Enter the initial concentration, reaction rate constant, and time into the calculator to determine the final concentration of a reactant according to the Brus equation.

Brus Equation Formula

The following formula is used to calculate the final concentration of a reactant:

[A]_t = [A]_0 * e^{(-kt)}

Variables:

  • [A]_t is the final concentration of the reactant (mol/L) at time t
  • [A]_0 is the initial concentration of the reactant (mol/L)
  • k is the reaction rate constant (1/s)
  • t is the time (s)

To calculate the final concentration of a reactant, multiply the initial concentration by the exponential of the negative product of the reaction rate constant and time.

What is the Brus Equation?

The Brus equation is a mathematical representation of the first-order reaction kinetics, where the rate of reaction is directly proportional to the concentration of one of the reactants. It is commonly used in chemical kinetics to describe the exponential decay of reactant concentration over time.

How to Calculate Final Concentration using the Brus Equation?

The following steps outline how to calculate the final concentration of a reactant using the Brus Equation.

  1. First, determine the initial concentration of the reactant ([A]_0) in mol/L.
  2. Next, determine the reaction rate constant (k) in 1/s.
  3. Next, determine the time (t) in seconds.
  4. Next, gather the formula from above = [A]_t = [A]_0 * e^(-kt).
  5. Finally, calculate the final concentration ([A]_t) in mol/L.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Initial concentration of the reactant ([A]_0) = 0.5 mol/L

Reaction rate constant (k) = 0.1 1/s

Time (t) = 30 s