Introduction:
Kolbe electrolysis is a method used to prepare alkanes from carboxylic acids. It involves the electrolysis of a mixture of sodium salts of carboxylic acids. In this case, we have a mixture of sodium ethanoate and sodium propanoate and we need to calculate the number of different hydrocarbons that can be formed through Kolbe electrolysis.

Explanation:
Kolbe electrolysis involves the oxidation of carboxylate ions at the anode and the reduction of water at the cathode. Let's break down the process step by step:

1. Oxidation at the anode:
- Sodium ethanoate (CH3COONa) is oxidized to form sodium acetate (CH3COOH).
- Sodium propanoate (CH3CH2COONa) is oxidized to form sodium propionate (CH3CH2COOH).

2. Decarboxylation:
- The carboxylic acids formed at the anode undergo decarboxylation, which involves the loss of a CO2 molecule.
- Sodium acetate (CH3COOH) undergoes decarboxylation to form methane (CH4).
- Sodium propionate (CH3CH2COOH) undergoes decarboxylation to form ethane (C2H6).

3. Reduction at the cathode:
- Water (H2O) is reduced to produce hydrogen (H2) gas.

Calculating the number of different hydrocarbons:
In this case, we have two carboxylic acids: acetic acid (CH3COOH) and propanoic acid (CH3CH2COOH). These acids will undergo decarboxylation to form two different hydrocarbons: methane (CH4) and ethane (C2H6).

Therefore, the total number of different hydrocarbons formed through Kolbe electrolysis is 2.

Conclusion:
When a mixture of sodium ethanoate and sodium propanoate undergoes Kolbe electrolysis, two different hydrocarbons are formed: methane (CH4) and ethane (C2H6). Thus, the correct answer is '2'.

In the Kolbe's electrolysis hydrocarbons formed at anode.