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Concentration Changes Over Time

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The integrated rate laws describe how concentration changes over time for each order. A zero-order reaction gives a straight line of [A] vs time; first-order, a straight line of ln[A] vs time; second-order, a straight line of 1/[A] vs time. Whichever plot is linear identifies the order, and its slope gives the rate constant k. Half-life behavior depends on the order too.

UNIT 5 TOPIC 5.3 • CONCENTRATION CHANGES OVER TIME INTEGRATED RATE LAWS The plot that becomes a straight line reveals the reaction order. ZERO ORDER [A] time FIRST ORDER ln[A] time SECOND ORDER 1/[A] time [A]t = [A]0 − kt slope = −k ln[A]t = ln[A]0 − kt slope = −k 1/[A]t = 1/[A]0 + kt slope = +k HALF-LIFE (FIRST ORDER) t1/2 = 0.693 / k Constant — independent of [A]₀. Radioactive decay is a classic first-order example. CED ANCHOR Graphing concentration data three ways and finding which plot is linear identifies the reaction order; the slope of that line gives the rate constant k. AP Chemistry · Unit 5 · Kinetics
Integrated rate laws turn order into a straight line. Zero order plots [A] linearly against time; first order plots ln[A]; second order plots 1/[A]. Whichever plot is linear reveals the order, and its slope gives the rate constant — and half-life behavior follows from the order.
Integrated Rate Plotter · Open the sandbox →

The errors involve detaching half-life from order, reading the wrong linear transform as giving k, and misusing the concentration-time data. Match the order to the plot that comes out straight, and read k from its slope.

The work

3 ways in · any order
Lesson
Integrated Rate Laws ›

Zero-, first-, and second-order reactions each straighten a different plot, revealing the order and rate constant. The lesson reads the linear transforms and half-lives, then closes with a ten-scenario check.

Skill check · 10 scenarios
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Diagnostic
10-item topic check ›

Ten items spanning the Topic 5.3 misconceptions: half-life detached from order, the wrong linear transform read as k, and integrated-rate data misused.

Not started · 10 items · ~15 min
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Targeted Practice
Drill a single misconception ›

Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.

Take the diagnostic to identify your misconceptions
Diagnostic first