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Whereas a concentration-time graph shows how [A] falls during the reaction, a rate-concentration graph (rate-[A]) plots instantaneous rate on the y-axis against [A] on the x-axis. The shape of this plot depends directly on the order:
Rate-[A] graphs are usually produced by:
For zero order, rate = k — rate does not depend on [A]. The plot is a horizontal straight line at height k.
Sketch description: Flat horizontal line starting at (0, k) extending rightwards.
For first order, rate = k[A]. The plot is a straight line passing through the origin with gradient k.
Sketch description: Straight line from (0,0) with positive gradient.
A rate-[A] plot is straight, passing through the origin. At [A] = 0.50 mol dm^-3 the rate is 0.020 mol dm^-3 s^-1. What is k?
Gradient k = rate / [A] = 0.020 / 0.50 = 0.040 s^-1
Units check: (mol dm^-3 s^-1) / (mol dm^-3) = s^-1 — correct for first order.
For second order, rate = k[A]^2. The plot is a parabolic curve passing through the origin, starting shallow and becoming steeper as [A] increases.
Sketch description: Curved line starting at origin, increasingly steep.
Plot rate (y) against [A]^2 (x). Gradient = k.
Example: A rate-[A]^2 plot has gradient 5.0 mol^-1 dm^3 s^-1. Then k = 5.0 mol^-1 dm^3 s^-1.
| Order | rate-[A] plot | Gradient | y-intercept |
|---|---|---|---|
| 0 | Horizontal line | 0 | k |
| 1 | Straight line through origin | k | 0 |
| 2 | Upward curve (parabola) | varies | 0 |
You might wonder: if concentration-time graphs show order from their shape, why also use rate-concentration graphs? Two reasons:
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