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[enthalpy] - [entropy] * [temperature]

Î”H

Î”S

50
^{\degree C}

-1000 ^{\degree C}

1000 ^{\degree C}

([temperature]*9/5)+32

Î”G = Î”H – TÎ”S

` ````
```Where:
Î”G = Gibbs free energy
Î”H = Enthalpy change
T = Absolute temperature
Î”S = Entropy change

Gibbs energy, also known as Gibbs free energy, is a thermodynamic potential that measures the maximum reversible work that can be performed by a system at constant temperature and pressure. It is denoted by the symbol G and is defined as the sum of the enthalpy (H) and the product of the temperature (T) and the entropy (S) of a system:

**G = H - TS**

Gibbs energy is a fundamental concept in thermodynamics and is used to determine whether a reaction will occur spontaneously at a given temperature and pressure. If the **Gibbs energy of a system is negative, **the **reaction will occur spontaneously, releasing energy in the process**. If the **Gibbs energy is positive**, the **reaction will not occur spontaneously** and will require external energy input to proceed.

Experimental research has been conducted to support the concept of Gibbs energy and its role in predicting the spontaneity of reactions. For example, a study by Ostwald in 1897 demonstrated the relationship between Gibbs energy and the equilibrium constant of a reaction. By measuring the equilibrium constant at different temperatures, Ostwald was able to calculate the Gibbs energy change of the reaction, showing that reactions with negative Gibbs energy are favored at equilibrium.

Another study by Gibbs himself in the late 19th century investigated the relationship between Gibbs energy and the maximum work that can be obtained from a system. Gibbs showed that the maximum work is equal to the free energy change of the system, providing a theoretical basis for the concept of Gibbs energy as a measure of the available energy in a system.

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Let's assume we have a reaction with an **enthalpy **change of -200 kJ/mol and an **entropy **change of 50 J/(molÂ·K). If the temperature is 298 K, calculate the Gibbs free energy change for the reaction.

**Given**

Î”H = -200 kJ/mol

Î”S = 50 J/(molÂ·K)

T = 298 K

**Plug in the values into the formula:**

Î”G = -200 kJ/mol - (298 K)(50 J/(molÂ·K))

Î”G = -200 kJ/mol - 14900 J/mol

Î”G = -200 kJ/mol - 14.9 kJ/mol

Î”G â‰ˆ -214.9 kJ/mol

See More Worked Example
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1. Calculate the change in Gibbs free energy when a reaction releases 100 kJ of heat at a temperature of 25Â°C.

2. At what temperature will a reaction become spontaneous if the change in Gibbs free energy is -200 kJ?

3. A reaction has a change in Gibbs free energy of 50 kJ and a change in entropy of -100 J/K. Calculate the temperature at which the reaction will be at equilibrium.

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1. Answer:Â **-100 kJ**

2. Answer:Â **250Â°C**

3. Answer:Â **500 K**

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