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Current Question (ID: 20853)

Question:

$\text{A compound consists of } 54.2\% \text{ carbon (C), } 9.2\% \text{ hydrogen (H), and } 36.6\% \text{ oxygen (O) by mass. The molar mass of the compound is } 132 \text{ g/mol.}$ $\text{Determine the molecular formula of the compound.}$ $\text{(Given -Relative atomic masses: C = 12, H = 1, O = 16)}$

Options:

1. $\text{C}_4\text{H}_9\text{O}_3$
2. $\text{C}_6\text{H}_{12}\text{O}_6$
3. $\text{C}_6\text{H}_{12}\text{O}_3$
4. $\text{C}_4\text{H}_8\text{O}_2$

Solution:

$\text{Hint: The empirical formula for the given compounds is } \text{C}_2\text{H}_4\text{O}$ $\text{Explanation:}$ $\text{The simplest ratio of the elements is calculated as follows:}$ $\frac{54.2}{12} : \frac{9.2}{1} : \frac{36.6}{16}$ $4.516 : 9.2 : 2.287$ $\frac{4.516}{2.287} : \frac{9.2}{2.287} : \frac{2.287}{2.287}$ $1.97 : 4.02 : 1$ $\text{C}_2\text{H}_4\text{O} \text{ is the empirical formula of the compound.}$ $\text{Empirical formula mass = } 24 + 4 + 16 = 44 \text{ and molar mass = 132}$ $\text{Hence, molecular formula } = (\text{C}_2\text{H}_4\text{O})_3 = \text{C}_6\text{H}_{12}\text{O}_3$ $\text{Therefore, option 3 is the correct answer.}$

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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
}