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Current Question (ID: 21391)

Question:

$\text{Resistance of 0.2 M solution of an electrolyte is } 50 \, \Omega. \text{ The specific conductance of the solution is } 1.3 \, \text{S m}^{-1}. \text{ If the resistance of the 0.4 M solution of the same electrolyte is } 260 \, \Omega, \text{ its molar conductivity is:}$

Options:

1. $6.25 \times 10^{-4} \, \text{S m}^2 \text{ mol}^{-1}$
2. $625 \times 10^{-4} \, \text{S m}^2 \text{ mol}^{-1}$
3. $62.5 \, \text{S m}^2 \text{ mol}^{-1}$
4. $6250 \, \text{S m}^2 \text{ mol}^{-1}$

Solution:

$\text{Molar conductivity } (\Lambda_m) = \frac{K}{c}$ $\text{Where } K = \frac{1}{R} \text{ and } c \text{ is concentration}$ $\Lambda_m = \frac{1.3}{0.4} = 6.25 \times 10^{-4} \, \text{S m}^2 \text{ mol}^{-1}$

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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
}