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Current Question (ID: 18215)

Question:

$\text{Value of } \wedge_m^0 \text{ for } \text{SrCl}_2 \text{ (strong electrolyte) in water at } 25^\circ \text{C from the data below is:}$ $\begin{array}{|c|c|c|} \hline \text{Conc. (mol/litre)} & 0.25 & 1 \\ \hline \wedge_m \left(\Omega^{-1} \text{ cm}^2 \text{ mol}^{-1}\right) & 260 & 250 \\ \hline \end{array}$

Options:

1. $270 \ \Omega^{-1} \text{ cm}^2 \text{ mol}^{-1}$
2. $260 \ \Omega^{-1} \text{ cm}^2 \text{ mol}^{-1}$
3. $250 \ \Omega^{-1} \text{ cm}^2 \text{ mol}^{-1}$
4. $255 \ \Omega^{-1} \text{ cm}^2 \text{ mol}^{-1}$

Solution:

$\text{Data given:}$ $\text{conc. (mol/lt)} \quad 0.25 \quad 1$ $\lambda_m \left(\Omega^{-1} \text{ cm}^2 \text{ mol}^{-1}\right) \quad 260 \quad 250$ $\text{Debye-Huckel onsagar equation:}$ $\lambda_m \text{ conductivity}$ $\text{at any concentration} = \lambda_m^0 \text{ conductivity}$ $\text{at infinite dilution} - b \sqrt{c_{\text{conc}}}$ $260 = \lambda_m^0 - b \sqrt{0.25} \quad \ldots (i)$ $250 = \lambda_m^0 - b \sqrt{1} \quad \ldots (ii)$ $\text{After solving equation (i) and (ii)}$ $\lambda_m^0 = 270 \ \Omega^{-1} \text{ cm}^2 \text{ mol}^{-1}$ $\text{Hence 1 is the correct option.}$

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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
}