Question

For a spontaneous process, which of the following is true?
A: $\mathrm{\Delta }{S}_{sys}$ is positive
B: $\mathrm{\Delta }{S}_{surr}$ is positive
C: $\mathrm{\Delta }{S}_{total}$ is positive
D: $\mathrm{\Delta }{S}_{total}$ is negative

Answer 1

Hint: A spontaneous process is a process which proceeds in a given direction without being driven by an outside energy source. While, a non-spontaneous process (also called an endergonic process) is a chemical process in which energy is being absorbed and standard change in the free energy is positive.

Complete step by step answer:
Spontaneous process releases the free energy as they proceed. This free energy involved in the process is most commonly known as Gibbs free energy and is denoted by G in the name of an American scientist i.e. Josiah Gibbs who contributed to thermodynamics in many ways.
The determining factors in case of a spontaneous process are enthalpy ($\mathrm{\Delta }H$) as well as entropy ($\mathrm{\Delta }S$) changes which occur for the system. Mathematically, change in the Gibbs free energy ($\mathrm{\Delta }G$) can be computed with the following expression:
$$\mathrm{\Delta }G=\mathrm{\Delta }H-T\mathrm{\Delta }S$$
A spontaneous process releases free energy which means that ΔG must be negative (< 0). This means that $\mathrm{\Delta }H$must be less than $T\mathrm{\Delta }S$. As a result, $\mathrm{\Delta }{S}_{total}$must be positive.

Hence, the correct answer is Option C.

Note:
Always remember that the temperature in Gibbs free energy expression is the Kelvin temperature, thus, it can only possess a positive value. If $\mathrm{\Delta }H$is negative and $\mathrm{\Delta }S$is positive, $\mathrm{\Delta }G$ is negative, indicating that the process is spontaneous at all the temperatures. In other cases if $\mathrm{\Delta }H$is positive and $\mathrm{\Delta }S$is negative, $\mathrm{\Delta }G$is positive, indicating that the process is nonspontaneous.