a) In a reaction, 2-methylbutan-1-ol is oxidised by potassium dichromate. Write equations for the two oxidation steps of this reaction.

Then name and draw (as displayed formula) the two products of this reaction.

b) One of the products gives a silver mirror when warmed with Tollen’s reagent. State the identity of this product and name the functional group that this product belongs to.

2-methylbutan-1-ol + [O] ==> 2-methylbutan-1-al + water

CH3CH2CH(CH3)CH2OH + [O] ==> CH3CH2CH(CH3)CHO + H2O
second step:
CH3CH2CH(CH3)CHO + [O] ==> CH3CH2CH(CH3)COOH
2-methylbutan-1-al + [O] ==> 2-methylbutanoic acid
b) Tollen's reagent is a basic solution of the silver amine complex ion. A positive test is exhibited by a precipitation of silver, often as a "mirror" on the inside of the reaction vessel (my personal experience is I NEVER got a mirror test but a black solution of colloidal silver metal). The aldehyde provides the positive test.

For part b:

What is the identity of the product?

What is the functional group that this product belongs to?

As I stated in my answer the aldehyde is the functional group. in this case it's the 2-methylbutan-1-al

Draw (as displayed formula) the two products of this reaction.

To write the equations for the oxidation steps of 2-methylbutan-1-ol (also known as isoamyl alcohol), we need to consider the oxidation states of the elements involved.

Step 1: Oxidation of 2-methylbutan-1-ol
The first step involves the primary alcohol group (-OH) of 2-methylbutan-1-ol being oxidized to an aldehyde. This conversion is achieved through the use of an oxidizing agent like potassium dichromate (K2Cr2O7) in acidic conditions (H2SO4).

The equation for this step is:
2-methylbutan-1-ol + [O] -> 2-methylbutanal

Step 2: Further oxidation of 2-methylbutanal
The aldehyde formed in the previous step, 2-methylbutanal, can be further oxidized to a carboxylic acid. This reaction requires additional oxidation.

The equation for this step is:
2-methylbutanal + [O] -> 2-methylbutanoic acid

Now, let's name and draw the two products:

Product 1: 2-methylbutanal
The first product is 2-methylbutanal, which is an aldehyde. Its displayed formula is:
CH3-CH(CH3)-CH2-CH=O

Product 2: 2-methylbutanoic acid
The second product is 2-methylbutanoic acid, which is a carboxylic acid. Its displayed formula is:
CH3-CH(CH3)-CH2-COOH

Moving on to part b:

The product that gives a silver mirror when warmed with Tollen's reagent is the aldehyde, 2-methylbutanal. This is due to the oxidation of the aldehyde group to a carboxylate anion (R-COO-) and the reduction of silver ions (Ag+) in Tollen's reagent to metallic silver (Ag). This reaction forms a silver mirror coating on the test tube.

The functional group that the product, 2-methylbutanal, belongs to is an aldehyde.