Question

Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement (s) is (are):
A. $\mathrm{\Delta }G$ is positive
B. $\mathrm{\Delta }{S}_{system}$ is positive
C. $\mathrm{\Delta }{S}_{surrounding}=0$
D. $\mathrm{\Delta }H=0$

Answer 1

Hint: To find the correct options of the given question, state about the Raoult’s law in ideal condition and what are the changes that the system undergoes. To find out about the entropy changes, refer to Gibbs free energy in ideal condition.

Complete step by step answer:
Before finding out the correct option, let us learn about some of the terms.
- Entropy: Entropy is defined as a measure of randomness or disorder of a system. So, we can say that greater is the disorderliness or randomness inside a system, greater will be its change in the entropy. The total entropy consists of the sum of the entropy of the system and the entropy of the surrounding or the environment. The change in entropy is denoted by $\mathrm{\Delta }S$.

-Enthalpy: Enthalpy is the quantity of heat in a system. This heat is utilised in the occurrence of a process. Any heat related system is called a thermodynamic system. So, enthalpy is referred to as a thermodynamic quantity. The change in enthalpy is denoted by $\mathrm{\Delta }H$.

- Gibbs free energy: Gibbs free energy, also known as the Gibbs function or Gibbs energy or free enthalpy; is a quantity that is used to measure the maximum amount of work done in a thermodynamic system when the temperature and pressure are kept constant. It is denoted by the symbol ‘G’.
As per the given question, Benzene and naphthalene form an ideal solution at room temperature.
So, coming to Raoult’s law at ideal condition, states that the solution enthalpy i.e. $\mathrm{\Delta }H$ is zero and the volume mixing will be also zero.
And, when an ideal solution is formed, the process is generally spontaneous. Since, there is no exchange of heat energy between the system and surroundings, the change in the surrounding i.e. $\mathrm{\Delta }{S}_{surrounding}$ will be always equals to zero, while the change in the entropy of the system i.e. $\mathrm{\Delta }{S}_{system}$ will always be greater than zero, so that the total change in entropy will be positive.

And, for an ideal solution, the Gibbs free energy of mixing is always negative, meaning that mixing of ideal solutions will be spontaneous. So, $\mathrm{\Delta }G$ will be negative.
Therefore, $\mathrm{\Delta }{S}_{system}$ is positive, $\mathrm{\Delta }{S}_{surrounding}=0$ and $\mathrm{\Delta }H=0$ for an ideal solution.
So, the correct answer is “Option B, C and D”.

Note: Remember, entropy helps for the measurement of the movements of molecules while enthalpy is composed of both the internal energy and energy flow. The Gibbs free energy equation can say about the relation between entropy and enthalpy and it is given by $\mathrm{\Delta }G=\mathrm{\Delta }H-T\mathrm{\Delta }{S}_{system}$.