Import Question JSON

Current Question (ID: 21429)

Question:

$\text{The density of a 3 M NaCl solution is 1 g/mL. The molality of the solution is 'x'. The value of } 2x \text{ is:}$ $\text{(Round off to nearest integer)}$

Options:

1. 7
2. 10
3. 13
4. 5

Solution:

$\text{Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent.}$ $\text{The relationship between density and molality is:}$ $m = \frac{M \times 1000}{1000 \times d_{\text{solution}} - M \times MM_{\text{solute}}}$ $m = \text{molality}$ $M = \text{molarity}$ $d = \text{density}$ $MM_{\text{solute}} = \text{molar mass of solute}$ $\text{Molality: } x = \frac{3}{824.5} \times 1000 = 3.63 \text{ molal}$ $\text{Hence, } 2x \approx 7$

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
}