Question

The latent heat of evaporation of water is $2\cdot 26$ KJ per gram at 1 atm and $100{}^\circ C$. Calculate the entropy change for evaporation of 1 mole of water at $100{}^\circ C$.

Answer 1

Latent heat of evaporation of water is the heat or amount of energy required to transform one mole of water into its gaseous state. It is also known as the latent heat of vaporization or enthalpy of vaporization. Entropy is a measure of randomness or molecular disorder; it is given by a system's thermal energy per temperature.
Formula Used: $\Delta S=\dfrac{\Delta H}{T}$
where $\Delta S$ is change in entropy
$\Delta H$ is enthalpy change or latent heat of evaporation
T is temperature in kelvin

Complete Step By Step Solution:
The latent heat of evaporation is given as$2\cdot 26$KJ/g which is equal to 2260J/g as the conversion of 1KJ = 1000J. We need to find the entropy change for 1 mole so we need to find the latent heat of evaporation for 1 mole.
Molar mass of water
$\begin{aligned} & ({{H}_{2}}O)=2\times 1+16 \\\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=18g \\\ \end{aligned}$
Latent heat of evaporation for 1g is 2260J and for 18g or 1 mole is $2260\times 18=40680J$/mol
So the entropy change for evaporation of 1 mole of water at $100{}^\circ C$ will be given by $\Delta S=\dfrac{\Delta H}{T}$
Given temperature is$100{}^\circ C$, converting it into kelvin we get- $100+273=373K$
Using the above formula for entropy we get, $\Delta S=\dfrac{40680J/mol}{373K}=109.06Jmo{{l}^{-1}}{{K}^{-1}}$

Additional Information:
Entropy is known as the measure or degree of randomness. It basically tells us about the evenly distribution of energy in a system. The entropy of the universe tends to increase because it depicts the spread of energy and energy in the universe spreads as much as possible. Entropy is an extensive property i.e. it is a property which changes with the sample’s size. For a reversible process there is no change in entropy but for irreversible processes entropy always tends to increase.

Note: The entropy can be increased by increasing the temperature because temperature imparts more energy to the molecules which result in disordering and hence leads to increase in entropy. Entropy can also be found in the units of calorie per mole per kelvin instead of joule per mole per kelvin for 1 mole of substance. The relation between calorie and joule is such that, 1 calorie $=4\cdot 18$ joules. So, the above change in entropy in calories will be given as $26\cdot 09\text{cal}\,\text{mo}{{\text{l}}^{-1}}\,{{K}^{-1}}$.