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Current Question (ID: 20801)

Question:

$\text{The number of moles of methane required for the combustion process to yield 81 grams of water is:}$

Options:

1. $2.25 \text{ mole}$
2. $4.5 \text{ mole}$
3. $9 \text{ mole}$
4. $1.125 \text{ mole}$

Solution:

$\text{Hint: Balance chemical reaction } \text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O} \text{ and follow mole concept}$ $\text{Step 1:}$ $\text{The reaction is as follows:}$ $\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}$ $\text{From the reaction, it is clear that 1 mole of } \text{CH}_4 \text{ produces 2 moles of water.}$ $\text{It is given that, 81 g of water is produced. Convert the amount of water into the number of moles as follows:}$ $\text{Number of moles of water} = \frac{81}{18}$ $= 4.5 \text{ mole}$ $\text{Step 2:}$ $\text{for 2 mol of water produced by 1 mol of } \text{CH}_4. \text{ Hence, for 1 mol of water } \frac{1}{2} \text{ mol of } \text{CH}_4 \text{ is required.}$ $\text{For 4.5 mol water} = \frac{1}{2} \times 4.5 \text{ mol of } \text{CH}_4$ $= 2.25 \text{ mol}$

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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
}