# Rate Constant Calculator

By Łucja Zaborowska, MD
Last updated: Oct 13, 2020

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. Choose the order of reaction:
• Zero - the speed of the reaction does not depend on the concentrations of the reagents, for example, `2NH₃(gas) → N₂(gas) + 3H₂(gas)`, photochemical reactions.
• 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 reaction quotient 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 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 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 Arrhenius equation: `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 a rate constant equations.

Be careful with 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 `
Łucja Zaborowska, MD
Order of reaction
First
Reaction constant (k)
/
sec
Concentration [A]
M
Reaction rate
M/
sec
Half life (T½)
sec
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