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16 Nov 2019
Boiling point elevation: Colligative properties depend upon the number of solute particles present in a solution, not so much upon their identity. In this problem, we shall derive relations for the boiling point elevation and freezing point depression. In each case, assume that solute B is dissolved in solvent A. Let T* denote either the normal boiling point (in 1) or freezing point (in 2) of pure A. Assuming that the chemical potential of the solvent A in the gas phase is mu_A(g) = mu*_A(g) such at there is no solute in the gas-phase and that A forms an ideal solution with B, use the Gibbs-Helmholtz equation to relate the mole fraction of A to boiling point of the AB solution. Finally, linearize your final equation to show that delta T approximately equal to RT*_2/delta vap H * x_B = K_bb where Kb is the boiling point constant and b is the molality of the solute.
Boiling point elevation: Colligative properties depend upon the number of solute particles present in a solution, not so much upon their identity. In this problem, we shall derive relations for the boiling point elevation and freezing point depression. In each case, assume that solute B is dissolved in solvent A. Let T* denote either the normal boiling point (in 1) or freezing point (in 2) of pure A. Assuming that the chemical potential of the solvent A in the gas phase is mu_A(g) = mu*_A(g) such at there is no solute in the gas-phase and that A forms an ideal solution with B, use the Gibbs-Helmholtz equation to relate the mole fraction of A to boiling point of the AB solution. Finally, linearize your final equation to show that delta T approximately equal to RT*_2/delta vap H * x_B = K_bb where Kb is the boiling point constant and b is the molality of the solute.