Oil/water partitioning of drugs. In the process of...

Oil/water partitioning of drugs. In the process of partitioning of a drug from oil into water, $\Delta s^{*}=$ $-50 \mathrm{cal} \mathrm{deg}^{-1} \mathrm{~mol}^{-1}$ and $\Delta h^{*}=0$ at $T=300 \mathrm{~K}$. (a) What is $\Delta \mu^{*}$ at $T=300 \mathrm{~K}$ ? (b) What is the partition coefficient from oil to water, $K_{\mathrm{oll}}^{\text {water }}$ at $T=300 \mathrm{~K} ?$ (c) Assume that $\Delta s^{*}$ and $\Delta h^{*}$ are independent of temperature. Calculate $K_{0}^{W}$ at $T=320 \mathrm{~K}$.

Oil/water partitioning of drugs. In the process of partitioning of a drug from oil into water, $\Delta s^{*}=$ $-50 \mathrm{cal} \mathrm{deg}^{-1} \mathrm{~mol}^{-1}$ and $\Delta h^{*}=0$ at $T=300 \mathrm{~K}$.
(a) What is $\Delta \mu^{*}$ at $T=300 \mathrm{~K}$ ?
(b) What is the partition coefficient from oil to water, $K_{\mathrm{oll}}^{\text {water }}$ at $T=300 \mathrm{~K} ?$
(c) Assume that $\Delta s^{*}$ and $\Delta h^{*}$ are independent of temperature. Calculate $K_{0}^{W}$ at $T=320 \mathrm{~K}$.

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Key Concepts

Gibbs Free Energy Change

This concept involves the energy available to do work during a process at constant temperature and pressure. It is defined by the relation ?G = ?H ? T?S. In partitioning processes, the free energy change determines the direction and extent of the transfer between phases. Even when the enthalpy change is zero, the entropy term can drive the process by contributing to the free energy change.

Partition Coefficient

The partition coefficient is a measure of how a compound distributes itself between two immiscible phases (commonly oil and water) at equilibrium. It is defined as the ratio of the concentrations of the compound in the two phases and is related to the difference in chemical potential between the phases by an exponential relationship, typically expressed as K = exp(???/RT).

Temperature Dependence of Equilibrium (van't Hoff Equation)

The van’t Hoff equation describes how the equilibrium constant, or partition coefficient in this context, changes with temperature. When ?H and ?S are assumed to be temperature-independent, this relationship shows that an increase in temperature will affect the equilibrium constant according to the free energy change ?G = ?H ? T?S, with implications on the partitioning behavior of the drug.

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