Solution Thermodynamics Questions and Answers

Answer: A

The definition holds temperature, pressure and the amounts of the other components fixed while one is varied. It is generally not equal to the pure component value, and the difference is what makes a solution non-ideal.

Answer: B

Adding magnesium sulphate to water contracts the solution, so its partial molar volume is negative even though the salt itself occupies space. Partial molar quantities describe the response of the mixture, not the size of the molecule.

Answer: C

Correct answer: partial molar Gibbs energy

\[ \mu_i = \bar{G}_i = \left(\frac{\partial (nG)}{\partial n_i}\right)_{T,P,n_j}. \] The identity holds for the Gibbs energy alone among the thermodynamic potentials, and it is what makes chemical potential the working criterion for equilibrium - equality of \( \mu_i \) across phases is what phase equilibrium means.

Answer: D

Both are true and the reason gives the argument: as long as a transfer can lower the Gibbs energy the system is not at its minimum, so equilibrium requires the potentials to be equal for every component in every phase.

Answer: A

It follows from the fact that the property is first order homogeneous in the amounts, and it is what makes partial molar properties useful rather than merely definable. The pure component sum is the ideal solution approximation instead.

Answer: B

For a binary at fixed temperature and pressure it links the two composition derivatives, so knowing one partial molar property across the range determines the other. It is the basis of every thermodynamic consistency test.

Answer: C

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: the Gibbs–Duhem equation relates the composition derivatives of the partial molar properties, and because it must be satisfied it serves as a consistency test on measured activity coefficient data. Statement 3 is wrong - it is derived from the fundamental relations and holds for any solution whatever, which is precisely why it can be used as a test of real data.

Answer: D

The Lewis-Randall rule states this proportionality with the pure component fugacity as the constant, and every ideal solution property follows from it. Molar mass has nothing to do with ideality. Chemical similarity is what matters in practice.

Answer: A

The first two vanish because ideal mixing changes no interactions, while the entropy rises simply from the greater number of arrangements. That entropy is what makes the Gibbs energy of mixing negative and mixing spontaneous.

Answer: B

Correct answer: False

The entropy of mixing for an ideal solution is \[ \Delta S^{mix} = -R\sum x_i\ln x_i, \] which is always positive, since every mole fraction is less than one. It is the *enthalpy* and *volume* of mixing that vanish for an ideal solution. The non-zero entropy is what drives mixing in the first place, and it is why the ideal Gibbs energy of mixing is negative.