Question

A container has hydrogen and oxygen mixture in ratio of \[4:1\] by weight, then
A. Internal energy of the mixture decreases
B. Internal energy of the mixture increases
C. Entropy of the mixture increases
D. Entropy of the mixture decreases

Answer 1

Hint: The term entropy was introduced by R.J.E Clausius. Entropy is the extent of disorder or randomness in a system. The entropy of a substance measures the disorder or randomness in a system. Entropy is denoted by letter \[{\rm{S}}\]. Sum total of different forms of energies like kinetic energy, potential energy, nuclear energy, chemical energy etc. associated with the molecules is called its internal energy or intrinsic energy. Internal energy is denoted by letter \[{\rm{U}}\].

Complete Step by Step Solution:
The internal energy of a system is the inherent energy present in the system by virtue of its position. It is a state function. The absolute value of the internal energy of a system cannot be determined because it is not possible to determine the exact values of constituent energies like translational energy, nuclear energy, vibrational energy etc.

Internal energy is an extensive property. The value of the internal energy of a substance depends upon factors such as the nature of the substance, pressure, temperature, etc. For example, the internal energy of one mole of \[{\rm{C}}{{\rm{O}}_2}\]is different from the internal energy of one mole of \[{{\rm{H}}_{\rm{2}}}{\rm{O}}\] under similar conditions of temperature and pressure.

Since internal energy does not depend upon an increase or decrease in impurities, it will have no effect on the given mixture of hydrogen and oxygen which are present in the ratio of \[4:1\].

The entropy of the system is an extensive property. Its value depends upon the amount of matter in the system. Adding impurities to the reaction mixture will result in more disorder (randomness) of the particles. Hence, the entropy of the mixture increases.
Therefore, option C is correct.

Note: Entropy is a state function like enthalpy and internal energy. So, it depends upon the final and initial states of a system. Thus, entropy change can be written as; \[{\rm{\Delta S}} = {{\rm{S}}_{{\rm{final state}}}} - {{\rm{S}}_{{\rm{initial state}}}}\]when a system undergoes a change from initial state to final state. For any chemical process, \[{\rm{\Delta S}} = {{\rm{S}}_{{\rm{(products)}}}} - {{\rm{S}}_{{\rm{(reactants)}}}}\]. For a reversible process, \[{\rm{\Delta S}} = \dfrac{{{{\rm{q}}_{{\rm{rev}}}}}}{{\rm{T}}}\]at equilibrium; where \[{{\rm{q}}_{{\rm{rev}}}}\] is the amount of heat supplied at temperature \[{\rm{T}}\]in a reversible process. Since \[{\rm{\Delta S}} = \dfrac{{{{\rm{q}}_{{\rm{rev}}}}}}{{\rm{T}}}\], therefore unit of entropy in S.I. units is Joule per Kelvin, $\dfrac{J}{K}mol$ (expressed as entropy unit E.U.). It is also expressed in calories per degree, \[{\rm{cal}}{{\rm{K}}^{ - 1}}{\rm{mo}}{{\rm{l}}^{ - 1}}\](expresses as entropy unit, eu) .