Import Question JSON

Current Question (ID: 19693)

Question:

$\text{A cylinder of a fixed capacity of } 44.8 \text{ litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of the gas in the cylinder by } 20.0^{\circ}\text{C will be:}$ $\text{(Given: gas constant } R = 8.3 \text{ JK}^{-1}\text{mol}^{-1})$

Options:

1. $249 \text{ J}$
2. $415 \text{ J}$
3. $498 \text{ J}$
4. $830 \text{ J}$

Solution:

$\text{Hint: } Q = nC_V\Delta T$ $\text{Step 1: Find the number of moles.}$ $\text{Given that the volume of the gas occupied is constant and equal to } 44.8\text{L.}$ $22.4 \text{ L of gas at STP contains 1 mole of gas, therefore } 44.8 \text{ L of gas at STP contains 2 moles of gas.}$ $\text{Step 2: Find the amount of heat needed to raise the temperature of the gas.}$ $\Delta Q = nC_V\Delta T = 2 \times \frac{3}{2} R(20)$ $= 2 \times \frac{3}{2} \times 8.31 \times 20$ $= 6 \times 83.1$ $= 498.6 \text{ J}$

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
}