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Current Question (ID: 20809)

Question:

$\text{The number of atoms in } 560 \text{ g of Fe (atomic mass } 56 \text{ g mol}^{-1}) \text{ is:}$

Options:

1. $\text{Twice that of } 70 \text{ g N}$
2. $\text{Half that of } 20 \text{ g H}$
3. $\text{Both 1 and 2}$
4. $\text{None of the above}$

Solution:

$\text{Hint: Compare the moles of nitrogen and hydrogen with Fe}$ $\text{Step 1:}$ $\text{First calculate number of atoms in } 560 \text{ g of Fe.}$ $\text{Number of mole of Fe} = \frac{\text{amount of Fe}}{\text{molar mass of Fe}}$ $560 \text{ g of Fe} = \text{Number of moles} = \frac{560 \text{ g}}{56 \text{ g}} = 10 \text{ mole}$ $1 \text{ mole contains } 6.022 \times 10^{23} \text{ atoms.}$ $\text{Hence, } 560 \text{ g of Fe} = 10 \text{ mol} = 10 \times 6.022 \times 10^{23} \text{ atoms} = 6.022 \times 10^{24} \text{ atoms.}$ $\text{Step 2:}$ $\text{Calculate the number of atoms in } 70 \text{ g of N as follows:}$ $70 \text{ g of N}$ $14 \text{ g} = 1 \text{ mole of N}$ $70 \text{ g} = 5 \text{ moles of N}$ $20 \text{ g H} = 20 \text{ moles of H-atoms}$ $\text{The moles of nitrogen is half as compare to mole of Fe.}$ $\text{Hence, number of atoms in } 560 \text{ g of Fe is twice that of } 70 \text{ g N.}$

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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
}