Maths for Chemists
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How do you work out the tangent of a graph? I know this isn't a strictly chemistry-related question but I need to plot tangents of my graphs of hydrochloric acid and magnesium to work out the activation energy.
Ulex replies
This is something of a challenge to explain without the use of a diagram but I will attempt it! Please imagine a circle first of all, with its centre clearly marked. Now, mentally, draw a straight line from the centre to any point on the circle. Next, and this is the important bit, mentally draw a another straight line which touches the point where the first line meets the circle and is at right-angles to it. This second straight line is called a tangent to the circle.
Your graph is, of course, not a circle but you can still draw tangents to it at various points along its length. You can’t use the right-angle trick of course because you can’t identify a centre point as you can with a circle but you can draw tangents which look right – i.e. seem to have equal angles between the tangent and the parts of the circle on both sides of the point where the tangent touches the circle.
Now that you have got your tangents you can measure their gradients in the usual way.
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updated: 19 January 2006
