Question

The internal energy change (in J) when \[90{\text{ }}g\] of water undergoes complete evaporation at \[100^\circ C\] is__________.
(Given: \[\Delta {H_{vap}}\] for water at 373 K \[ = 41{\text{ }}kJ/mol\] ,\[R = 8.314{\text{ }}J\,{K^{-1}}\,mo{l^{-1}}\] )

Answer 1

Hint: Thermal energy is another name for internal energy. It is the energy of a substance as a result of the kinetic and potential energies connected to the ad hoc motion of all the constituent particles. The English letter "U" is used to represent it.

Formula Used:
The relationship between internal energy and enthalpy is as follows:
\[\Delta H = \Delta U + \Delta nRT\]
Here, \[\Delta H\] is change in enthalpy, \[\Delta U\] change in internal energy, \[\Delta {n_g}\] is the change in the moles, \[R\] is gas constant, \[T\] is temperature.

Complete Step by Step Solution:
The given data is as follows:
\[R = 8.314{\text{ }}J\,{K^{-1}}\,mo{l^{-1}}\]
\[ T = 100^\circ C \\
   \Rightarrow T = 100 + 273 \\
   \Rightarrow T = 373\,K \\ \]
Firstly, to understand the concept behind this question we should know the enthalpy of vaporisation.

Enthalpy of vaporisation is the difference in enthalpy that occurs when a liquid transforms into a vapour or when a vapour transforms into a liquid state.
\[\Delta {H_{vap}} = 41{\text{ }}kJ/mol\]
\[\Delta {H_{vap}}\] is given for 1 mol. \[\Delta {H_{vap}}\] for \[18\,g\] is \[41\,kJ\].
Calculate the value of \[\Delta {H_{vap}}\] for \[90{\text{ }}g\] or \[5\,mol\] of water as follows:
\[ \Delta {H_{vap}} = 41 \times 5\,kJ \\
   \Rightarrow \Delta {H_{vap}} = 205\,kJ \\
   \Rightarrow \Delta {H_{vap}} = 205000\,J \\ \]
The chemical equation for the reaction is as follows:
\[{H_2}O(l)\xrightarrow{{}}{H_2}O(g)\]

We know that,
\[\Delta H = \Delta U + \Delta nRT\]
Substituting the values,
\[ 205000 = \Delta U + \left( 5 \right)\left( {8.314} \right)\left( {373} \right) \\
   \Rightarrow \Delta U = 205000 - 15505.61 \\
   \Rightarrow \Delta U = 189494.39\,J \\ \]
Therefore, the change in internal energy is \[189494.39\,J\] .

Additional Information: The sum of the translational, rotational, binding and chemical energies of each particle in the system is the total internal energy formula. Potential energy is a component of internal energy. Chemical bonding, attraction, or repulsion serve as storage sites for potential energy. Additionally, kinetic energy is produced by the movement, translation, rotation, and vibration of the system's particles.

Note: A small quantity of heat from the environment is absorbed as a liquid evaporates. According to the discussion above, enthalpy refers to the entire amount of energy that a system has stored. So, since this process absorbs heat, which is also a type of energy, we may say that evaporation of the liquid is performed by an increase in enthalpy.