Import Question JSON

Current Question (ID: 7431)

Question:

If the density of methanol is 0.793 kg L$^{-1}$, the volume needed for making 2.5 L of its 0.25 M solution would be:

Options:

1. 22.25 mL
2. 24.78 mL
3. 25.22 mL
4. 22.52 mL

Solution:

\text{Hint: Find the molarity of methanol solution and use } M_1 V_1 = M_2 V_2\n\n\text{Step 1: Calculate the molarity of methanol solution}\n\n\text{Molar mass of methanol } (\text{CH}_3 \text{ OH}) = (1 \times 12) + (4 \times 1) + (1 \times 16)\n= 32 \text{ g mol}^{-1}\n= 0.032 \text{ kg mol}^{-1}\n\n\text{Molarity of methanol solution} = \frac{0.793 \text{ kg/L}}{0.032 \text{ kg/mol}}\n= 24.78 \text{ mol/L}\n\n(\text{Since density is mass per unit volume})\n\n\text{Step 2: Applying,}\n\nM_1 V_1 = M_2 V_2\n\n(\text{Given solution}) (\text{Solution to be prepared})\n\n(24.78 \text{ mol/L}) \times V_1 = (2.5 \text{ L}) \times (0.25 \text{ mol/L})\n\nV_1 = 0.0252 \text{ L}\n\nV_1 = 25.22 \text{ mL}\n\n\text{Hence, option third is the correct answer.}

Import JSON File

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
}