AP® Chemistry · Unit 5 · Topic 5.1
Measuring Rate from Data
Reaction rate measures how fast concentration changes over time. Average rate comes from a straight-line slope between two points; instantaneous rate comes from the tangent slope at one point.
As a reaction runs, reactant concentration drops fastest at the start, when molecules are packed in and collisions happen constantly. As reactant gets used up, collisions become rarer, so the curve of concentration versus time flattens out. That's why the slope keeps getting shallower: the slope at any point on that curve IS the rate at that moment, and it naturally decays as reactant disappears.
Average rate over an interval is just the total change in concentration divided by the total time — the slope of the straight secant line connecting the start and end points on the curve. Instantaneous rate is the slope of the tangent line touching the curve at a single point, found by drawing that tangent and reading its slope directly. Because the curve bends downward (concave up, flattening), the secant line averages in the flat, slow later part along with the steep early part, so the average rate always comes out smaller in magnitude than the instantaneous rate at the start of that same interval.
This sets up everything else in kinetics. Once you can read rate off a curve, you can compare rates at different concentrations to figure out the rate law and reaction order — the next step in the unit. Real data rarely comes from watching concentration by eye: a spectrophotometer measures how much light a solution absorbs, and since absorbance is proportional to concentration, it lets you track concentration continuously and non-destructively, point by point, generating exactly the curve you need to pull rates from.
Key terms
- Average rate
- The magnitude of the change in concentration divided by the elapsed time, found as a secant-line slope.
- Instantaneous rate
- The rate at one specific moment, found as the slope of the tangent line to the concentration curve at that point.
- Secant line
- A straight line connecting two points on a curve, whose slope gives the average rate of change between them.
- Tangent line
- A line touching a curve at a single point with the same slope as the curve there, giving the instantaneous rate.
- Spectrophotometer
- An instrument that measures light absorbance to track concentration continuously without disturbing the reaction.
Watch it explained
- How it worksHow do you pull an instantaneous rate off a curve using a tangent line?
- Worked exampleFind the average rate of a reaction where 0.80 M drops to 0.50 M over 60 seconds.
- Common mistakeWhy isn't the average rate over an interval the same as the rate at the start of it?
- Ties togetherHow does a spectrophotometer let you watch concentration change without stopping the reaction?
Check yourself
End of topic.