Rate Equations

After reading these notes, test your knowledge with free interactive questions on Seneca — used by over 10 million students.

Reading Rate Graphs

Reaction rates can be measured over time. We plot this data on graphs, and you need to be able to read them.

A rate of reaction is defined as the change in concentration of a reactant or product over time.
- This means that if you plot concentration against time, the rate is the gradient of the graph.

The above graph is a straight line graph showing the concentration against time.
To calculate the gradient of the graph (and the rate) you find the change in concentration divided by the change in time.
In practice: pick two points and read off the x and y values.
- Calculate the differences in concentration values and the time, values and then divide the one by the other.

Not all reaction rates are constant - a reaction may slow down or speed up with time.
- For reactions like this, you get a curved graph.
You can calculate the rate at any point in time by calculating the gradient of a point on the graph.
- To do this, you need to draw a tangent on the graph at this point.

A tangent is a straight line which just touches the curve in one place.
To draw the tangent, choose your point and draw a straight line through it. You want to have an equal distance to the curve from the line on each side of the point.
- An example is above.

You can calculate rates of reactions by finding their rate equations. These link the concentration of each reactant to the rate of the equation.

Reactions happen when molecules collide into one another.
- In a reaction between molecule A and B, the rate will be proportional to the number of collisions between A and B.
If you double the concentration of B, you should have double the collisions between A and B.
- So, you would expect the reaction rate to double.
In reality, this is an over-simplification because you have multiple steps in most reactions, which may or may not involve each molecule.

A rate equation is always written of the form:
- Rate = k × [A]^m[B]ⁿ
k is called the rate constant.
The numbers m and n tell you how the rate depends on the reactants.
- They are called the order of the reaction with respect to each reactant.

Just as we define an order for the reactants, we define an overall order for the reaction.
The overall order is given by m + n.
- You very rarely get any value above 2 for an order with respect to a reactant, or less than zero.

The rate constant k has a few key features:
- It’s temperature dependent.
- It has different units for different reactions.
The units of the reaction rate have to be concentration over time.
But the units of the product of the reactants are never that, so you need to assign units to k to sort it out.
- The larger the rate constant, the faster the reaction.

You need to be able to do a whole bunch of calculations with rate equations.

$Calculating the rate of reactions$

The rate of a reaction can be calculated if you know its rate constant, the reactant concentrations, and the order of the reaction with respect to each reactant.
E.g. if a reaction obeys the equation:
- Rate = k[A][B], where the rate constant is 0.5dm³mol^-1t^-1, and the reactant concentrations are both 2moldm^-3
- The rate is 2moldm^-3 × 2moldm^-3 × 0.5dm³mol^-1t^-1 = 2moldm^-3t^-1

$Calculating the rate constant$

You can be given a rate equation and told to calculate the rate constant given some concentration data.
- E.g. the rate equation for the production of I-Cl is: Rate = k[I₂]¹[Cl₂]¹
Given that the concentrations of I₂ and Cl₂ are 1moldm^-3, and the rate of reaction is 40moldm^-3t^-1, what is the value of k?
- k = 40moldm^-3t^-1 ÷ (1moldm^-3)² = 40mol^-1dm³t^-1