Molar Entropy Of Water
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Molar Entropy Of Water

Phase Diagram Of Water

The molar entropy of ice at 0oC is given as 51.84 J deg-1 mole-1.

(a) What is the molar entropy of water at 0oC?
(b) What is the molar entropy of water at 25oC ?

The strings:

S7P5A51 (Change - Physical Change)

The math:
Pj Problem of Interest is of type change (physical change). Entropy is a state variable and the problem of interest is a change in entropy (ΔS). Phase changes are physical changes hence the change is physical change.

Phase Diagram of Water

(a) Heat of fusion during the melting of one mole of ice = 6010 J deg-1
So, system absorbs 6010 J deg-1 without change in temperature.
So, entropy increases by 6010/273.15 = 22 J deg-1 mole-1
where 273.15 is from the Kelvin temperature scale.
So, molar entropy of water at 0oC = 51.84 + 22 = 73.84 J deg-1 mole-1

(b) To obtain the molar entropy of water at 250, determine increase in entropy due to increase in temperature from 0oC to 25oC (273oK to 298oK)
So increase in entropy = ΔS = ∫273298 Cp(dT/T).
where T is temperature and Cp is heat capacity at constant pressure.
So, ΔS = Cpln(298/273) = 0.0880Cp
Cp = 75.3 J deg-1 mole-1 (from commonly available heat capacity /specific heat table).
So, ΔS = 0.0880 x 75.3 = 6.63.
So, molar entropy of water at 25oC = 73.84 + 6.63 = 80.47 J deg-1 mole-1

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