Mistake Master
Concentration changes over time
The order of a reaction leaves a fingerprint: it is the plot that comes out as a straight line. Match the order to the linear plot, and its slope hands you the rate constant.
§1
One order, one straight line.
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The integrated rate laws tell how concentration changes with time for each order, and each makes a different plot linear. Zero order: [A] vs time is a straight line. First order: ln[A] vs time is straight. Second order: 1/[A] vs time is straight.
Whichever plot is linear identifies the order, and the slope of that line gives the rate constant k (its sign depending on the form).
Half-life also fingerprints the order. For a first-order reaction the half-life is constant (independent of concentration); for zero and second order it changes with concentration.
§2
Reading the plots.
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Match the linear plot to the order, then read k.
- Try the three plots. Plot [A], ln[A], and 1/[A] against time.
- Find the linear one. Zero order → [A] linear; first order → ln[A] linear; second order → 1/[A] linear.
- Read k from the slope. The magnitude of the slope of the linear plot gives the rate constant.
- Use half-life as a check. A constant half-life confirms first order; a changing half-life rules it out.
§3
The pieces you'll meet.
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Match order, plot, and half-life.
§4
Worked example: identify the order.
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Data. For a reaction, a plot of ln[A] versus time is a straight line, but plots of [A] and 1/[A] versus time are curved.
Order. Only ln[A] is linear, which is the fingerprint of a first-order reaction.
Rate constant. The slope of the ln[A] line equals −k, so k is the magnitude of that slope.
Half-life check. A first-order reaction has a constant half-life; measuring it and finding it unchanged as the reaction proceeds confirms first order.
§5
Mistakes that cost real points.
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"Half-life behavior has nothing to do with the reaction order."
Half-life is tied to order. A first-order reaction has a constant half-life; a zero-order half-life shortens as the reaction proceeds; a second-order half-life lengthens. The way the half-life behaves is itself a test of order.
Fix. Use half-life behavior as an order fingerprint: constant → first order; changing → zero or second.
"Any straight-line plot's slope gives the rate constant."
Only the correct linear transform for the reaction's order gives k from its slope. If you read the slope off the wrong plot (say, [A] vs time for a first-order reaction), you get a meaningless number.
Fix. First identify which plot is linear (the order), then read k from that plot's slope, not from a curved one.
"A first-order reaction's [A]-vs-time graph is a straight line."
For first order, it is ln[A] vs time that is linear, not [A] vs time (which is curved). Only a zero-order reaction gives a straight [A]-vs-time line. Matching the wrong plot to the order is the classic slip.
Fix. Remember the pairings: zero → [A] linear, first → ln[A] linear, second → 1/[A] linear.
§6
Skill Check.
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Ten scenarios. Pick the chips that match your answer, then check. A scenario marks complete the first time every part is right. Progress saves on this device.