Animated Solution for Chemistry - Chemical Thermodynamics: A process will be spontaneous at all temperature if

Have you ever wondered why ice melts at room temperature, but water doesn't spontaneously freeze unless you put it in a freezer? Or why a drop of ink spreads in a glass of water, but never gathers back into a single drop? This is the concept of spontaneity in thermodynamics. A spontaneous process is one that occurs on its own, without any continuous external input of energy.

To understand spontaneity, we need to look at two fundamental driving forces in the universe: Enthalpy and Entropy.

Enthalpy ($\Delta H$) is essentially the heat content of a system. The universe is lazy; it prefers states of lower energy. Therefore, processes that release heat—exothermic processes where $\Delta H<0$—are generally favored. Think of a ball rolling down a hill; it naturally wants to go to a state of lower potential energy.

Entropy ($\Delta S$), on the other hand, is a measure of randomness or disorder. The universe loves chaos! According to the Second Law of Thermodynamics, the total entropy of the universe is always increasing. Therefore, processes that increase the disorder of a system—where $\Delta S>0$—are favored. Think of your bedroom; it naturally gets messy over time, not cleaner!

But what happens when these two forces disagree? What if a process is endothermic (unfavored) but increases entropy (favored)? Who wins?

Gibbs Free Energy

To settle this battle, Josiah Willard Gibbs introduced a brilliant concept called Gibbs Free Energy ($G$). The change in Gibbs Free Energy ($\Delta G$) combines both enthalpy and entropy into a single master equation:

Here, $T$ is the absolute temperature in Kelvin.

The ultimate rule of the universe is this: For any process to be spontaneous, $\Delta G$ must be strictly negative ($\Delta G<0$). If $\Delta G$ is positive, the process is non-spontaneous. If $\Delta G$ is exactly zero, the system is at equilibrium.

Our question asks for a process that is spontaneous at all temperatures. This means we need $\Delta G$ to be negative regardless of the value of $T$. Since $T$ is the absolute temperature, it is always a positive number.

Let's break down the equation $\Delta G=\Delta H-T\Delta S$ term by term to see how we can guarantee a negative result.

1. The Enthalpy Term ($\Delta H$): To help make $\Delta G$ negative, we want $\Delta H$ to be negative. This means the process should be exothermic ($\Delta H<0$). 2. The Entropy Term ($-T\Delta S$): We have a minus sign in front of $T\Delta S$. To make this entire second term negative, we need $\Delta S$ to be positive. Since $T$ is positive, subtracting a positive number ($-T\times \text{positive}$) gives a negative value. This means the process should increase the randomness of the system ($\Delta S>0$).

When we combine these two ideal conditions: - $\Delta H$ is negative. - $-T\Delta S$ is negative.

A negative number plus a negative number will always result in a negative number.

Therefore, if $\Delta H<0$ and $\Delta S>0$, the process is guaranteed to be spontaneous at any temperature!

It is highly beneficial to understand all four possible combinations of $\Delta H$ and $\Delta S$, as this is a favorite concept in JEE and NEET exams. Let's summarize them:

Notice how temperature plays a crucial role when the signs of $\Delta H$ and $\Delta S$ are the same. If both are negative, the process is only spontaneous at low temperatures where the enthalpy term dominates. If both are positive, the process is only spontaneous at high temperatures where the entropy term dominates.

But in our specific problem, the universe is in perfect harmony. Both the drive for lower energy and the drive for higher chaos are satisfied, making the process unstoppable at any temperature!