What is Gibbs Free Energy?

Have you ever wondered why some processes happen naturally, while others need extra energy to get started? This is where Gibbs Free Energy comes into play. It helps us understand whether a process can occur on its own or whether we need to supply energy. In this post, we’ll break down the concept of Gibbs Free Energy using simple terms and a real-life example of a hot cup of tea cooling down.

Gibbs Free Energy is calculated using the formula:

Where:

• $\mathrm{\Delta }G$ is the change in Gibbs Free Energy (whether the process will happen naturally).

• $\mathrm{\Delta }H$ is the change in enthalpy (total heat energy in the system).

• $T$ is the temperature in Kelvin.

• $\mathrm{\Delta }S$ is the change in entropy (disorder or randomness in the system).

Let’s break each part down and make it easy to understand.

What Does $\mathrm{\Delta }H$ (Enthalpy) Mean?

Enthalpy (H) represents the heat content of a system. It tells us how much energy the system has in the form of heat.

• When the system loses heat (like the tea cooling down), $\mathrm{\Delta }H$ is negative.

• When the system gains heat, $\mathrm{\Delta }H$ is positive.

In our tea example, the tea is cooling down and losing heat to the surroundings, so $\mathrm{\Delta }H$ will be negative.

What Does $\mathrm{\Delta }S$ (Entropy) Mean?

Entropy (S) measures the disorder or randomness of the system. The more disordered the system, the higher its entropy.

• When the system becomes more ordered, entropy decreases ($\mathrm{\Delta }S$ is negative).

• When the system becomes more disordered, entropy increases ($\mathrm{\Delta }S$ is positive).

In our example, as the tea cools and releases heat, that heat spreads into the room, making the molecules in the air more disordered. This means the entropy of the surroundings increases, so $\mathrm{\Delta }S$ is positive.

What Does Temperature (T) Do?

The temperature (T) in the equation is always positive (in Kelvin). It plays a role in determining how much disorder (entropy) is involved in a process.

• Higher temperature means more energy is available to cause disorder.

• Lower temperature means less energy for disorder.

In our example, the temperature of the room is 298 K (about 25°C), and the temperature of the tea is 363 K (about 90°C).

Putting It All Together: Gibbs Free Energy in Action

Now that we know the basics, let’s use the example of a hot cup of tea cooling down to understand how Gibbs Free Energy works.

Step 1: The Tea Cooling Down

• The tea starts hot, with high enthalpy (H) because it has a lot of energy.

• As the tea cools, it loses heat to the environment, so $\mathrm{\Delta }H$ is negative.

• The heat transferred to the air increases the disorder (entropy) of the room, so $\mathrm{\Delta }S$ is positive.

Step 2: Calculating Gibbs Free Energy

Let’s use a numerical example to see this in action:

• $\mathrm{\Delta }H$ = -50 J (the tea loses 50 joules of heat).

• $\mathrm{\Delta }S$ = +0.1 J/K (the entropy of the surroundings increases as the heat spreads).

• $T=298K$ (the room temperature).

Now, apply the equation: