Which of the following compounds has a degree of unsaturation equal to $2$?

• A. $C_4{H}_{10}$
• B. $C_4{H}_8$
• C. $C_4{H}_6$
• D. $C_3{H}_8$

Answer: (C)

Verified step by step guidance

1. Recall that the degree of unsaturation (DoU) indicates the number of rings and/or multiple bonds (double bonds or triple bonds) in a molecule. It can be calculated using the formula: \[ \text{DoU} = \frac{2C + 2 - H}{2} \] where \(C\) is the number of carbons and \(H\) is the number of hydrogens in the molecular formula.
2. Apply the formula to each given molecular formula to find their degree of unsaturation. For example, for \(C_4H_{10}\), substitute \(C=4\) and \(H=10\) into the formula: \[ \text{DoU} = \frac{2 \times 4 + 2 - 10}{2} \]
3. Calculate the numerator for each formula (without final division) to see how many degrees of unsaturation each compound has. Repeat this for \(C_4H_8\), \(C_4H_6\), and \(C_3H_8\) by substituting their respective values of \(C\) and \(H\).
4. Identify which molecular formula yields a degree of unsaturation equal to 2 by comparing the results from the previous step. This will tell you which compound has exactly two rings and/or multiple bonds.
5. Confirm your answer by considering the structural implications: a DoU of 2 means the compound could have two double bonds, one triple bond, one ring plus one double bond, or two rings. This helps verify the correctness of your calculation.