Hess's Law And Gibbs Free Energy: What's The Connection?

Hess's Law states that the change in enthalpy for a reaction is the same whether the reaction occurs in a single step or a series of steps. This is because enthalpy is a state function, and so the route taken to convert molecules is irrelevant. Gibbs Free Energy is also a state function, and so Hess's Law can be applied to it. This means that the change in Gibbs Free Energy for a reaction is the same whether the reaction occurs in a single step or a series of steps.

Hess's Law can be used to calculate Gibbs Free Energy

Hess's Law states that the total enthalpy change for a reaction is the same whether the reaction takes place in one step or a series of steps. This is because enthalpy is a state function, and so the route the conversion takes does not matter, only the enthalpies of the reactants and products.

Gibbs Free Energy is also a state function. Therefore, Hess's Law can be used to calculate the change in Gibbs Free Energy for a reaction. This is done by applying the same strategy used for enthalpy calculations: calculating the change in Gibbs Free Energy for a stepwise reaction from the sum of the changes in Gibbs Free Energy for each step.

For example, to calculate the free energy of the reaction producing methanol (CH3OH) from carbon monoxide and hydrogen gas, we can use the following three combustion reactions:

• 2CO(g) + O2(g) → 2CO2(g), ΔGo= -514 kJ
• 2H2(g) + O2(g) → 2H2O(g), ΔGo = -458 kJ
• 2CH3OH(g) + 3O2(g) → 2CO2(g) + 4H2O(g), ΔGo = −1378 kJ

The third equation must be reversed because methanol is a reactant in the target equation. We then add the three equations together:

• 2CO(g) + O2(g) → 2CO2(g), ΔGo = -514 kJ
• 2H2(g) + O2(g) → 2H2O(g), ΔGo = -458 kJ
• 2CO2(g) + 4H2O(g) → 2CH3OH(g) + 3O2(g), ΔGo = +1378 kJ

We then notice that there are four moles of water on the left side of equation 3, but only two moles on the right side of equation 2. So, we multiply equation 2 by two:

2a. 4H2(g) + 2O2(g) → 4H2O(g), ΔGo = -916 kJ

Now we can add equations 1, 2a, and 3a:

• 2CO(g) + O2(g) → 2CO2(g), ΔGo = -514 kJ
• 4H2(g) + 2O2(g) → 4H2O(g), ΔGo = -916 kJ
• 2CO2(g) + 4H2O(g) → 2CH3OH(g) + 3O2(g), ΔGo = +1378 kJ

We then cancel the same molecules on both sides of the equation:

2CO(g) + O2(g) + 4H2(g) + 2O2(g) + 2CO2(g) + 4H2O(g) → 2CO2(g) + 4H2O(g) + 2CH3OH(g) + 3O2(g)

ΔGo = -514 kJ + (-916 kJ) + 1378 kJ/mol = -52 kJ

2CO(g) + 4H2(g) → 2CH3OH(g), ΔGo = -52 kJ

Finally, we divide the equation by two to match the target reaction:

CO(g) + 2H2(g) → CH3OH(g), ΔGo = -26 kJ

This is the change in Gibbs Free Energy for the reaction.

Enthalpy is a state function

For example, if you have $1000 in a savings account and withdraw $500, it does not matter if you take out the $500 in one transaction or multiple transactions—your final balance will still be $500. Here, the bank balance is a state function, as it does not depend on the path or way taken to withdraw or deposit money.

Similarly, the enthalpy of a reaction is independent of the elementary steps and depends only on the final state of the products and the initial state of the reactants. For instance, in the reaction:

> H2 (g) + 1/2O2 (g) → H2O (g) ΔH° = -572 kJ

> 2H2 (g) + O2 (g) → 2H2O (g) ΔH° = -1144kJ

Doubling the molar amounts simply doubles the enthalpy of the reaction. The enthalpy remains the same whether the reaction takes place in one step or a series of steps, as long as the temperature remains the same.

Hess's Law, which states that the total enthalpy change for a reaction is the sum of all changes, is a manifestation of the fact that enthalpy is a state function. This law allows us to calculate the overall change in enthalpy by summing up the changes for each step of a reaction until the product is formed.

Gibbs Free Energy is a measure of the thermodynamic potential of a system

Gibbs free energy, denoted as G, is a thermodynamic potential that combines enthalpy and entropy into a single value. It is a measure of the maximum amount of non-pressure-volume expansion work that can be extracted from a closed system at a constant temperature and pressure.

The change in free energy, ΔG, is equal to the sum of the enthalpy and the product of the temperature and entropy of the system. ΔG can predict the direction of a chemical reaction under two conditions: constant temperature and pressure.

If ΔG is positive, the reaction is non-spontaneous, meaning external energy input is necessary for the reaction to occur. If ΔG is negative, the reaction is spontaneous and occurs without external energy input.

The concept of Gibbs free energy was developed in the 1870s by the American scientist Josiah Willard Gibbs, who originally termed this energy as the "available energy" in a system. In his 1873 paper, "Graphical Methods in the Thermodynamics of Fluids," Gibbs outlined how his equation could predict the behaviour of systems when they are combined.

The Gibbs free energy is defined as:

> G(p,T)=U+pV-TS=H-TS

Where:

• U is the internal energy of the system
• H is the enthalpy of the system
• S is the entropy of the system
• T is the temperature of the system
• V is the volume of the system
• P is the pressure of the system (which must equal the pressure of the surroundings for mechanical equilibrium)

The change in Gibbs free energy, ΔG, is given by:

> ΔG=ΔH−TΔS

Where ΔH is the change in enthalpy and ΔS is the change in entropy.

Gibbs Free Energy can be used to determine whether a reaction can occur spontaneously

Gibbs free energy, denoted by the symbol G, combines enthalpy and entropy into a single value. The change in free energy, ΔG, is equal to the sum of the enthalpy plus the product of the temperature and entropy of the system. ΔG can predict the direction of a chemical reaction under two conditions: at a constant temperature, and if the reaction is occurring in a closed system.

If ΔG is positive, the reaction is non-spontaneous, meaning an input of external energy is necessary for the reaction to occur. If ΔG is negative, the reaction is spontaneous and occurs without external energy input. Spontaneous reactions are considered natural because they occur without any external influence. Conversely, non-spontaneous reactions require a constant input of external energy to continue, and will cease once this input stops.

The equation for calculating ΔG is:

ΔG = ΔH - TΔS

Where:

• ΔG is the change in free energy
• ΔH is the change in enthalpy (total enthalpy of the products minus the enthalpy of the reactants)
• T is the temperature in Kelvin
• ΔS is the change in entropy

The sign of ΔG indicates the direction of a chemical reaction and determines whether a reaction is spontaneous or not. A negative ΔG indicates a spontaneous reaction, while a positive ΔG indicates a non-spontaneous reaction.

Hess's Law states that the total enthalpy change for a reaction is the same whether the reaction takes place in one step or a series of steps. This law is a result of enthalpy being a state function, and it can be used to calculate other state functions like changes in Gibbs' energy and entropy.

Hess's Law states that the enthalpy change for a reaction is the same whether it takes place in one step or a series of steps

Hess's Law, also known as Hess's Law of Constant Heat Summation, is a principle in thermochemistry that relates to the concept of enthalpy change in a reaction. Enthalpy, a key concept in chemistry, can be understood as the sum of the internal energy of a system and the product of its volume multiplied by the pressure exerted on it.

Hess's Law states that the enthalpy change for a reaction remains the same whether the reaction occurs in a single step or through a series of intermediate steps. In other words, the total enthalpy change for a reaction is the sum of all the enthalpy changes that occur during the individual steps. This principle is based on the fact that enthalpy is a state function, which means that it only depends on the initial and final states of a system, regardless of the specific path taken.

To illustrate this concept, consider the reaction:

A → B → C

In this reaction, substance A undergoes a transformation to become substance B, which then undergoes another reaction to form substance C. According to Hess's Law, the total enthalpy change (ΔH) for the overall reaction is equal to the sum of the enthalpy change from A to B (ΔHA→B) and the enthalpy change from B to C (ΔHB→C). Mathematically, this can be expressed as:

ΔHA→C = ΔHA→B + ΔHB→C

This principle can be applied to more complex reactions with multiple steps, and it allows chemists to calculate the overall enthalpy change for a reaction by summing up the enthalpy changes at each step.

Furthermore, Hess's Law is not limited to enthalpy changes. It can also be applied to other state functions, such as changes in Gibbs' free energy and entropy. Gibbs' free energy is a measure of the thermodynamic potential of a system to perform work, and it takes into account both the enthalpy and entropy changes of a reaction. By using Hess's Law, one can calculate the change in Gibbs' free energy for a reaction, even if it occurs in multiple steps, by summing up the changes in free energy at each step.

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