Acetic acid can form a dimer (CH3CO2H)2 in gas phase. The dimer of acetic acid is held together by H-bonds. If at 27°C, the equilibrium constant for dimerization is e10 and |∆S°| for dimerization is y cal/K, then the value of y10 is ________.Given : Hydrogen bond enthalpy =−7.5 kcal/mol, R = 2 cal mole–1 K–1.

(30)ΔrG°=−15000−300(−y)=−2×300lne10Sol. 2CH3CO2H⇌(CH3CO2H)2 ΔrH°=−7.5×2 kcal/mol=−15 kcal/mol ΔrS°=−y cal/K −15000+300y=−6000 300y=9000,y=9000300=30,y10=3

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Acetic acid can form a dimer (CH₃CO₂H)₂in gas phase. The dimer of acetic acid is held together by H-bonds. If at 27°C, the equilibrium constant for dimerization is e¹⁰ and | $∆$ S°| for dimerization is y cal/K, then the value of $\frac{y}{10}$ is ________.Given : Hydrogen bond enthalpy $= - 7.5 k c a l / m o l$ , R = 2 cal mole^–1 K^–1.

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answer is 3.

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Detailed Solution

(30) $Δ_{r} G ° = - 15000 - 300 (- y) = - 2 \times 300 \ln e^{10}$
Sol.    $2 C H_{3} C O_{2} H ⇌ {(C H_{3} C O_{2} H)}_{2}$
   $Δ_{r} H ° = - 7.5 \times 2 k c a l / m o l = - 15 k c a l / m o l$
   $Δ_{r} S ° = - y c a l / K$
   $- 15000 + 300 y = - 6000$
$300 y = 9000,$ $y = \frac{9000}{300} = 30, \frac{y}{10} = 3$