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Current Question (ID: 11126)

Question:

$\text{An ideal gas is initially at temperature } T \text{ and volume } V. \text{ Its volume increases by } \Delta V \text{ due to an increase in temperature } \Delta T, \text{ pressure remaining constant. The quantity } \delta = \frac{\Delta V}{(V \Delta T)} \text{ varies with temperature as:}$

Options:

1. $\text{Graph 1}$
2. $\text{Graph 2}$
3. $\text{Graph 3}$ (Correct)
4. $\text{Graph 4}$

Solution:

$\text{From the ideal gas equation } PV = RT \text{ (for one mole) .....(i) and at constant pressure, we have } P \Delta V = R \Delta T \text{ .....(ii). Dividing equation (ii) by equation (i) we get } \frac{P \Delta V}{PV} = \frac{R \Delta T}{RT} \implies \frac{\Delta V}{V} = \frac{\Delta T}{T} \implies \frac{\Delta V}{V \Delta T} = \frac{1}{T}. \text{ Since } \delta = \frac{\Delta V}{(V \Delta T)} \text{, we have } \delta = \frac{1}{T}. \text{ This shows an inverse relationship between } \delta \text{ and } T, \text{ which is the equation of a rectangular hyperbola. Hence, graph 3 is the correct representation.}$

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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
}