What is Eyring’s Formula?

Eyring’s formula is a mathematical equation used to calculate the reaction rate of chemical reactions. The formula was developed by American physical chemist Henry Eyring in 1935. The formula is based on the theory of activated complex, which states that chemical reactions involve the formation of an intermediate state known as the activated complex. The activated complex is a transient state that exists between the reactants and the products of the chemical reaction.

The formula is expressed as k = (k_BT/h)e^(-ΔG/RT), where k is the rate constant, k_B is the Boltzmann constant, T is the temperature in kelvin, h is Planck’s constant, ΔG is the change in Gibbs free energy, R is the gas constant, and e is the base of the natural logarithm.

Eyring’s formula is widely used in chemical kinetics to predict the rate of chemical reactions.

Understanding the Chemical Kinetics

Chemical kinetics is the study of the rate of chemical reactions and the factors that affect the rate of chemical reactions. Chemical reactions occur when two or more molecules interact to form new molecules. The rate of a chemical reaction is determined by the rate at which a reactant is consumed or a product is formed.

Eyring’s formula is based on the theory of activated complex, which states that chemical reactions involve the formation of an intermediate state known as the activated complex. The activated complex is a transitional state that exists between the reactants and the products of the chemical reaction. The rate of the chemical reaction is dependent on the rate at which the activated complex is formed and the rate at which it decomposes into products.

Eyring’s formula takes into account the energy required to form the activated complex and the energy required to break the bonds in the reactants. The formula also takes into account the temperature and pressure of the system, as these factors can affect the rate of the chemical reaction.

Formula Application Examples

Eyring’s formula can be applied in a wide range of chemical reactions. For example, it can be used to calculate the reaction rate of the decomposition of hydrogen peroxide. The reaction is represented by the equation: 2 H2O2 → 2 H2O + O2. The activation energy of the reaction is 75.3 kJ/mol, and the rate constant at 298 K is 6.8 × 10^-4 s^-1. Using Eyring’s formula, the rate constant at 310 K can be calculated as 2.2 × 10^-3 s^-1.

Another example is the reaction between acetic acid and ethanol to form ethyl acetate and water. The activation energy of the reaction is 56.1 kJ/mol, and the rate constant at 298 K is 2.3 × 10^-3 s^-1. Using Eyring’s formula, the rate constant at 310 K can be calculated as 7.5 × 10^-3 s^-1.

Eyring’s formula can also be used to determine the activation energy of a chemical reaction by measuring the rate constant at different temperatures and calculating the slope of the ln(k/T) vs. 1/T graph.

Advantages and Limitations

The advantage of Eyring’s formula is that it provides a quantitative prediction of the rate of chemical reaction based on the energy required to form the activated complex and the energy required to break the bonds in the reactants. The formula takes into account the temperature and pressure of the system, which can affect the rate of the chemical reaction.

The limitation of Eyring’s formula is that it assumes a one-step reaction mechanism and does not take into account the complexity of multi-step reactions. The formula also assumes that the reactants and products are in a state of equilibrium, which may not always be the case in real-world chemical reactions. Additionally, the formula requires accurate values of the activation energy and rate constant, which may be difficult to determine experimentally.