Import Question JSON

Current Question (ID: 11122)

Question:

$\text{PV versus T graphs of equal masses of } \text{H}_2, \text{He} \text{ and } \text{O}_2 \text{ are shown in the figure. Choose the correct alternative:}$

Options:

1. $\text{A corresponds to } \text{H}_2, \text{ B to } \text{He} \text{ and C to } \text{O}_2$
2. $\text{A corresponds to } \text{He}, \text{ B to } \text{H}_2, \text{ and C to } \text{O}_2$
3. $\text{A corresponds to } \text{He}, \text{ B to } \text{O}_2, \text{ and C to } \text{H}_2$
4. $\text{A corresponds to } \text{O}_2, \text{ B to } \text{He} \text{ and C to } \text{H}_2$ (Correct)

Solution:

$\text{From the ideal gas equation } PV = nRT, \text{ where } n \text{ is the number of moles. The number of moles can be expressed as } n = \frac{m}{M}, \text{ where } m \text{ is the mass and } M \text{ is the molar mass. Substituting this into the ideal gas equation, we get } PV = \frac{m}{M}RT. \text{ Rearranging for the relationship shown in the graph, we get } \frac{PV}{T} = \frac{mR}{M}. \text{ Since the masses } (m) \text{ of all the gases are equal and } R \text{ is the universal gas constant, we have } \frac{PV}{T} \propto \frac{1}{M}. \text{ This means that the slope of the } PV \text{ versus } T \text{ graph, which is equal to } \frac{PV}{T}, \text{ is inversely proportional to the molar mass } (M). \text{ From the graph, the slopes are in the order } \text{Slope}_A < \text{Slope}_B < \text{Slope}_C. \text{ This implies that } \left( \frac{PV}{T} \right)_A < \left( \frac{PV}{T} \right)_B < \left( \frac{PV}{T} \right)_C. \text{ Based on the inverse relationship, the molar masses are in the order } M_A > M_B > M_C. \text{ The molar masses of the given gases are: } M_{\text{O}_2} \approx 32 \frac{g}{mol}, M_{\text{He}} \approx 4 \frac{g}{mol}, \text{ and } M_{\text{H}_2} \approx 2 \frac{g}{mol}. \text{ The order of molar masses is } M_{\text{O}_2} > M_{\text{He}} > M_{\text{H}_2}. \text{ Therefore, curve A corresponds to } \text{O}_2, \text{ curve B to } \text{He}, \text{ and curve C to } \text{H}_2. \text{ This corresponds to option 4.}$

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
}