Maths for A Level Chemistry - updated edition

The gradient, m , is found forming a triangle. Gradient = change in the y -values change in the x -values = 30 20 = 1.5 Intercept on the y- axis, c = 10 Hence equation of the straight line y = mx + c y = 1.5 x + 10 Straight line graphs showing direct proportion If the straight line passes through the origin (0,0) or simply O, then the quantity on the y- axis is directly proportional to the quantity on the x- axis. Directly proportional means that if, for example, the quantity on the x- axis doubles then the quantity on the y- axis doubles. In other words, whatever you multiply the quantity on the x- axis by, the quantity on the y- axis will go up by the same factor. Drawing a straight line graph from experimental data Most graphs in chemistry arise from experimental data (i.e. each data point is the result of a measurement of combination of measurements). When the points are plotted they often involve a degree of scatter owing to some uncertainty in the measurements. If the points look as though they suggest a straight line then we need to draw a straight line of best ϐit. Line of best fit To draw a line of best ϐit: • Use a transparent ruler to draw a line that matches the gradient suggested by the data points. • Ensure that the points are scattered equally above and below the line. Calculating the rate of change from a graph showing a linear relationship Graphs used to determine the rate of change of a quantity plotted on the y- axis always have time along the x- axis. Such graphs can be used to determine the rate of change of the quantity on the y- axis. In the following example a graph of volume of oxygen in m 3 is plotted on the y- axis and the time in seconds is plotted on the x- axis. The rate of change of the quantity (i.e. volume of oxygen) on the y- axis is determined from the gradient of the graph. Example Hydrogen peroxide (H 2 O 2 ) decomposes to form oxygen (O 2 ) and water (H 2 O) according to the equation 2H 2 O 2 → 2H 2 O + O 2 Pointer The values of m and c obtained from the graph are substituted into the general equation for a straight line. 4 Graphs 41