The gradient is the steepness of a graph; on a volume-time or mass-time curve the gradient at a point equals the rate of reaction at that moment.
The gradient is the steepness of a graph; on a volume-time or mass-time curve the gradient at a point equals the rate of reaction at that moment. Malay: kecerunan · Chinese: 梯度.
Because the rate of reaction is a change in quantity divided by time, and a rate graph plots quantity against time, the slope of the graph is exactly the rate. A steep part of the curve means a fast rate; a shallow part means a slow rate; a flat part, the plateau, means a rate of zero. To find the rate at a chosen moment, you draw a tangent to the curve at that point and calculate its gradient by dividing the change on the vertical axis by the change on the horizontal axis.
Example. On a graph of gas volume against time, suppose a tangent at the start rises by 30 cm3 over 10 s. Its gradient is 30 divided by 10, which is 3 cm3 s−1, and that is the instantaneous rate at the start. Later the curve is less steep, its tangent gives a smaller gradient, and the rate is lower, because the reactants are running out.
Confusion to avoid. Do not read a single point’s height as the rate; the rate is the slope, not the value. Also, for an average rate you take the gradient of the straight chord between two points, but for an instantaneous rate you take the gradient of a tangent at one point. Mixing up the chord and the tangent gives the wrong rate.
The gradient is the tool that turns a rate graph into numbers, connecting the rate concept with the average and instantaneous rates, and reading it correctly is essential for the graph questions in SPM Chemistry.
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