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Current Question (ID: 18118)

Question:

$\text{A pair of isotonic solutions, among the following, is (assuming temperature to be the same):}$ $1.\ 0.1\ \text{(M) urea and}\ 0.1\ \text{(M) NaCl}$ $2.\ 0.1\ \text{(M) urea and}\ 0.2\ \text{(M) MgCl}_2$ $3.\ 0.1\ \text{(M) NaCl and}\ 0.1\ \text{(M) Na}_2\text{SO}_4$ $4.\ 0.1\ \text{(M) Ca(NO}_3)_2\ \text{and}\ 0.1\ \text{(M) Na}_2\text{SO}_4$

Options:

1. $0.1\ \text{(M) urea and}\ 0.1\ \text{(M) NaCl}$
2. $0.1\ \text{(M) urea and}\ 0.2\ \text{(M) MgCl}_2$
3. $0.1\ \text{(M) NaCl and}\ 0.1\ \text{(M) Na}_2\text{SO}_4$
4. $0.1\ \text{(M) Ca(NO}_3)_2\ \text{and}\ 0.1\ \text{(M) Na}_2\text{SO}_4$

Solution:

$\text{Hint: Isotonic solutions have same osmotic pressure.}$ $\text{Step 1:}$ $\text{Isotonic solution has same osmotic pressure. The formula of osmotic pressure is}$ $\pi = iCRT$ $\text{Here, C, R and T are constant. Hence, } \pi \propto i$ $\text{Step 2:}$ $\text{Those substances have same } i \text{ value then the osmotic pressure is also same.}$ $\text{As the number of ionic species produced after complete dissociation of } 0.1\ \text{(M) Ca(NO}_3)_2 \text{ and } 0.1\ \text{(M) Na}_2\text{SO}_4 \text{ are same. Hence, they are isotonic solution.}$

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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
}