Import Question JSON

Current Question (ID: 18072)

Question:

$\text{The vapour pressure of water in the solution having 50 g of urea dissolved in 850 g of water is-}$ $\text{(Vapor pressure of pure water at 298 K is 23.8 mm Hg)}$

Options:

1. $23.40 \text{ mm of Hg}$
2. $33.46 \text{ mm of Hg}$
3. $12.76 \text{ mm of Hg}$
4. $87.12 \text{ mm of Hg}$

Solution:

$\text{Hint: } \frac{p_1^0 - p_1}{p_1^0} = \frac{n_2}{n_1 + n_2}$ $\text{Step 1: It is given the vapour pressure of water, } p_1^0 = 23.8 \text{ mm of Hg}$ $\text{Weight of water taken, } w_1 = 850 \text{ g}$ $\text{Weight of urea taken, } w_2 = 50 \text{ g}$ $\text{The molecular weight of water, } M_1 = 18 \text{ g mol}^{-1}$ $\text{Molecular weight of urea, } M_2 = 60 \text{ g mol}^{-1}$ $\text{Step 2: Now we have to calculate the vapour pressure of water in the solution. We take vapour pressure as } p_1$ $\frac{p_1^0 - p_1}{p_1^0} = \frac{w_2}{M_2} \cdot \frac{M_1}{w_1}$ $\Rightarrow \frac{23.8 - p_1}{23.8} = \frac{50}{60} \cdot \frac{18}{850}$ $\Rightarrow \frac{23.8 - p_1}{23.8} = 0.0173$ $\Rightarrow 23.8 - p_1 = 0.41234$ $\Rightarrow p_1 = 23.4 \text{ mm of Hg}$ $\text{So, the vapour pressure of water in the solution is 23.4 mm of Hg}$

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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
}