Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
The alkane has three isomers: pentane, 2-methylbutane and 2,2-dimethylpropane. Lucia replaces one hydrogen atom by one chlorine atom, in every possible place, in each isomer. She collects the distinct products. Some of the products have a carbon atom with four different groups. Count the structural isomers of . Count the primary ones, which have chlorine on a carbon with one carbon neighbour. Count the ones that can exist as mirror-image forms. Then count all the stereoisomers.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Go through each carbon skeleton and place the chlorine on every different carbon.
Step 1. Pentane. Three: 1-chloropentane (primary), 2-chloropentane (secondary) and 3-chloropentane (secondary).
Step 2. 2-Methylbutane. Four: 1-chloro-2-methylbutane (primary), 2-chloro-2-methylbutane (tertiary), 2-chloro-3-methylbutane (secondary) and 1-chloro-3-methylbutane (primary).
Step 3. 2,2-Dimethylpropane. One: 1-chloro-2,2-dimethylpropane (primary). All four methyl groups are equal.
Step 4. Count. structural isomers. Primary: 1-chloropentane, 1-chloro-2-methylbutane, 1-chloro-3-methylbutane and 1-chloro-2,2-dimethylpropane, which is 4.
Step 5. Stereocentres. 2-Chloropentane (carbon 2 holds H, Cl, CH3 and a propyl group), 1-chloro-2-methylbutane (carbon 2) and 2-chloro-3-methylbutane (carbon 2) each have one. That is 3 compounds, and each exists as a pair, so stereoisomers.
Answer: 8 structural isomers, 4 primary, 3 with mirror-image forms and 11 stereoisomers in all.
Check. 3-Chloropentane has two identical ethyl groups on its carbon 3, so it is not chiral.
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A haloalkane is primary, secondary or tertiary by the number of carbon atoms joined to the carbon that holds the halogen. Isomers are counted by listing every carbon skeleton and every place for the halogen, then removing repeats. A carbon with four different groups is a stereocentre, and it doubles the count for its compound.