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Current Question (ID: 18194)

Question:

$\text{The specific conductance of a } 0.1 \text{ M KCl solution at } 23^\circ \text{C is } 0.012 \, \Omega^{-1} \text{ cm}^{-1}. \text{ The resistance of the cell containing the solution at the same temperature was found to be } 55 \, \Omega. \text{ The cell constant will be:}$

Options:

1. $0.142 \, \text{cm}^{-1}$
2. $0.66 \, \text{cm}^{-1}$
3. $0.918 \, \text{cm}^{-1}$
4. $1.12 \, \text{cm}^{-1}$

Solution:

$\text{Conductivity} = \text{Conductance} \times \text{Cell constant}$ $\text{STEP 1:}$ $\text{The formula of specific conductance is as follows:}$ $k = G \times \text{cell constant}$ $\text{Specific conductivity, } k = 0.012 \, \Omega^{-1} \text{ cm}^{-1}$ $K = \frac{1}{\text{Resistance}} \times \frac{1}{a}$ $\text{and}$ $G = \frac{1}{R}$ $\text{STEP 2:}$ $\frac{1}{a} = \text{cell constant}$ $\frac{1}{a} = 55 \times 0.012 = 0.66 \, \text{cm}^{-1}$

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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
}