Import Question JSON

Current Question (ID: 19719)

Question:

$\text{Two moles of helium gas are mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of the mixture at constant volume?}$ $\left( R = 8.3 \text{ J/mol K} \right)$

Options:

1. $21.6 \text{ J/mol K}$
2. $19.7 \text{ J/mol K}$
3. $15.7 \text{ J/mol K}$
4. $17.4 \text{ J/mol K}$

Solution:

$\text{Hint: } (C_v)_{\text{mix}} = \frac{n_1C_{v1} + n_2C_{v2}}{n_1 + n_2}$ $\left( C_v \right)_{\text{mix}} = \frac{n_1C_{v1}}{n_1} + \frac{n_2C_{v2}}{n_2}$ $= \left( 2 \right) \left[ \frac{fR}{2} \right]_{\text{mono}} + 3 \left[ \frac{fR}{2} \right]_{\text{diatomic}}$ $= \frac{2 \left( \frac{3R}{2} \right) + 3 \left( \frac{5R}{2} \right)}{5}$ $= \frac{21R}{10}$ $= \frac{21 \times 8.3}{10}$ $= 17.4 \text{ J/mol K}$

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
}