Instantaneous rate

The instantaneous rate is the rate of reaction at one particular moment, found from the gradient of a tangent drawn to the curve at that point. Malay: kadar serta-merta · Chinese: 瞬时速率.

Because the rate of a reaction keeps changing as it proceeds, a single average value cannot describe the speed at every instant. The instantaneous rate captures the speed at just one chosen time. To find it on a volume-time or mass-time graph, you draw a straight line that just touches the curve at the point of interest, called a tangent, and then calculate the gradient of that tangent. The steeper the tangent, the higher the instantaneous rate at that time.

Example. Suppose the curve of gas volume against time is steepest at the very start, where a tangent has a gradient of 3 cm³ s⁻¹. That means the instantaneous rate at t = 0 is 3 cm³ s⁻¹. Later, at t = 40 s, the curve is flatter and a tangent there gives 1 cm³ s⁻¹, so the reaction has slowed to a third of its opening speed. On the flat plateau the tangent is horizontal, so the instantaneous rate is zero.

Confusion to avoid. Do not confuse the instantaneous rate with the average rate. The average rate uses two points and the straight chord between them, giving one figure for a whole interval. The instantaneous rate uses a tangent at a single point. At the start of a reaction the instantaneous rate is the highest of all, and it is always larger than the average rate taken over a later interval.

The instantaneous rate connects the idea of rate to the gradient work in the graphs part of this chapter, and reading a tangent correctly is a skill SPM Chemistry often tests in the practical and Paper 2 questions.