Calculating rates of reactions

In a nutshell

Many factors affect the rate of reactions including temperature, pressure, concentration and particle size. In this lesson you will learn more about these factors and how to calculate the rate of reaction and mean rate of reaction from graphs.

Equations 

​$$rate \space of \space reaction= \space \frac{amount \space of \space reactant \space used/amount \space of \space product \space formed}{time}\\ \ \\ \ \\gradient= \frac{change \space in \space y-axis}{change \space in \space x-axis}\\ \ \\ \ \\mean \space rate \space of \space reaction= \space \frac{amount \space of \space reactant \space used/amount \space of \space product \space formed \space in \space the \space whole \space reaction}{reaction \space time}$$​​

Collision theory 

The collision theory states that the rate of a reaction depends on the energy of the reactants and the frequency at which the reactants collide. 

In a chemical reaction, the reactants must collide with at least the activation energy for a reaction to take place.

The higher the collision frequency (the more frequently the reactants collide), the more successful collisions occur and the higher the rate of reaction.

Temperature 

Increasing the temperature of a reaction will result in particles moving quicker and colliding more frequently. Furthermore, increasing the temperature of a reaction increases the energy of the reactants; more reactants will have the activation energy and the number of successful collisions increases.

Pressure/concentration

Increasing the pressure of a gas results in more gas particles being packed in a given volume; this increases the rate of collisions and therefore the rate of reaction.

Increasing the concentration of a solution results in more reactant particles being present in a given volume which increases the frequency of collisions and therefore the rate of reaction.

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Size of particles​​

Smaller particles have a relatively large surface area exposed compared to their volumes. They have a high surface area to volume ratio. The greater the surface area of particles, the more frequently collisions occur and the higher the rate of reaction.

Measuring the rate of reaction 

The rate of a reaction can be calculated from graphs which show the rate at which reactants are used up or the rate at which products form over time.

​$$rate \space of \space reaction= \space \frac{amount \space of \space reactant \space used/amount \space of \space product \space formed}{time}$$​​

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Graphs 

The $$x$$-axis of the graph should show time. The $$y$$​-axis should show the amount of reactants used up or the amount of products formed.

The gradient of the line is the rate of reaction, therefore the steeper the gradient the higher the rate of reaction. 

To calculate the gradient of a line the following equation is used:

$$gradient= \frac{change \space in \space y-axis}{change \space in \space x-axis}$$

Example

The graph below shows the amount of gas formed over time. A triangular segment is marked and the gradient of the line is calculated.

$$rate \space of \space reaction= \space \frac{amount \space of \space product \space formed}{time} \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \\ \ \\ =\frac{30 \, cm^3-10 \, cm^3}{22.5 \,s -7.5 \, s} = \frac{20 \, cm^3}{15 \,s}=1.33 \, cm^3 s^{-1}$$​​

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1.33 \, Cm^3 s^{-1}The gradient of the line and therefore the rate of reaction is $$\underline{1.33 \,cm^3 s^{-1}}$$. 
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Curved lines

If a graph has a curved line, the rate of reaction will not be constant throughout the reaction. To work out the rate of reaction at a certain point on a curved line, a tangent is drawn at the point.

The gradient of the tangent must be the same as the gradient of the line at that given point. When drawing tangents, there must be the same amount of space between the tangent and either side of the line.

Example 

The graph below shows the amount of product formed over time. A tangent has been drawn on the graph to calculate the rate of reaction at that given point.

​$$rate \space of \space reaction= \frac{change \space in \space y-axis}{change \space in \space x-axis} \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \\ \ \\ =\frac{15g}{42 \, s-16 \,s}= \frac{15}{26}=0.58 \, g \, s^{-1}$$​

The rate of reaction at that given point is ​$$\underline{0.58 \, g \, s^{-1}}$$. 

Mean rate of reaction 

To work out the mean rate of reaction for a curved line, you need to know the total amount of reactant used or product formed in the reaction. 

The end of a reaction is reached when the curved line plateaus and the amount of substance remains constant.

​$$mean \space rate \space of \space reaction= \space \frac{amount \space of \space reactant \space used/amount \space of \space product \space formed \space in \space the \space whole \space reaction}{reaction \space time}$$​

Example 

The mean rate of reaction for the graph above has been calculated. In the reaction $$38 \,g$$ of product is formed in $$55 \,s$$55 \,s38 \,g38 \,g38 \,g.

​Rate \space of \space reaction= \space \frac{amount \space of \space reactant \space used/amount \space of \space product \space formed}{time}= \frac{15}{42-16}= \frac{15}{26}=0.58 \, g \, s^

$$mean \space rate \space of \space reaction= \frac{38 \, g}{55 \, s}= 0.69 \, g \, s^{-1}$$​

​Rate \space of \space reaction= \space \frac{amount \space of \space reactant \space used/amount \space of \space product \space formed}{time}= \frac{15}{42-16}= \frac{15}{26}=0.58 \, g \, s^{-1}
​Rate \space of \space reaction= \space \frac{amount \space of \space reactant \space used/amount \space of \space product \space formed}{time}= \frac{15}{42-16}= \frac{15}{26}=0.58 \, g \, s^{-1}

The mean rate of reaction for the graph above is $$\underline{0.69 \, g \, s^{-1}}$$.