ΔG is net energy available to do useful work and is thus a measure of “free energy”. Show mathematically that ΔG is a measure of free energy. Find the unit of ΔG. If a reaction has positive enthalpy change and positive entropy change, under what condition will the reaction be spontaneous?

<p>This is a Long Answer Type Questions as classified in NCERT Exemplar</p><p>We know, </p><p>ΔS_total = ΔS_sys + ΔS_surr</p><p>When a system is in thermal equilibrium with its surroundings, the surroundings' temperature is the same as the system's. Furthermore, a rise in the enthalpy of the surroundings equals a decrease in the system's enthalpy. As a result of the entropy shift in the environment, </p><p>ΔS_surr = ΔH_surr/T = -ΔH_sys/T</p><p>ΔS_total = ΔS_sys = (-ΔH_sys/T)</p><p>Rearranging the above equation:</p><p>ΔS_total = TΔS_sys - ΔH_sys</p><p>For spontaneous process, </p><p>ΔS_total &gt; 0, so&nbsp;</p><p>TΔS_sys - ΔH_sys&gt; 0</p><p>⇒ ( - ΔH_sys - TΔS_sys) &gt; 0</p><p>The above equation can be written as</p><p>- ΔG &gt; 0</p><p>ΔG = ΔH - TΔS &lt; 0</p><p>ΔH_sys is the enthalpy change of a reaction, TΔS_sys is the energy which is not available to do</p><p>useful work. As a result, G is a measure of 'free energy, ' as it is the net energy available to conduct beneficial work. As a result, it's also known as the reaction's free energy. At constant pressure and temperature, G gives a set of conditions for spontaneity, </p><p> (i) If ΔG is negative (&lt;0), the process is spontaneous.</p><p> (ii) If ΔG is positive (&gt;0), the process is nonspontaneous.</p><p>&nbsp;Unit of ΔG is Joule.</p><p>&nbsp;The reaction will be spontaneous at high temperature.</p>

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