Import Question JSON

Current Question (ID: 18984)

Question:

$\text{In Vander Wall's equation } \left[ P + \frac{a}{V^2} \right] \left[ V - b \right] = RT; \ P \text{ is pressure, } V \text{ is volume, } R \text{ is universal gas constant and } T \text{ is temperature. The ratio of constants } \frac{a}{b} \text{ is dimensionally equal to:}$

Options:

1. $\frac{P}{V}$
2. $\frac{V}{P}$
3. $PV$
4. $PV^3$

Solution:

$\text{The dimensional formula of } a \text{ is } \left[ M^1L^5T^{-2} \right]$ $\text{The dimensional formula of } b \text{ is } \left[ L^3 \right]$ $\text{Therefore, the dimensional formula of } \frac{a}{b} \text{ is } \left[ M^1L^2T^{-2} \right]$ $\text{This is dimensionally equal to pressure } P$ $\text{Thus, the correct answer is } PV$

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
}