts as a nucleophile and undergoes a substitution reaction with the carbocation intermediate. The nucleophile attacks the carbocation, displacing the leaving group (-OH) and forming a new bond with the carbon atom.

Based on the mechanism of the reaction, this process is likely to undergo a combination of both SN1 and SN2 mechanisms, known as a mixed mechanism or SN1/SN2. The rate-determining step is the formation of the carbocation intermediate, which occurs through ionization of the alcohol group. The nucleophilic attack by the bromide ion can happen both in a unimolecular (SN1) and bimolecular (SN2) fashion, depending on the particular reaction conditions.

As for the resulting alkyl halide, the bromide ion replaces the hydroxyl group, resulting in the formation of 2,4-dimethyl-3-pentyl bromide.

Now, let's consider the reactions with 1-propanol and 2-pentanol:

For the reaction of 1-propanol with NaBr and sulfuric acid:

The same general steps as described above will occur: protonation of the alcohol group by sulfuric acid and nucleophilic attack by bromide ion. However, the resulting product will be 1-bromopropane. Since 1-propanol is a primary alcohol, the reaction is likely to undergo an SN2 mechanism due to the ease of backside attack of the nucleophile on the less hindered primary carbon.

For the reaction of 2-pentanol with NaBr and sulfuric acid:

Again, the same general steps will take place. In this case, the resulting product will be 2-bromopentane. 2-pentanol is a secondary alcohol, so the reaction can follow both the SN1 and SN2 mechanisms. However, the SN1 pathway is more favorable due to the stability of the secondary carbocation intermediate formed.

Remember, the exact nature of the reaction mechanism may depend on the reaction conditions (e.g., concentration of reagents, temperature), so there may be variations from the ideal scenarios described above.