Relationship between rate constant and temperature

Reaction rate doubles for every 10 degc temperature increase. This can be explained by using Arrhenius equation.

The Arrhenius equation is a mathematical expression that describes the relationship between the rate constant (K) of a chemical reaction, the activation energy (Ea) required for the reaction to occur, and the temperature (T) at which the reaction takes place.

The equation is written as: K = A e^(-Ea/RT)

Where: - K is the rate constant of the reaction

- A is the pre-exponential factor, which represents the frequency of collisions ?between reactant molecules

- e is the base of the natural logarithm ?(approximately equal to 2.71828)

- Ea is the activation energy, which is the minimum amount of energy required for the reaction to occur

- R is the gas constant (8.314 J/molK)

- T is the temperature in Kelvin Each term in the Arrhenius equation relates to the reaction rate as follows:

- The pre-exponential factor (A) accounts for the frequency of collisions between reactant molecules.

Higher values of A indicate a greater frequency of collisions, which can increase the reaction rate.

The activation energy (Ea) represents the minimum energy required for the reaction. Higher values of Ea result in a slower reaction rate, as more energy is needed for the reactants to overcome the energy barrier and form products.

The temperature (T) affects the reaction rate by influencing the kinetic energy of the reactant molecules.

As the temperature increases, the kinetic energy of the molecules increases, leading to more collisions and a higher reaction rate. This effect is captured in the exponential term e^(-Ea/RT) in the Arrhenius equation.

Overall, the Arrhenius equation provides a quantitative relationship between a chemical reaction's rate constant, activation energy, and temperature.

The reaction rate doubles for every 10 degc temperature increase.

Example

Let's consider a hypothetical reaction where the rate constant is 0.1 s^-1 at 25°C (298 K). If we increase the temperature by 10°C to 35°C (308 K), the rate constant is expected to double.

Let's use the Arrhenius equation to calculate the new rate constant at 35°C:

Given: - k1 = 0.1 s^-1 at 25°C (298 K)

T1 = 298 K

T2 = 308 K (10°C higher than T1)

We can use the equation as follows:

We can use the equation as follows

:k2 = k1 e^[(Ea/R) (1/T1 - 1/T2)]

Assuming Ea/R is a constant:

k2 = k1 e^(ln(2))

Solving for k2:

k2 = 0.1 x 2

k2 = 0.2 s^-1

Therefore, at a temperature of 35°C, the rate constant is 0.2 s^-1, which is double the rate constant at 25°C. This demonstrates the principle that the rate doubles with every 10°C increase in temperature.