At the aqueous solubility of heptane ( )

PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Thermodynamic potentials and the formal structure of thermodynamics

Soft Matter at the Thermal Scale, Ch Amphiphiles and self-assembly

Problem

At 298 K298\,\mathrm{K} the aqueous solubility of heptane (C7H16\mathrm{C_7H_{16}}), expressed as a mole fraction, is X7=5.0×10−6X_7 = 5.0\times10^{-6}, and that of undecane (C11H24\mathrm{C_{11}H_{24}}) is X11=1.33×10−8X_{11} = 1.33\times10^{-8}. Undecane has four more CH2\mathrm{CH_2} groups in its tail than heptane. Treating each solute as dilute in water, so that its chemical potential is μ=μ∘+kBTln⁡X\mu = \mu^\circ + k_BT\ln X, and assuming the standard chemical potential μ∘\mu^\circ changes by the same amount for each added CH2\mathrm{CH_2} group, estimate the free energy change per CH2\mathrm{CH_2} group on transferring a tail out of water, in units of kBTk_BT and in kJ mol−1\mathrm{kJ\,mol^{-1}}.

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