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Solutions question

2010 · Shift 0 · Q22
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Solutions question

2010 · Shift 0 · Q22

JEE MainChemistrySolutionsMCQ+4 / −1
On mixing, heptane and octane form an ideal solution. At 373 K, the vapour pressures of the two liquid components (heptane and octane) are 105 kPa and 45 kPa respectively. Vapour pressure of the solution obtained by mixing 25.0g of heptane and 35 g of octane will be (molar mass of heptane = 100 g mol–1 and of octane = 114 g mol–1)
  1. A
    72.0 kPa
  2. B
    36.1 kPa
  3. C
    96.2 kPa
  4. D
    144.5 kPa
View written solutionFree

Correct answer: A

  1. Use Raoult’s law for an ideal solution

For a binary ideal solution, Ptotal=xheptanePheptane0+xoctanePoctane0P_{\text{total}}=x_{\text{heptane}}P^0_{\text{heptane}}+x_{\text{octane}}P^0_{\text{octane}}Ptotal​=xheptane​Pheptane0​+xoctane​Poctane0​

Given:

  • Pheptane0=105 kPaP^0_{\text{heptane}}=105\,\text{kPa}Pheptane0​=105kPa
  • Poctane0=45 kPaP^0_{\text{octane}}=45\,\text{kPa}Poctane0​=45kPa
  1. Calculate moles of each component

For heptane: nheptane=25.0100=0.25 moln_{\text{heptane}}=\frac{25.0}{100}=0.25\,\text{mol}nheptane​=10025.0​=0.25mol

For octane: noctane=35114=0.307 moln_{\text{octane}}=\frac{35}{114}=0.307\,\text{mol}noctane​=11435​=0.307mol

  1. Calculate mole fractions in liquid phase

Total moles: ntotal=0.25+0.307=0.557 moln_{\text{total}}=0.25+0.307=0.557\,\text{mol}ntotal​=0.25+0.307=0.557mol

Mole fraction of heptane: xheptane=0.250.557≈0.449x_{\text{heptane}}=\frac{0.25}{0.557}\approx 0.449xheptane​=0.5570.25​≈0.449

Mole fraction of octane: xoctane=0.3070.557≈0.551x_{\text{octane}}=\frac{0.307}{0.557}\approx 0.551xoctane​=0.5570.307​≈0.551

  1. Apply Raoult’s law

Ptotal=(0.449)(105)+(0.551)(45)P_{\text{total}}=(0.449)(105)+(0.551)(45)Ptotal​=(0.449)(105)+(0.551)(45)

Ptotal=47.145+24.795P_{\text{total}}=47.145+24.795Ptotal​=47.145+24.795

Ptotal≈71.94 kPaP_{\text{total}}\approx 71.94\,\text{kPa}Ptotal​≈71.94kPa

So, Ptotal≈72.0 kPaP_{\text{total}}\approx 72.0\,\text{kPa}Ptotal​≈72.0kPa

  1. Evaluate options
  • A: 72.0 kPa72.0\,\text{kPa}72.0kPa ✅
  • B: 36.1 kPa36.1\,\text{kPa}36.1kPa ❌
  • C: 96.2 kPa96.2\,\text{kPa}96.2kPa ❌
  • D: 144.5 kPa144.5\,\text{kPa}144.5kPa ❌

Therefore, the correct option is A.

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