Question

2 moles of ideal gas at \[{27^o}{\text{C}}\] temperature is expanded reversibly from 2L to 20L. Find entropy change: \[\left( {{\text{R}} = 2\dfrac{{{\text{cal}}}}{{{\text{mol}} - {\text{K}}}}} \right)\]
A. \[92.1\]
B.0
C.4
D. \[9.2\]

Answer 1

Hint:Entropy is the measure of randomness in the system. As we cannot calculate mathematically entropy, but change in entropy can be determined.
Formula Used: \[\Delta {\text{S}} = 2.303{\text{nRlog}}\dfrac{{{{\text{V}}_2}}}{{{{\text{V}}_1}}}\]
where n is the number of moles of gas, R is universal gas constant, \[{{\text{V}}_2}\] is final volume and \[{{\text{V}}_1}\] is initial volume.

Complete step by step answer:
Entropy is qualitatively defined as a measure of how much the energy of atoms and molecules become more spread out in a process and can be defined in terms of statistical probabilities of a system. For a reversible process the entropy generation is zero and the entropy change of a system is equal to net entropy transfer. The entropy balance is analogous to energy balance relation. Change of entropy can be calculated quantitatively.
As given in question, 2 moles of ideal gas at \[{27^o}{\text{C}}\] temperature is expanded reversibly from 2L to 20L. Putting the given values in the equation of change in entropy we get:
 \[\Delta {\text{S}} = 2.303 \times 2 \times 2 \times {\text{log}}\dfrac{{20}}{2}\]
 \[\Delta {\text{S}} = 2.303 \times 2 \times 2 \times {\text{log10}}\]
Solving, we get:
 \[\Delta {\text{S}} = 9.212{\text{cal}}\]

Hence, the correct option is D.
Additional information:
 \[\Delta {\text{G}} = \Delta {\text{H}} - {\text{T}}\Delta {\text{S}}\] is the relation used to determine change in Gibbs free energy, change in enthalpy, change in entropy in single equation. If change of Gibbs free energy is positive, reaction is non spontaneous and negative change corresponds to spontaneous reaction. If enthalpy is positive and negative then free energy is never negative because if entropy is negative then the product of entropy with temperature becomes negative and the subtraction of negative value from the given positive value of enthalpy can never result in negative Gibbs free energy.

Note:
 \[\Delta {\text{H}}\] means change in enthalpy. Gibbs free energy is the energy associated with a chemical reaction that can be used to do work, and is the sum of its absolute enthalpy and the absolute entropy of the system. If change in Gibbs free energy is positive then the reaction is non spontaneous and if it is negative, then reaction is spontaneous.