Ch 8 Factors Affecting Reaction Rate

Gibbs Free Energy and Reaction Spontaneity

Introduction to Spontaneous Reactions

• spontaneous reaction: any reaction that occurs under a given set of conditions without any external intervention.

• Spontaneous reactions generally occur when:

  • They do not require a large input of energy (related to enthalpy, \Delta H).

  • The product is less ordered than the reactant, meaning it has higher entropy, \Delta S

  • These factors interact at a certain temperature, T.

Examples of Spontaneous and Non-Spontaneous Processes:

• Rusting:- A spontaneous, exothermic process.

  • Results in a decrease in enthalpy (\Delta H < 0).

  • Leads to an increase in disorder or entropy (\Delta S > 0).

• Ice Melting:- A spontaneous, endothermic process.

  • Results in an increase in enthalpy (\Delta H > 0).

  • Melted ice is more disordered than solid ice, so there is an increase in disorder or entropy (\Delta S > 0).

• Removal of Sugar from Coffee:- A non-spontaneous process.

  • Requires a large input of energy (enthalpy increases) (\Delta H > 0).

  • Results in a solution that is more ordered than what was started with (disorder or entropy decreases) (\Delta S < 0).

Gibbs Free Energy (G)

Gibbs free energy, denoted as G, determines whether a reaction is spontaneous or requires energy to proceed. Spontaneity depends on enthalpy, entropy, and temperature.

Standard Free Energy Change Equation:

The equation for Gibbs free energy change is:

\text{change in Gibbs free energy} = \text{change in enthalpy} - (\text{temperature} \times \text{change in entropy})

Expressed mathematically:

\text{ΔG} = \text{ΔH} - \text{TΔS}

Where:

• \text{ΔG} : Change in Gibbs free energy.

• \text{ΔH} : Change in enthalpy (energy, typically in Joules per mole or kJ/mol).

• \text{T} : Temperature (measured in Kelvin, K).

• \text{ΔS} : Change in entropy (disorder, typically in Joules per Kelvin per mole or J/(K·mol)).

Interpreting the Value of \text{ΔG} :

• If \text{ΔG < 0} : The reaction is spontaneous (also called exergonic).- Rusting: \text{ΔH} decreases and \text{ΔS} increases, leading to \text{ΔG < 0} .

  • Ice melting: Even though \text{ΔH} increases, the increase in disorder (\text{ΔS} ) is significant enough that \text{ΔG} is still less than zero (\text{ΔG < 0} ).

• If \text{ΔG > 0} : The reaction is non-spontaneous (also called endergonic).- Removal of sugar from coffee: Large input of enthalpy (\text{ΔH} is high) and decrease in entropy (\text{ΔS} is low), resulting in \text{ΔG > 0} .

• If \text{ΔG = 0} : The reaction is at chemical equilibrium.

Important Distinction:

Do not confuse exergonic (\text{ΔG < 0} ) and endergonic (\text{ΔG > 0} ) with exothermic (\text{ΔH < 0} ) and endothermic (\text{ΔH > 0} ). Exergonic/endergonic refer to Gibbs free energy (G), while exothermic/endothermic refer to enthalpy (H).

Relationship Between Enthalpy, Entropy, Temperature, and Spontaneity

Numerical Examples:

Example 1: Spontaneous Reaction

• Given values: \text{ΔH} = 10 \text{ J/mol}, T = 10 \text{ K}, \text{ΔS} = 5 \text{ J/(K·mol)}

• Equation: \text{ΔG} = \text{ΔH} - \text{TΔS}

• Calculation: \text{ΔG} = 10 \text{ J/mol} - (10 \text{ K} \times 5 \text{ J/(K·mol)}) = 10 \text{ J/mol} - 50 \text{ J/mol} = -40 \text{ J/mol}

• Result: Since \text{ΔG = -40 J/mol} (\text{ΔG < 0} ), the reaction is exergonic and spontaneous.

Example 2: Non-Spontaneous Reaction (Temperature Change)

• Given values: \text{ΔH} = 10 \text{ J/mol}, T = 1 \text{ K} (decreased temperature), \text{ΔS} = 5 \text{ J/(K·mol)}

• Equation: \text{ΔG} = \text{ΔH} - \text{TΔS}

• Calculation: \text{ΔG} = 10 \text{ J/mol} - (1 \text{ K} \times 5 \text{ J/(K·mol)}) = 10 \text{ J/mol} - 5 \text{ J/mol} = 5 \text{ J/mol}

• Result: Since \text{ΔG = 5 J/mol} (\text{ΔG > 0} ), the reaction is endergonic and non-spontaneous.

This demonstrates that temperature plays a crucial role in determining whether a reaction is spontaneous.

Factors Affecting Reaction Rate and Spontaneity

1. Temperature

• For most reactions, chemical bonds must break and others must form. This requires substances to collide in a specific orientation that brings involved electrons closer.

• Kinetic energy (or movement energy) is measured as temperature.- At low temperatures, molecules move more slowly, decreasing the likelihood of effective collisions.

  • At high temperatures, molecules move more rapidly, increasing kinetic energy, leading to more frequent and effective collisions, thus making bond breaking/forming more likely.

2. Concentration

• Concentration refers to the amount of material or molecules per unit volume.

• When the concentration of reactants is high, there are more molecules available, increasing the likelihood of collisions.

• More collisions lead to a faster reaction rate.

• This effectively means that high reactant concentration tends to decrease \text{ΔG} and favor spontaneity (though a modified equation exists, it is not covered here).- Analogy: Waiting in line at Disney World pre-COVID versus during COVID; higher concentration of people leads to more bumps.

How Non-Spontaneous Reactions Occur: Energetic Coupling

Non-spontaneous (endergonic) reactions can occur because they are coupled to spontaneous (exergonic) reactions.

Energetic Coupling Mechanism:

1. Exergonic Reaction: Releases energy (specifically, Gibbs free energy).

   • Starts with a high-energy reactant (e.g., a molecule with equally shared electrons, storing significant potential energy).

   • This reactant transforms into a molecule with less potential energy (e.g., one with polar bonds or unequally shared electrons).

   • The difference in potential energy is released.

2. Endergonic Reaction: Requires an input of energy.

   • This released energy from the exergonic reaction is then used to drive a lower-energy reactant to form a higher-energy product. The energy released from the exergonic reaction effectively makes the overall coupled process spontaneous.