Import Question JSON

Current Question (ID: 18170)

Question:

$\text{By how much will the potential of half cell Cu}^{2+}\mid\text{Cu change if the solution is diluted to 100 times at 298 K. It will -}$

Options:

1. $\text{Increase by 59 mV}$
2. $\text{Decrease by 59 mV}$
3. $\text{Increase by 29.5 mV}$
4. $\text{Decrease by 29.5 mV}$

Solution:

$\text{HINT: } E_{\text{cell}} = E^{\circ}_{\text{cell}} + \frac{0.059}{n} \log \frac{A_{\text{ox}}}{A_{\text{red}}}$ $\text{STEP 1:}$ $\text{Nernst equation at 25}^\circ \text{C, whereas } E_{\text{cell}} = E^{\circ}_{\text{cell}} + \frac{0.059}{n} \log \frac{A_{\text{ox}}}{A_{\text{red}}}$ $\text{As Cu}^{2+} \text{ is reductant and its conc. is getting reduced by 100 times, so the log value will increase by the factor of 2. Also the value of } n \text{ is 2.}$ $\text{STEP 2:}$ $\text{Suppose, initial concentration of } [\text{Cu}^{2+}] = 1 \text{M}$ $E_{\text{cell1}} = E^{0}_{\text{cell}} + \frac{0.059}{2} \log 1$ $E_{\text{cell1}} = E^{0}_{\text{cell}}$ $E_{\text{cell2}} = E^{0}_{\text{cell}} + \frac{0.059}{2} \log 0.01$ $E_{\text{cell2}} = E^{0}_{\text{cell}} - 0.059 \text{ V}$

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
}