Question 1 The osmotic pressure (π) of a solution is given by −RT ln xA =...

Question 1

The osmotic pressure (π) of a solution is given by −RT ln xA = πVm where Vm is the molar volume of the pure solvent, and xa is the mole fraction of the solvent. Show that in the case of a dilute solution RT xB ≈ πVm where xB is the mole fraction of the solute. Remember that the mole fractions of the solute and the solvent need to add up to 1.

Question 2

The following expression is known as the Butler-Volmer equation, and it is used in elec- 46 CHAPTER 3. SERIES trochemistry to describe the kinetics of an electrochemical reaction controlled solely by the rate of the electrochemical charge transfer process. j = j0(e (1−α)f η − e −αf η), 0 < α < 1 and f > 0, η > 0 Show that j ≈ j0fη when fη << 1.

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