Question

1)The Gibbs energy of liquid water is more sensitive to the change of temperature at constant pressure than Ice I. Briefly explain. 2) The Gibbs energy of nitrogen gas is more sensitive to the change of pressure at constant temperature than liquid nitrogen. Briefly explain.

Answer 1

Solution

1)

According to the Gibbs-Helmholtz equation, the relationship between Gibbs free energy and the change in temperature at constant pressure is as

(dG/dT)_p = -S

From this equation, it is clear that sharpness of the decrease of Gibbs free energy decreases with temperature at constant pressure is determined by the entropy of the system. As we know that order of entropy is as

Gas > liquid >solid

So, the sensivity of Gibbs free energy with changes in temperature is greatest for the gas, then liquid, then solid. Therefore, the Gibbs energy of liquid water (having more entropy) is more sensitive to the change of temperature at constant pressure than Ice (having less entropy).

2)

According to the Gibbs-Helmholtz equation, the relationship between Gibbs free energy and the change of pressure at constant temperature is as

(dG/dP)_T = V

From this equation, it is clear that V is positive, then Gibbs free energy always increases when the pressure increases at constant temperature. Thus, the sensitivity of Gibbs free energy to changes in pressure is greatest for gases. Therefore, the Gibbs energy of nitrogen gas is more sensitive to the change of pressure at constant temperature than liquid nitrogen.