Identify the given reaction.

The reaction is between butanoic acid ($\text{CH}_3\text{—CH}_2\text{—CH}_2\text{—C(O)OH}$) and chlorine ($\text{Cl}_2$) in the presence of red phosphorus. This is a Hell-Volhard-Zelinsky (HVZ) reaction.

The HVZ reaction is a specific method for halogenating carboxylic acids at the alpha-carbon. The alpha-carbon is the carbon atom directly adjacent to the carboxyl group ($\text{—C(O)OH}$).

We number the carbon atoms starting from the carboxyl group (C1):

The carbon atom directly adjacent to the carboxyl group (C1) is C2. This is the alpha-carbon.

In the HVZ reaction, a hydrogen atom on the alpha-carbon is replaced by a halogen atom. Therefore, the substitution will occur at the carbon atom numbered 2.

The ordinal number of the carbon atom where the substitution of a hydrogen atom by a chlorine atom will occur is $\boxed{\text{2}}$.