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From Atkins' Physical Chemistry, 8th Edition. Problem 3.1.

Calculate the difference in molar entropy (a) between liquid water and ice at -5 degrees C, (b) between liquid water and its vapour at 95 degrees C and 1.00 atm. The differences in heat capacities on melting and on vaporization are 37.3 J/K*mol and -41.9 J/K*mol, respectively. Distinguish between the entropy changes of the sample, the surroundings, and the total system, and discuss the spontaneity of the transitions at the two temperatures.

(1) [tex]\Delta S = \frac{\Delta_{fus}H}{T}[/tex]

(2) [tex]\Delta S_{trs} = \frac{\Delta_{trs}H}{T_{trs}}[/tex]

(3) [tex]S(T_f)=S(T_i) + C_p ln(\frac{T_f}{T_i})[/tex]

where [tex]C_p[/tex] is the Heat Capacity at constant pressure.

The problem I am having is that I don't understand what the question is asking. It gives me the differences in heat capacity, but the temperature doesn't seem to be changing. The given heat capacities seems to imply that I should use equation three, but if I use the constant temperature the [tex]\Delta S[/tex] goes to zero, which is wrong.

Alternatively, I think I could use equation 2 by using the molar heat of fusion (and vaporization) and then just dividing by the temperature. But I don't understand how the phase transition can occur at the temperatures given.

Can someone help me understand what this question is asking for?

## Homework Statement

From Atkins' Physical Chemistry, 8th Edition. Problem 3.1.

Calculate the difference in molar entropy (a) between liquid water and ice at -5 degrees C, (b) between liquid water and its vapour at 95 degrees C and 1.00 atm. The differences in heat capacities on melting and on vaporization are 37.3 J/K*mol and -41.9 J/K*mol, respectively. Distinguish between the entropy changes of the sample, the surroundings, and the total system, and discuss the spontaneity of the transitions at the two temperatures.

## Homework Equations

(1) [tex]\Delta S = \frac{\Delta_{fus}H}{T}[/tex]

(2) [tex]\Delta S_{trs} = \frac{\Delta_{trs}H}{T_{trs}}[/tex]

(3) [tex]S(T_f)=S(T_i) + C_p ln(\frac{T_f}{T_i})[/tex]

where [tex]C_p[/tex] is the Heat Capacity at constant pressure.

## The Attempt at a Solution

The problem I am having is that I don't understand what the question is asking. It gives me the differences in heat capacity, but the temperature doesn't seem to be changing. The given heat capacities seems to imply that I should use equation three, but if I use the constant temperature the [tex]\Delta S[/tex] goes to zero, which is wrong.

Alternatively, I think I could use equation 2 by using the molar heat of fusion (and vaporization) and then just dividing by the temperature. But I don't understand how the phase transition can occur at the temperatures given.

Can someone help me understand what this question is asking for?

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