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Current Question (ID: 10533)

Question:

$\text{With an increase in temperature, the viscosity of:}$ $\text{(a) gases decrease. (b) liquids increase.}$ $\text{(c) gases increase. (d) liquids decrease.}$ $\text{Which of the following options is/are correct?}$

Options:

1. $\text{(b), (c)}$
2. $\text{(a), (d)}$
3. $\text{(c), (d)}$
4. $\text{(a), (b)}$

Solution:

\textbf{Hint:} \text{The viscosity of a liquid depends on intermolecular forces, while} \text{the viscosity of gases depends on molecular movement.} \textbf{Step 1:} \text{Variation of viscosity of liquids with temperature} \text{For liquids: } \eta_{liquid} \propto \frac{1}{\sqrt{T}} \text{Therefore, with increase in temperature, } \eta_{liquid} \text{ decreases.} \textbf{Step 2:} \text{Variation of viscosity of gases with temperature} \text{For gases: } \eta_{gas} \propto \sqrt{T} \text{Therefore, with increase in temperature, } \eta_{gas} \text{ increases.} \textbf{Conclusion:} \text{Statements (c) gases increase and (d) liquids decrease are correct.}

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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
}