# Rate Constant Calculator

Created by Łucja Zaborowska, MD, PhD candidate
Reviewed by Bogna Szyk and Jack Bowater
Last updated: May 30, 2022

Our rate constant calculator computes both the rate and half life of the reaction. It also allows you to discover the rate constant, and the concentration of the given substance, if your query is based on the rate laws, that is.

Remember, our calculators work both ways. Whatever it is you're trying to calculate, we're here to help. 🙋

In the article below, we'll focus on finding the rate constant, and the theoretical bases of the reaction order calculator.

## How to use the rate constant calculator?

In the beginning, think about what you're trying to find - find all the useful data provided in your query.

1. Select how many molecules interact in the elementary step.

2. Choose the order of reaction for each molecule:

• Zero — the speed of the reaction does not depend on the concentrations of the reagent, for example, 2NH₃(gas) → N₂(gas) + 3H₂(gas), photochemical reactions. Note, that you cannot set zero for any of the reagents in a bimolecular or trimolecular step. In these cases, please treat the zero-order reagent as non-existent.
• First — the rate of the reaction depends on the concentration of a single reagent, for example, C₂H₆(g) → 2CH₃(g), radioactive decay reactions.
• Second — Can be described as a reaction where the rate depends on two molecules. This can be either two different reagents, or a molecule reacting with itself, for example, H₂(g) + I₂(g) → 2HI(g) or 2NO₂ (g) → 2NO(g) + O₂(g).

(🤔 Are you familiar with the equilibrium constant of the above reactions? If not, try our equilibrium constant tool!)

1. Enter the concentration of the substance.

2. Choose the result you want:

• Are you trying to calculate the value of the rate constant k? If so, leave this section of the calculator blank.
• Play with the calculator as much as you like to find out how different values affect the final result.

What is half-life (T½)?

Half-life is the period in which one-half of the substrate will have undergone the chemical transformation. Let's depict it with a quick example. Our initial concentration, [S] is 20 M, and the T½ = 2 min.

❓ Are you familiar with the equilibrium constant of the above reactions? If not, try our equilibrium constant tool!

1. Enter the concentration of the substance.

2. Choose the result you want:

• Are you trying to calculate the value of the rate constant k? If so, leave this section of the calculator blank.
• Play with the calculator as much as you like to find out how different values affect the final result.

What is half-life (T½)?

Half-life is the period in which one-half of the substrate will have undergone the chemical transformation. Let's depict it with a quick example. Our initial concentration, [S] is 20 M, and the T½ = 2 min.

[S]

20

10

5

2.5

1.25

...

time (min)

0

2

4

6

8

...

What is the rate of reaction?

The rate of the reaction characterizes the speed of the reaction, described in M/sec, M/min, or mol / (sec * L), that is, how many moles react per liter of substance per second. ( Molar concentration [M] = mol/L)

What is the rate constant of the reaction?

The rate constant is simply a proportionality coefficient, specific for a given temperature and the type of reaction. It is described by many different equations and is usually found experimentally (see the section below).

📚 Preparing for an exam? Try our helpful tools for other types of reactions:

## How to calculate the rate constant?

1. The most obvious answer to the question "How to find the rate constant?" is to modify the equations for the rate of the reaction or its half-life. If you know the order of reaction, the concentration of the substance, or the rate/half-life of the reaction, this may be a method for you. (It's also the easiest method for zero-order reactions since the rate of the reaction is equal to the rate constant!)

2. The dependence of the rate constant on temperature is well defined by the : k = A * exp(-E /(R * T)).

3. If you were wondering how to determine the rate constant for reversible reactions, here's an easy equation that works for the majority of the cases: K = k₁ / k₋₁, where K = equilibrium constant of the reaction, k₁ & k₋₁ = rate constants of the forward and backward reactions, respectively.

## Theory behind the rate law calculator

Below you will find all the necessary equations for calculating the rate of a zero, first, and second-order reaction. Look at the formulas below, and compare them with the slopes of the below graphs. Keep in mind that all of these formulas can serve as rate constant equations.

Be careful with the slope of first-order reactions: it may look similar to the zero one, but in fact, it contains the natural logarithm of [A] on the Y-axis!

1. Zero order
• Half life = A / (2 * k)
• Rate of the reaction = k
1. First order
• Half life = 0.693 / k
• Rate of the reaction = k * A
1. Second order
• Half life = 1 / (k * A)
• One substance: Rate of the reaction = k * A * A
• Two substances: Rate of the reaction = k * A * B

## FAQ

### How to find the rate constant?

To find the rate constant:

1. Determine how many atoms are involved in the elementary step of the reaction.
2. Find out the order of reaction for each atom involved in the reaction.
3. Raise the initial concentration of each reactant to its order of reaction, then multiply them all together.
4. Divide the rate by the result of the previous step.
5. Your rate constant's units will depend on the total order of the reaction.

### What factors affect the rate constant?

Only temperature will affect the rate constant. You may think that changing the initial concentration will affect the rate constant, but this will only alter the rate. You could introduce a catalyst to provide a different reaction pathway with lower activation energy, but this is actually a different reaction.

### How to find activation energy from rate constant?

To find activation energy from the rate constant:

1. Find the Arrhenius constant for the reaction.
2. Subtract the natural logarithm of the rate constant from the natural logarithm of the Arrhenius constant.
3. Multiply the result of the previous step by the reaction's temperature in Kelvin and the ideal gas constant.
4. The result is your activation energy in the same energy units as the ideal gas constant.

### Which situation shows a constant rate of change?

First-order reactions show a constant rate of change as long as the temperature remains the same. That is because the reaction rate changes proportional to the remaining reactants. This is best shown if you construct a graph of the rate of change and differentiate it with respect to time; it should show a straight line.

Łucja Zaborowska, MD, PhD candidate
Elementary step
Unimolecular
Molecule A
Order of reaction
First
Concentration [A]
M
Half life (T½)
sec
Results
Total order of reaction
1
Reaction constant (k)
M⁽¹⁻ⁿ⁾/
sec
Rate of reaction
M s⁻¹
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