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Current Question (ID: 18069)

Question:

$\text{Heptane and octane form an ideal solution. At 373 K, the vapour pressures of the two liquid components are 105.2 kPa and 46.8 kPa respectively. The vapour pressure of a mixture of 26.0 g of heptane and 35 g of octane would be:}$

Options:

1. $43.45 \text{ kPa}$
2. $78.96 \text{ Pa}$
3. $73.43 \text{ kPa}$
4. $65.72 \text{ Pa}$

Solution:

$\text{Hint: Use Raoult's law}$ $\text{Step 1:}$ $\text{Vapour pressure of heptane } (p_1^0) = 105.2 \text{ kPa}$ $\text{Vapour pressure of octane } (p_2^0) = 46.8 \text{ kPa}$ $\text{Number of moles of heptane} = \frac{26}{100} \text{ mol} = 0.26 \text{ mol}$ $\text{Number of moles of octane} = \frac{35}{114} \text{ mol} = 0.31 \text{ mol}$ $\text{Mole fraction of heptane, } x_1 = \frac{0.26}{0.26+0.31} = 0.456$ $\text{And, mole fraction of octane, } x_2 = 1 - 0.456 = 0.544$ $\text{Step 2:}$ $\text{Now, partial pressure of heptane, } P_1 = x_1 p_1^0$ $= 0.456 \times 105.2$ $= 47.97 \text{ kPa}$ $\text{Partial pressure of octane, } P_2 = x_2 p_2^0$ $= 0.544 \times 46.8$ $= 25.46 \text{ kPa}$ $\text{Hence, vapour pressure of solution, } P_{\text{total}} = P_1 + P_2 = 47.97 + 25.46 = 73.43 \text{ kPa}$

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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
}