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Current Question (ID: 21416)

Question:

$\text{On mixing, heptane, and octane form an ideal solution at 373 K, the vapor pressures of the two liquid components (Heptane and octane) are 105 kPa and 45 kPa respectively.}$ $\text{Vapour pressure of the solution obtained by mixing 25.0 g of heptane and 35 g of octane will be:}$ $\text{(molar mass of heptane = 100 g mol}^{-1}\text{ and of octane =114 g mol}^{-1}\text{)}$

Options:

1. $144.5 \text{ kPa}$
2. $72.0 \text{ kPa}$
3. $36.1 \text{ kPa}$
4. $96.2 \text{ kPa}$

Solution:

$\text{Hint: } P_T = P^\circ_{\text{heptane}} X_{\text{(mole fraction of heptane)}} + P^\circ_{\text{octane}} X_{\text{(mole fraction of octane)}}$ $\text{Step 1:}$ $P_T = P_{\text{heptane}} + P_{\text{octane}}$ $P = P^\circ X \text{(mole fraction)}$ $P_T = P^\circ_{\text{heptane}} X_{\text{(mole fraction of heptane)}} + P^\circ_{\text{octane}} X_{\text{(mole fraction of octane)}}$ $\text{Step 2:}$ $= 105 \times \frac{25}{100} + 45 \times \left(1 - X_{\text{heptane}}\right)$ $= 105 \times \frac{25}{25 + 35} + 45 \times \left(1 - 0.45\right)$ $= 105 \times 0.25 + 45 \times (1 - 0.45)$ $= 47.2 + 24.8$ $= 72 \text{ kPa}$ $\text{Thus, option second is the correct answer.}$

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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
}