Calculating the rate of reaction

In a nutshell

The rate of a reaction is how fast the reaction occurs. It's the ratio of the change of the amount of products or reactants with time. The rate of a reaction can be worked out by finding the gradient of a graph.

Rate of reaction

The rate of a reaction is how fast the product is getting produced or how fast the reactants are getting used up, usually per second ( $s^{-1}$ ).

The rate of a reaction can be worked out by finding the gradient of a graph. The $y$ -axis will be the quantity of the products or reactants throughout the reaction. The $x$ -axis will be time.

Below is the procedure on how to find the rate of a reaction from a graph.

procedure

1.	Draw a line of best fit
2.	Choose two points on the line
3.	Draw vertical line down and horizontal line to form a triangle
4.	Measure the vertical and horizontal line
5.	Insert values in the gradient equation $Gradient=\dfrac{Change\>in\>y}{Change\>in\>x}$

Example

A student has plotted the volume of gas produced per minute during their experiment. They drew the triangle to figure out the gradient. Help them finish finding the gradient. Round your answer to $2\ s.f.$

Chemistry; Kinetics I; KS5 Year 12; Calculating the rate of reaction

Measure the vertical line. This is the same as the change in y.

$Change\>in\>y=8.5-1=7.5\>cm^3$

Measure the horizontal line. This is the same as the change in x.

$Change\>in\>x=18-2=16\>min$

Insert values into the gradient equation.

$Gradient= \dfrac{Change\>in\>y}{Change\>in\>x}=\dfrac{7.5\>cm^3}{16\>min}=0.46875\>cm^3\>min^{-1}$

Then round your answer to $2\ s.f.$ 

$Gradient={0.47\>cm^3\>min^{-1}}$

The gradient is $\underline{0.47\>cm^3\>min^{-1}}$ . This is the rate of a reaction.

Note: The units has the quantity unit ( $cm^3$ ) and per time ( $min^{-1}$ ) unit.

Curved graphs

Not all graphs are straight lines. It's possible you have to work out the gradient from a curved graph.

The procedure on how to find the rate of a reaction from a curved graph is shown below.

procedure

1.	Find the point of interest on the curve
2.	Put the ruler on the point
3.	Position the ruler so the top and bottom spaces between the ruler and the curve are the same
4.	Draw a line across the graph along the ruler to create the tangent
5.	Work out the gradient by drawing a triangle and using $Gradient=\dfrac{Change\>in\>y}{Change\>in\>x}$

Example

The ruler is placed at the point of interest and is positioned so that the top and bottom spaces between the ruler and curve are even. A (change in $y$ ) is the concentration and B (change in $x$ ) is the time. The tangent is drawn. This means the triangle can be drawn to work out the gradient.

Chemistry; Kinetics I; KS5 Year 12; Calculating the rate of reaction

Initial rate of reaction

The initial rate of reaction is the reaction rate when time is zero. This can be worked out from a graph by finding the gradient of the tangent when time is zero.

Below is the procedure on how to find the initial rate of a reaction from a graph.

procedure

1.	Draw a tangent when $Time = 0$
2.	Draw the triangle
3.	Work out the gradient using $Gradient=\dfrac{Change\>in\>y}{Change\>in\>x}$

Example

Work out the initial rate of a reaction. Give your answer to $3\ s.f.$ 

Chemistry; Kinetics I; KS5 Year 12; Calculating the rate of reaction

The tangent at $Time=0$ is drawn. The triangle is drawn to work out the gradient.

Measure change in y.

$Change \>in\>y=30-3=27\>mol\>dm^{-3}$

Measure change in x.

$Change\>in\>x=7-0=7\>min$

Work out gradient using the gradient equation.

$Gradient = \dfrac{Change\>in\>y}{Change\>in\>x}=\dfrac{27\>mol\>dm^{-3}}{7\>min}=3.857142 \>mol\>dm^{-3}\>min^{-1}$

Round to $3\ s.f.$ 

$Gradient=3.86\>mol\>dm^{-3}\>min^{-1}$

The gradient is the initial rate of a reaction.

$Gradient=Initial \>rate\>of\>reaction={3.86\>mol\>dm^{-3}\>min^{-1}}$

The initial rate of reaction is $\underline{3.86\>mol\>dm^{-3}\>min^{-1}}$ .

Working out rates without a graph

If experimental data has been given instead, the reaction rate can be worked out without plotting a graph. A graph would be more accurate, but it's still possible to calculate the rate without it.

This method is useful for experiments when a change is due to take please, for example, a colour change. A colour change could indicate the product is formed.

Example

Hydrochloric acid and zinc were left in a flask to react. After $20 \>seconds$ , $40\>cm^3$ of gas was collected in a syringe. What is the rate of the reaction?

First write down the rate equations.

$Rate= \dfrac{Amount\> of\> reactant \>used\>or\>amount\>of\>product\>produced}{Time\>taken}$ 

Then find the product, in this case the gas produced is the product.

$Amount\>of\>product\>produced=Amount\>of\>gas\>produced=40\>cm^3$ 

Insert known values into the rate equation.

$Rate=\dfrac{40\>cm^3}{20\>s}={2\>cm^3\>s^{-1}}$

The rate of the reaction is $\underline{2\>cm^3\>s^{-1}}$ .