2.2.1

# Rate Equations (A2 Only)

Test yourself

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

### Definition of a rate

• 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.

### A simple 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.

### Curved graphs

• 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.

### Drawing tangents

• 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.

## Rate Equations

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

### Physical basis

• 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.

### The rate equation

• 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.

### The order of reaction

• 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

• 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.

## Calculations of Rate Equations

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