Question

For a particular reversible reaction at temperature $T,\Delta H$ and $\Delta S$ were found to be both $+ ve$ . If ${T_e}$ is the temperature at equilibrium, the reaction would b spontaneous when:
A. ${T_e} > T$
B. $T > {T_e}$
C. ${T_e}$ is 5 times $T$
D. $T = {T_e}$

Answer 1

A reversible reaction is the reaction where the reactants and products react together to give the product and the product can be possibly brought back to the previous state as it was earlier, before the reaction. A reaction is said to be spontaneous when it has a negative value of change in the Gibbs free energy.

Complete step by step answer:
As mentioned in the question, for a particular reversible reaction at a given temperature $T$ , the change in enthalpy ($\Delta H$ ) and the change in entropy ($\Delta S$ ) were found to be positive. The change in Gibbs free energy is zero at equilibrium which means that the concentration of reactants and products are equal at equilibrium. Mathematically, we can write this as:
$\Delta G = 0$
From the relation between change in enthalpy, change in Gibbs free energy and change in entropy, we have the following equation at equilibrium:
$\Delta G = \Delta H - {T_e}\Delta S$ …. (i)
Where, ${T_e} =$ equilibrium temperature
Since, $\Delta G = 0$, from equation (i), we have:
$\Delta H = {T_e}\Delta S$
Hence, ${T_e} = \dfrac{{\Delta H}}{{\Delta S}}$ … (ii)
Now, for a spontaneous reaction, the change in Gibbs free energy is greater than zero or is positive. This can be written mathematically as:
$\Delta G < 0$
This means, $\Delta H - T\Delta S < 0$
$\Rightarrow T > \dfrac{{\Delta H}}{{\Delta S}}$ …. (iii)
Thus, from equation (ii) and (iii), we have:
$T > {T_e}$
Thus, the correct option is B. $T > {T_e}$ .

Note:
A spontaneous reaction is a reaction that favors the formation of products at the conditions under which the reaction is occurring. In thermodynamics, in other words, a spontaneous process is the time-evolution of a system in which it releases free energy and it moves to a lower, more thermodynamically stable energy state.