the excess Gibbs free energy

 $\frac{\Delta G^{excess}}{RT}$  is

•  $\sum_i^{ }x_i\ln\gamma_i$  

•  $\sum_i^{ }x_i\ln x_i$  

•  $\sum_i^{ }\gamma_i\ln x_i$  

•  $\sum_i^{ }\gamma_i\ln\gamma_i$  

 $\ln\gamma_i$  is a partial molar property with respect to 

•  $\frac{\Delta G^{excess}}{RT}$  

•  $\frac{\Delta G}{RT}$  

•  $\frac{\Delta H^{excess}}{RT}$  

•  $\frac{\Delta H}{RT}$  

The Gibbs-Duhem equation at constant T and P is

• $\sum_ì^{ }x_i\overline{dM_i}\ =0$

• $\sum_ì^{ }x_i\overline{M_i}\ =0$

• $\sum_ì^{ }\overline{M_i}\ dx_i\ =0$

• $\sum_ì^{ }x_idM_i\ =0$

when liquid and gas phases are both present in reacting system, at equilibrium the reaction must be considered

• to occur in the liquid phase

• to occur in the gas phase

• to occur both in the liquid and in the gas phase

• any possible choice

in the decomposition of CaCO3, the activity of CaO is considered as equal to

• 1

• $x_{CaO}$

• $x_{CaO}y_{CaO}$

• $f_{CaO}$

in an equimolar oil/water mixture at equilibrium, the molar fraction of water

 $x_w$  in the oil phase is

•  $x_w=0$  

•  $x_w<<1$  

•  $x_{w\ }=0.5$  

•  $x_{w\ }=0.25$  

a stability condition of a single-phase binary system is

• $\frac{d\mu_i}{dx_i}>0$

• $\frac{d\mu_i}{dx_i}<0$

• $\frac{d\mu_i}{dx_i}=0$

• $\frac{d\mu_i}{dx_i}=1$

in the reaction

 $NH_{4\left(s\right)}=NH_{3\left(g\right)}+HCl_{\left(g\right)}$  . if  $NH_4$  only is initially present

• the decomposition pressure depends on  $NH_{4\left(s\right)}$  concentration

• there is a given decomposition pressure at a given T

• there is more than one decomposition pressure at a given T

• decomposition cannot take place

Osmotic pressure is caused by

• the flow of a particles through a semipermeable membrane

• the flow of particles through a permeable membrane

• the flow of water through a semipermeable membrane

• the flow of water through a permeable membrane

osmotic pressure is given by

• $\pi=cRT$

• $\pi=nRT$

• $\pi=xRT$

• $\pi V=cRT$