Import Question JSON

Current Question (ID: 8795)

Question:

$\text{For a real gas the equation of gas is given by;}$ $\left(P + \frac{an^2}{V^2}\right)(V - bn) = nRT. \text{ If symbols have their usual meaning, then the dimensions of } \frac{V^2}{an^2} \text{ is same as that of:}$

Options:

1. $\text{compressibility}$
2. $\text{bulk modulus}$
3. $\text{viscosity}$
4. $\text{energy density}$

Solution:

[P] = \left[\frac{an^2}{V^2}\right] = \text{dimension of bulk modulus} \text{So, } \frac{V^2}{an^2} \text{ has dimension of compressibility.}

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
}