GIBBS FREE ENERGY EQUATION

The American scientist Josiah Willard Gibbs invented Gibbs’s free energy equation in the 1870s. He said energy is an “available energy” in a system. The benefits of thermodynamics laws and Gibb’s free energy equation are that they reduce experimental cost and time. 

Gibbs free energy is based on thermodynamic second law, Which means “In an isolated system entropy of a system is always increasing if there is no additional force”. For example, if we keep hot metal and cold metal together, heat will only pass from hot metal to cold metal.

Gibbs free energy Equation 

Gibbs free energy is defined as the enthalpy of the system minus products of temperature and entropy of the system. Here, the SI unit for Gibbs free energy is Joules. Gibbs’s free energy can balance the potential driving forces of chemical reactions.

G = H-TS Where,

G – Gibbs free Energy

H – Enthalpy

T – Temperature

S – Entropy

Entropy (S):

Entropy is defined as a thermal energy per unit temperature that is unavailable in the system to do useful work. SI unit for entropy is Joule / Kelvin.

Enthalpy (H):

Enthalpy is defined as a sum of internal energy and pressure time’s volume. SI unit for enthalpy is Joule.

H = U + PV.

Here, “U” is Internal energy, and the SI unit for internal energy is Joule.

“P” is Pressure, and the SI unit for pressure is Pascal. And “V” is Volume, the SI unit for Volume is M3

If the change in Gibbs free energy occurs, there will also be a change in enthalpy and entropy. So, we can express that: Δ G = Δ H – Δ (TS)

If the reaction has occurred at a constant temperature, we can express the equation as follows:

ΔG = ΔH – TΔS

Δ G = G (Final) – G (Initial)

If the process is occurred spontaneously, change in Gibbs free energy will be “negative” (ΔG)

Following are some examples of Gibb’s free energy equations

• Spontaneous Process:

If the reaction occurs without any additional force it is known as a spontaneous process, which may be slower or faster. The spontaneity of the system does not depend upon kinetic or reaction.

Example: Carbon diamond turning into graphite

• Non-Spontaneous Process: 

If the reaction occurs with any additional force is known as the Non-spontaneous process.

Example: Melting of ice into water.

• Exergonic Process:

The exergonic reaction is defined as a reaction where energy releases without any additional force. Here, the change in free energy will be negative; therefore, ΔG < 0 (“G” is Negative).

• Endergonic Process: 

Endergonic reaction is defined as a reaction where energy is released with any additional force. Here, the change in free energy will be positive. The endergonic process will act in the reverse direction to obtain more starting material.

ΔG > 0 (“G” is Positive)

• If ΔG is negative for any reaction means, ΔH will be negative, and ΔS will be positive, which will be a spontaneous process.

• If ΔG is Positive for any reaction means, ΔH will be positive, and ΔS will be Negative, which will be a Non-spontaneous process.

• ΔG is constant in chemical equilibrium.

• ΔG depends on cell voltage in electrochemistry.

Examples for Gibbs free energy Equation calculation:

Problem:

Calculate Gibbs free energy (G) for the following reaction and assure the reaction occurs spontaneously or not? Entropy (ΔS) of reaction is -284.8 J/K, Enthalpy (ΔH) of reaction is -176 KJ at room temperature 250 C.

 NH3 + HCl                               NH4Cl

Solution:

Given data,                      

Entropy, ΔS = – 284.8 J/K

Enthalpy, ΔH = – 176 KJ

Temperature T =    250 C

Gibbs energy formula, ΔG = ΔH – TΔS 

ΔS = – 284.8 J/K   x ( 1 KJ1000 J )

Entropy,ΔS = – 0.2848 KJ/K

T =    250 C + 273.15 K

Temperature = 298 K

Gibbs free energy, ΔG = ΔH – TΔS

= -176 KJ – (298 K) (-0.2848 KJ/K)

= -176 KJ – ( -84.9 KJ)

Gibbs free energy, ΔG = – 91.1 KJ

Since the Gibbs free energy (ΔG) is negative, this is a spontaneous process at room temperature 250 C.

Conclusion

Gibbs’s free energy formula will help to find the result of experiments before doing work, which will allow finding other parameters like Enthalpy (Δ H), Entropy (Δ S), and Process direction (Spontaneous or nonspontaneous). Gibbs free energy is defined as the enthalpy of the system minus products of temperature and entropy of the system.