Certainly! Let's break down the problem step by step to determine the molecular formula of iso-pentane, given that n-pentane has the molecular formula [tex]\( C_5H_{12} \)[/tex].
1. Understanding Isomers:
- Isomers are molecules that have the same molecular formula but different structural arrangements.
- Since n-pentane and iso-pentane are isomers, they must have the same molecular formula, because isomers only differ in the arrangement of atoms, not in the number of atoms present.
2. Given Molecular Formula:
- The molecular formula of n-pentane is [tex]\( C_5H_{12} \)[/tex].
3. Analyzing Options:
- We need to determine which of the given options has the same molecular formula as n-pentane:
- Option A: [tex]\( C_5H_{10} \)[/tex]
- Option B: [tex]\( C_5H_{12} \)[/tex]
- Option C: [tex]\( C_5H_9 \)[/tex]
4. Comparing Molecular Formulas:
- Option A: [tex]\( C_5H_{10} \)[/tex] - This has two fewer hydrogen atoms than n-pentane, so it cannot be correct.
- Option B: [tex]\( C_5H_{12} \)[/tex] - This has the same number of carbon and hydrogen atoms as n-pentane, making it the same molecular formula.
- Option C: [tex]\( C_5H_9 \)[/tex] - This has three fewer hydrogen atoms than n-pentane, so it is also incorrect.
5. Conclusion:
- Since iso-pentane is an isomer of n-pentane, and they must share the same molecular formula, the correct molecular formula for iso-pentane must be identical to that of n-pentane.
Therefore, the correct molecular formula for iso-pentane is:
[tex]\[ \boxed{C_5H_{12}} \][/tex]
Hence, the correct answer is option B: [tex]\( C_5H_{12} \)[/tex].
