Related Formula
Mass percentage of Br = Mass of BrMolar mass of compound × 100$$\text{Mass percentage of Br} = \frac{\text{Mass of Br}}{\text{Molar mass of compound}} \times 100$$
Core Logic
The given compound is a cycloalkane. Since it consumes one mole of bromine and undergoes addition/substitution giving a C:Br ratio of 3:1, let's analyze the formula.
Bromination of an alkane normally requires UV light and is a substitution reaction, yielding mono or dibromo products. But the problem says it "consumes one mole of bromine" to give a product. If it's a cyclopropane or cyclobutane ring, it might undergo ring-opening addition. Let's assume the product has 2 bromine atoms since Br₂$Br_2$ is consumed entirely per mole.
If Br = 2$Br = 2$, then from the C:Br = 3:1$C:Br = 3:1$ ratio, Carbon atoms = 3 × 2 = 6$= 3 \times 2 = 6$.
So the cycloalkane (X) has 6 carbon atoms. Being a cycloalkane, its formula is C₆H₁₂$C_6H_{12}$.
Wait, the solution provided states C₆H₁₀ Br₂ C₆H₁₀Br₂$C_6H_{10} \xrightarrow{Br_2} C_6H_{10}Br_2$. This implies X is cyclohexene (a cycloalkene), not a cycloalkane!
Since we must follow the PDF's logic precisely: The PDF assumes X$X$ is C₆H₁₀$C_6H_{10}$ (cyclohexene) despite the text saying 'cycloalkane'. It undergoes addition of Br₂$Br_2$ to form C₆H₁₀Br₂$C_6H_{10}Br_2$.
For C₆H₁₀Br₂$C_6H_{10}Br_2$:
Number of C = 6, Number of Br = 2. C:Br ratio = 6:2 = 3:1. This perfectly fits the given condition.
Step 1: Calculate Molar Mass
Molar mass of product (Y) C₆H₁₀Br₂$C_6H_{10}Br_2$:
M = (12 × 6) + (1 × 10) + (80 × 2)$M = (12 \times 6) + (1 \times 10) + (80 \times 2)$
M = 72 + 10 + 160 = 242 g mol⁻¹$M = 72 + 10 + 160 = 242\text{ g mol}^{-1}$
Step 2: Calculate Percentage
% of Br = (160)/(242) × 100 ≈ 66.11%$$\% \text{ of Br} = \frac{160}{242} \times 100 \approx 66.11\%$$
Step 3: Rounding
Nearest integer is 66.
Pattern Recognition
Be prepared to spot exam typos (like 'cycloalkane' instead of 'cycloalkene') when a fixed atomic ratio constraint immediately points to a specific molecular formula.
Chapter Mix
Class 11 Chemistry: Hydrocarbons
Class 11 Chemistry: Some Basic Concepts of Chemistry