Import Question JSON

$\text{Hint: Molecular mass of the compound is } 162$ $GMM \text{ of } \text{C}_{10}\text{H}_{14}\text{N}_2$ $\Rightarrow 120 + 14 + 28$ $\Rightarrow 162$ $\text{To identify the compound, we need to calculate the empirical formula}$ $\text{based on the given percentages and then determine which option}$ $\text{matches the molecular formula with a molecular mass of } 162 \text{ g/mol.}$ $\text{Step 1: Calculate Moles of Each Element:}$ $\text{Given:}$ $\text{Hydrogen (H) = } 8.64\%$ $\text{Carbon (C) = } 74\%$ $\text{Nitrogen (N) = } 17.36\%$ $1. \text{Hydrogen: } \frac{8.64 \text{ g}}{1.008 \text{ g/mol}} = 8.57 \text{ moles}$ $2. \text{Carbon: } \frac{74 \text{ g}}{12.01 \text{ g/mol}} = 6.16 \text{ moles}$ $3. \text{Nitrogen: } \frac{17.36 \text{ g}}{14.01 \text{ g/mol}} = 1.24 \text{ moles}$ $\text{Step 2: Find the Simplest Whole Number Ratio}$ $\text{Divide each value by the smallest number of moles (1.24):}$ $1. \text{Hydrogen: } \frac{8.57}{1.24} \approx 6.91 \approx 7$ $2. \text{Carbon: } \frac{6.16}{1.24} \approx 4.97 \approx 5$ $3. \text{Nitrogen: } \frac{1.24}{1.24} = 1$ $\text{The empirical formula is } \text{C}_5\text{H}_7\text{N}.$ $\text{Empirical formula mass of } \text{C}_5\text{H}_7\text{N}:$ $(5 \times 12.01) + (7 \times 1.008) + (1 \times 14.01) = 60.05 + 7.056 + 14$ $\text{Step 4: Determine the Molecular Formula}$ $\text{The molecular mass of the compound is given as } 162 \text{ g/mol. To find}$ $\text{the molecular formula, divide the molecular mass by the empirical}$ $\text{formula mass:}$ $\frac{162}{81.12} \approx 2$ $\text{This means the molecular formula is } \text{C}_{10}\text{H}_{14}\text{N}_2.$