What a learner can do afterwards
- Takes tangents from a concentration-time curve to get rates and plots rate against concentration
- Identifies zero, first and second order from the shape of a rate-concentration graph
- Measures successive half-lives and uses their constancy to argue for first order
- Finds the rate constant from a gradient or from a half-life
1 · Read
Pick a few times on a concentration-time curve and draw a tangent at each one. The steepness of each tangent is the rate at that moment, and you then plot those rates against the concentration left at each time.
Picture the rate against concentration plot for hydrogen peroxide breaking down. A flat line means zero order, a straight line through the start means first order, and a curve bending upward means second order among the three shapes compared here.
Now watch the half-life, the time for the concentration to halve, again and again. If every halving takes the same time, your reaction is first order, and if the times drift, it is not.
For the rate constant, take a gradient magnitude: the gradient of the rate against concentration line for a first order reaction, or minus the gradient of the straight concentration-time line for a zero order one. You can also use k = 0.693 divided by the half-life, which gives k in matching inverse time units, per second when the half-life is in seconds.
Tangents give rates, shapes give orders, steady half-lives mean first order, and gradients or half-lives give k.
Recognising reaction order and Tangent rates were written for this dataset. The reading 12.4: Integrated Rate Laws is retained from library:book-page:chem-chemistry-2e-openstax:134-12-04-integrated-rate-laws; its source credit remains unchanged.
2 · Watch
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Where it sits
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Optional connections
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8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.