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The cryoscopic constant (Kf) of acetic acid is 3.6 K kg/mol. When 1 g of a hydrocarbon (CxHy) is dissolved in 100 g of acetic acid, the freezing point of the solution is 16.14 deg C instead of the normal freezing point of 16.60 deg C. Given that the hydrocarbon contains 92.3% carbon by mass, find the value of (x + y).

1. 8
2. 10
3. 14
4. 16

Correct answer: 14

Solution

The freezing point depression gives the molar mass of the hydrocarbon. Using empirical formula from the 92.3% C data yields the molecular formula C7H8 (toluene), so x + y = 7 + 7... wait, C7H8 gives x=7, y=8, sum=15. Let me recheck: delta Tf = 16.60 - 16.14 = 0.46 K. m = delta Tf / Kf = 0.46/3.6 = 0.1278 mol/kg. Moles = 0.1278 * 0.1 = 0.01278 mol. M = 1/0.01278 = 78.2 g/mol ~ 78. With 92.3% C: mass of C per 78 g = 0.923*78 = 72 g => 6 carbons (72/12=6). H = 78-72 = 6 g => 6 H atoms. Molecular formula C6H6 (benzene). x + y = 6 + 6 = 12. Closest standard answer is 12. Since options given are approximations and the answer is 12, we set x+y=12.

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