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Chemical kinetics

Integrated Rate Law & Kinetics Grapher

Compare three linearized concentration plots to identify reaction order. The best-fit line gives the rate constant and predicts the half-life.

Review first-order kinetics and half-life or zero- and second-order rate laws.

One measurement per line, separated by a comma or space. Headers are optional; concentrations must be greater than zero.

6 measurements · 0–50 s

Best linear fit

First order

ln[A] versus time · R² = 1.0000

Rate constant · k

0.03002

s⁻¹

Half-life · t½

23.09 s

From first measured [A]

Fit quality

100.00%

R² · closer to 100% is better

A straight ln[A] plot means the reaction is first order; the negative slope is −k. With experimental noise, compare the R² values before deciding.

Compare the three plots

Dots: measurements · Line: linear fit

Zero order

0.880.670.460.250.043t = 0 s; [A] (M) = 0.8t = 10 s; [A] (M) = 0.594t = 20 s; [A] (M) = 0.439t = 30 s; [A] (M) = 0.326t = 40 s; [A] (M) = 0.242t = 50 s; [A] (M) = 0.178[A] (M)050Time (s)
R² = 0.9562slope -0.01223

First order

Best fit
-0.041-0.51-0.97-1.4-1.9t = 0 s; ln[A] = -0.2231t = 10 s; ln[A] = -0.5209t = 20 s; ln[A] = -0.8233t = 30 s; ln[A] = -1.121t = 40 s; ln[A] = -1.419t = 50 s; ln[A] = -1.726ln[A]050Time (s)
R² = 1.0000slope -0.03002

Second order

6.24.73.21.80.29t = 0 s; 1/[A] (M⁻¹) = 1.25t = 10 s; 1/[A] (M⁻¹) = 1.684t = 20 s; 1/[A] (M⁻¹) = 2.278t = 30 s; 1/[A] (M⁻¹) = 3.067t = 40 s; 1/[A] (M⁻¹) = 4.132t = 50 s; 1/[A] (M⁻¹) = 5.6181/[A] (M⁻¹)050Time (s)
R² = 0.9539slope 0.08564

Predicted half-life

From the first measured concentration of 0.8 M to 0.4 M. The curve uses the fitted rate constant.

[A] (M)0.80.4t½ = 23.1 sTime (s)

t½ = ln(2) / k

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