Step 1: 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. Step 2: Understand the mechanism of the 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 ($\text{—C(O)OH}$). Step 3: Number the carbon atoms in butanoic acid. We number the carbon atoms starting from the carboxyl group (C1): $$ \overset{4}{\text{CH}}_3\text{—}\overset{3}{\text{CH}}_2\text{—}\overset{2}{\text{CH}}_2\text{—}\overset{1}{\text{C}}\text{(O)OH} $$ The carbon atom directly adjacent to the carboxyl group (C1) is C2. This is the alpha-carbon. Step 4: Determine the position of substitution. 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 $\boxed{\text{2}}$. 3 done, 2 left today. You're making progress.