Import Question JSON

Current Question (ID: 20825)

Question:

$\text{Calculate the molality of 500 mL solution of } \text{CuSO}_4 \text{ having density of } 1.25 \text{ g mL}^{-1} \text{ and having molarity } 2 \times 10^{-1} \text{ M at } 32^\circ \text{C.}$ $\text{What is the value of } x \text{ if the molality calculated is } x \times 10^{-2} \text{ molal?}$

Options:

1. $16$
2. $19$
3. $25$
4. $50$

Solution:

$\text{Hint: Molarity } = \frac{n_{\text{CuSO}_4}}{V_{\text{sol}}^n}$ $\text{Molarity } = 0.2 = \frac{n_{\text{CuSO}_4}}{V_{\text{sol}}^n}$ $\Rightarrow n_{\text{CuSO}_4} = 0.2 \times \frac{500}{1000} = 0.1$ $\text{mass of solution } = 1.25 \times 500 = 625 \text{ g}$ $\text{mass of solvent } = 625 - 0.1 \times (159.5) = 609.05 \text{ g}$ $\text{Molality } = \frac{n_{\text{CuSO}_4}}{m_{\text{solvent}} \text{ (in kg)}}$ $= \frac{0.1 \times 1000}{609.05}$ $= 0.164$ $= 16.4 \times 10^{-2}$ $\text{So, } x \simeq 16$

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
}