The percentage of hydrogen in the sixth member of the class of the aliphatic alkanes is  [H =1, C =12 ]

1. Analyze the question

We need to find the percentage composition of hydrogen in the sixth member of the alkane homologous series.

2. Explain the concept

• General Formula: The general formula for alkanes is $C_nH_{2n+2}$.
• Sixth Member: Since the first member ($n=1$) is methane ($CH_4$), the sixth member ($n=6$) is hexane ($C_6H_{14}$).
• Percentage Composition Formula: $$\text{Percentage of element} = \left( \frac{\text{Total mass of element in compound}}{\text{Molar mass of compound}} \right) \times 100\%$$

3. Show the solution

Step 1: Determine the molecular formula of the sixth member. Using $n=6$: $C_6H_{2(6)+2} = C_6H_{14}$

Step 2: Calculate the molar mass of $C_6H_{14}$.

• Atomic mass of Carbon (C) = 12
• Atomic mass of Hydrogen (H) = 1
• Molar mass = $(6 \times 12) + (14 \times 1)$
• Molar mass = $72 + 14 = 86 \text{ g/mol}$

Step 3: Calculate the total mass of Hydrogen in the compound.

• Mass of H = $14 \times 1 = 14 \text{ g/mol}$

Step 4: Calculate the percentage of Hydrogen.

• $\%H = \left( \frac{14}{86} \right) \times 100$
• $\%H = 0.16279 \times 100$
• $\%H \approx 16.28\%$

4. Identify the answer

Comparing our result to the options provided, the correct value is 16.28%. This matches option C.

5. Tip

When dealing with homologous series, always remember the general formula ($C_nH_{2n+2}$ for alkanes, $C_nH_{2n}$ for alkenes). A common mistake is to forget that the "sixth member" is $n=6$, not $n=5$. Always write out the formula first to avoid calculation errors!