Let's analyze which of the given reactions is an addition reaction.
An addition reaction occurs when two or more molecules combine to form a larger molecule, with no other products formed. Here, we need to look for a reaction where the reactants combine to form a single product without any by-products like water, hydrogen, halides, etc.
Evaluate the three given reactions one by one:
1. [tex]\( H_2C=CH_2 + Br_2 \rightarrow H_2BrC-CH_2Br \)[/tex]
This reaction involves an unsaturated molecule (ethene, [tex]\( H_2C=CH_2 \)[/tex]) reacting with bromine ([tex]\( Br_2 \)[/tex]) to form a dibromoethane ([tex]\( H_2BrC-CH_2Br \)[/tex]), with both bromine atoms adding across the double bond of ethene. This is an example of an addition reaction because the two reactants combine to form a single product without any by-products.
2. [tex]\( H_2C=CH_2 + HBr \rightarrow H_3C-CH_2Br \)[/tex]
This reaction involves ethene ([tex]\( H_2C=CH_2 \)[/tex]) reacting with hydrogen bromide ([tex]\( HBr \)[/tex]) to form bromoethane ([tex]\( H_3C-CH_2Br \)[/tex]). Here also, the hydrogen atom and the bromine atom add across the double bond of ethene, forming a single product. This is another example of an addition reaction.
3. [tex]\( H_3C-CH_2Cl + NaOH \rightarrow H_3C-CH_2OH + NaCl \)[/tex]
This reaction involves bromoethane ([tex]\( H_3C-CH_2Cl \)[/tex]) reacting with sodium hydroxide ([tex]\( NaOH \)[/tex]) to form ethanol ([tex]\( H_3C-CH_2OH \)[/tex]) and sodium chloride ([tex]\( NaCl \)[/tex]). This reaction results in the substitution of chlorine by a hydroxyl group, producing two products instead of one. This is known as a substitution reaction, not an addition reaction.
Given the above evaluations, we can conclude:
The second reaction, [tex]\( H_4C_2 + HBr \rightarrow H_5C_2Br \)[/tex], is an addition reaction.
