Q. \( \mathrm{C_4H_{10}} \) isomers.

We are asked: \(\mathrm{C_4H_{10}}\) isomers.

Step 1: Identify the molecular formula and its relevance.

\(\mathrm{C_4H_{10}}\) is an alkane (it has the general formula \( \mathrm{C_nH_{2n+2}}\)).

For \(n=4\), we get \( \mathrm{H}=2(4)+2=10\), which matches. So we are counting structural (constitutional) isomers of butane.

Step 2: Understand what counts as an isomer here.

For alkanes, different bonding arrangements lead to different constitutional isomers. For \(\mathrm{C_4H_{10}}\), we consider all possible carbon skeletons that can be formed with 4 carbons, and then account for possible distinct connectivity.

Step 3: List the possible carbon skeletons for \(4\) carbons.

1. Straight-chain (n-butane): One way is to place all 4 carbons in a continuous line.

Structure: \(\mathrm{CH_3-CH_2-CH_2-CH_3}\)

2. Branched-chain (isobutane): The alternative is to have a branch: one carbon connected to three others, making a “single-center” structure.

Structure: \(\mathrm{(CH_3)_3CH}\), which is \(\mathrm{CH_3-CH(CH_3)-CH_3}\)

This corresponds to the unique branched connectivity for \(\mathrm{C_4}\): a central carbon attached to three methyl groups total in the molecule.

Step 4: Check if there are any additional constitutional isomers.

With only 4 carbons and single bonds (alkanes), there are only two distinct connectivity patterns: an unbranched chain and a single branching pattern. Any other arrangement would be a repetition of these through relabeling of equivalent atoms.

Final Answer: \(\mathrm{C_4H_{10}}\) has 2 isomers.