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Current Question (ID: 20812)

Question:

$\text{A hydrocarbon has a molar mass of } 84 \text{ g/mol and contains } 85.8\% \text{ carbon by mass. How many hydrogen atoms are present in one molecule of this hydrocarbon?}$

Options:

1. $8$
2. $10$
3. $12$
4. $14$

Solution:

$\text{Hint: Molecular formula = } n \times \text{ empirical formula}$ $\text{Step 1: Calculations for the empirical formula:}$ $\begin{array}{c|c|c} \text{C} & 85.8 & \frac{85.8}{12} = 7 & 1 \\ \text{H} & 14.2 & \frac{14.2}{1} = 14 & 2 \end{array}$ $\text{Empirical formula = } \text{CH}_2$ $\text{Step 2: Molecular formula = } n \times \text{ empirical formula}$ $n = \frac{\text{molar mass}}{\text{empirical formula weight}} = \frac{84}{14} = 6$ $\text{Therefore, Molecular formula = } \text{C}_6\text{H}_{12}$ $\text{So, total number of H-atoms in one molecule of hydrocarbon = 12.}$ $\text{Thus, option 3 is the correct answer.}$

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Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}