Import Question JSON

Current Question (ID: 8125)

Question:

$\text{At } 0^{\circ}\text{C, the density of a certain oxide of a gas at 2 bar is the same as that of dinitrogen at 5 bar.}$ $\text{The molecular mass of the oxide would be -}$

Options:

1. $35 \text{ g/mol}$
2. $45 \text{ g/mol}$
3. $70 \text{ g/mol}$
4. $60 \text{ g/mol}$

Solution:

$\text{Hint: Use density and molecular mass relation.}$ $\text{Step 1: See the density and molecular mass relation.}$ $\text{Density (d) of the substance at temperature (T) can be given by the expression,}$ $d = \frac{MP}{RT}$ $\text{Let density of oxide} = d_1 \text{; density of dinitrogen gas} = d_2$ $\text{Step 2: According to the given question,}$ $d_1 = d_2$ $\text{Therefore,}$ $\frac{M_1P_1}{RT} = \frac{M_2P_2}{RT}$ $\Rightarrow M_1P_1 = M_2P_2$ $\text{Given,}$ $P_1 = 2 \text{ bar}$ $P_2 = 5 \text{ bar}$ $\text{The molecular mass of nitrogen, } M_2 = 28 \text{ g/mol}$ $M_1 = \frac{M_2P_2}{P_1}$ $M_1 = \frac{28 \times 5}{2}$ $M_1 = 70 \text{ g/mol}$

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
}