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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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