Calculating Gradients Flashcards

All 5 cards in this deck

What does the slope (gradient) of a tangent drawn to a rate curve tell you?

The rate of reaction at that specific time.

What are the steps to find the rate of reaction at a specific time from a curved graph?
e.g. the rate at 40 s on a gas volume–time graph

1. Draw a tangent that just touches the curve at 40 s.
2. Read a y-step and an x-step from the tangent, e.g. 30 cm$^3$ and 60 s.
3. Rate = y-step ÷ x-step = $0.5$ cm$^3$/s

What is the formula for the gradient of a tangent on a rate graph?

Gradient = y-step ÷ x-step (change in quantity ÷ change in time).

What unit does the gradient of a tangent give on a graph of gas volume (cm$^3$) against time (s)?

cm$^3$/s.

True or false? Joining two points on a curve with a straight line and finding its gradient gives the rate at a specific time.

False. That gives the mean rate between those times; a tangent is needed for the rate at a specific time.