Maths for A Level Chemistry - updated edition

0 50 100 150 200 250 300 Time/s Volume O 2 /cm 3 25 20 15 10 5 0 10 100 Hence Initial rate of production of oxygen = gradient = 10 100 = 0.1 cm 3  s −1 4.3 Drawing and using the slope of a tangent to a curve to determine rate of change Many quantities in chemistry do not vary linearly with each other so their graphs are not straight lines. Instead their graphs are curves so the gradient is no longer constant and it depends on where on the graph it is measured. Look at the graph below and you can see that the gradient at the point x 1 can be found by drawing a tangent (i.e. a straight line which skims the curve) and then ϐinding the gradient of the line. You can see that the gradient at point x 2 is larger than at x 1 . y x 0 x 1 x 2 Pointer Note that we could have used a larger triangle but it is more convenient to use a triangle where the line cuts the corner of one of the grid squares. 4 Graphs 43