Molar Entropy Of Water

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{5}A_{51} Base Sequence = 12735 String Sequence = 12735 - 5 - 51 **

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Molar Entropy Of Water

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The molar entropy of ice at 0^{o}C is given as 51.84 J deg^{-1} mole^{-1}.

(a) What is the molar entropy of water at 0^{o}C?

(b) What is the molar entropy of water at 25^{o}C ?

**The strings**:

S_{7}P_{5}A_{51} (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.

(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 0^{o}C = 51.84 + 22 = 73.84 J deg^{-1} mole^{-1}

(b) To obtain the molar entropy of water at 25^{0}, determine increase in entropy due to increase in temperature from 0^{o}C to
25^{o}C (273^{o}K to 298^{o}K)

So increase in entropy = ΔS = ∫_{273}^{298} C_{p}(dT/T).

where T is temperature and C_{p} is heat capacity at constant pressure.

So, ΔS = C_{p}ln(298/273) = 0.0880C_{p}

C_{p} = 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 25^{o}C = 73.84 + 6.63 = 80.47 J deg^{-1} mole^{-1}

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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