Termodinamica 4

what is the correct expression of the Gibbs-Duhem equation?

• $\left[\frac{\partial M}{\partial P}\right]_{T,x}\ dP+\left[\frac{\partial M}{\partial T}\right]_{P,x}\ dT\ +\ \sum_{ }^{ }x_{i\ }d\overline{M_i}$

• $\left[\frac{\partial M}{\partial P}\right]_{P,x}\ dP+\left[\frac{\partial M}{\partial T}\right]_{T,x}\ dT\ +\ \sum_{ }^{ }x_{i\ }d\overline{M_i}$

• $\left[\frac{\partial M}{\partial P}\right]_{T,x}\ dP+\left[\frac{\partial M}{\partial T}\right]_{P,x}\ dT\ =0$

• $\left[\frac{\partial M}{\partial P}\right]_{T,x}\ dP+\left[\frac{\partial M}{\partial T}\right]_{P,x}\ dT\ +\ \sum_{ }^{ }\overline{M_i}\ dx_i$

 $\frac{\Delta G^{excess}}{RT}$  function is located:

• in the negative part of the diagram

• in the positive part of the diagram

• it depends on the shape of the miscibility gap

• in both the positive and the negative part

what is the condition of stability in terms of

 $\frac{\Delta G^{excess}}{RT}$  

•  $\frac{\text{d}^2\left(\frac{^{ }\Delta G^{excess}}{RT}\right)}{\text{d}x_1^2}>-\frac{1}{x_1x_2}$  

•  $\frac{\text{d}^{ }\left(\frac{^{ }\Delta G^{excess}}{RT}\right)}{\text{d}x_1^{ }}>-\frac{1}{x_1x_2}$  

•  $\frac{\text{d}^2\left(\frac{^{ }\Delta G^{excess}}{RT}\right)}{\text{d}x_1^2}<\frac{1}{x_1x_2}$  

•  $\frac{\text{d}^2\left(\frac{^{ }\Delta G^{excess}}{RT}\right)}{\text{d}x_1^2}=-\frac{1}{x_1x_2}$  

Once we know that our partial molar property is

 $\overline{M_i}\ =\ln\gamma_{i\ }$  , applying the Gibbs-Duhem eq. (constant P and T), what it the final result in terms of stability ? 

•  $\frac{\text{d}\ln\gamma_1}{\text{d}x_{1\ }}>-\frac{1}{x_1}$  

•  $\frac{\text{d}\ln\gamma_1}{\text{d}x_{1\ }}>\frac{1}{x_1}$  

•  $\frac{\text{d}\ln\gamma_1}{\text{d}x_{1\ }}<-\frac{1}{x_2}$  

•  $\frac{\text{d}\ln\gamma_1}{\text{d}x_{1\ }}=-\frac{1}{x_1}$  

in order to have stability in our system:

• the derivative of the chemical potential with respect to x1 (reference) must be positive (also in terms of fugacity)

• the derivative of the chemical potential with respect to x1 (reference) must be positive (but not in terms of fugacity)

• the derivative of the chemical potential with respect to x1 (reference) must be negative (also in terms of fugacity)

• the derivative of the chemical potential with respect to x1 (reference) must be equal to zero (also in terms of fugacity)

if we have this situation, what is the way in which the system reach the equilibrium?

• the system tends to move the solute from the left side to the right side

• the system tends to move the solvent from the right side to the left side

• the system tends to move the solvent from the left side to the right side

• the system cannot reach the equilibrium due to the presence of the solute

if we have this system, what is the condition of stability?

•  $\frac{\text{d}f_1}{\text{d}x_1}+\frac{\text{d}f_2}{\text{d}x_2}>0$  

•  $\frac{\text{d}f_2}{\text{d}x_2}>0$  

•  $\frac{\text{d}f_1}{\text{d}x_1}<0$  

•  $\frac{\text{d}f_2}{\text{d}x_1}>0$  

what is the correct expression of the Poynting factor? 

 $\pi\ =\ osmotic\ pressure$  
(il caso fatto in classe)

•  $\frac{f_2\left(P+\pi,x_2\right)}{f_2\left(P.x_2\right)}$  

•  $\frac{f_2\left(P,x_2\right)}{f_1\left(P.x_1\right)}$  

•  $\frac{f_2\left(P-\pi,x_2\right)}{f_2\left(P.x_2\right)}$  

•  $\frac{f_1\left(P+\pi,x_1\right)}{f_1\left(P.x_1\right)}$  

what is the correct expression of the Van't Hoff equation?

• $\frac{\pi V_2}{RT}=x_1$

• $\frac{\pi V_1}{RT}=x_2$

• $\frac{\pi V_2}{RT}=x_1x_2$

• $\pi=x_1RT$

What is the expression of $\frac{\Delta G^{excess}}{RT}$  if we use the Margules equations for a binary system?

•  $\frac{\Delta G^{excess}}{RT}=Ax_1x_{2\ }$  

•  $\frac{\Delta G^{excess}}{RT}=A^2x_1x_{2\ }$  

•  $\frac{\Delta G^{excess}}{RT}=Ax_1+Ax_2$  

•  $\frac{\Delta G^{excess}}{RT}=A>0$