Chemistry

Zero-Order Integrated Rate Law

Track reactant concentration when its disappearance rate is constant.

C_{t} = C_{0} - k t

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Difficulty

Intermediate

Read time

3 min

Prerequisites

Algebra, logarithms, and molar quantities

Review statusNeeds review

Source

OpenStax, Chemistry 2e, §12.4

Adapted from Teng-Jui Lin’s CHEM 155 equation sheet. The linked textbook reference was used to check the equation and its physical context. Pending editorial review.

Adapted from Teng-Jui Lin, Equation Sheets, under CC BY 4.0.

FormuLab adapted notation and chemical symbols, added variable meanings, units, applicability conditions, and an original worked example. Defined k using the reactant-disappearance rate, absorbing any stoichiometric normalization into k.

Definition

Understanding the core concept

For zero-order disappearance, concentration decreases linearly with time. The expression stops being physically valid at depletion and must not be extended to negative concentrations.

Variables & Units

Understanding each component

Symbol	Meaning	Units
$C_{t}$	Reactant concentration at elapsed time t	$mol L^{- 1}$
$C_{0}$	Initial reactant concentration	$mol L^{- 1}$
$k$	Zero-order disappearance-rate constant	$mol L^{- 1} s^{- 1}$
$t$	Elapsed time	$s$

Real-World Applications

Where this formula is used in practice

Concentration tracking

Predict concentration during a zero-order regime.

Depletion estimates

Estimate the time at which the idealized zero-order model reaches zero concentration.

Worked Example

Step-by-step calculation with real numbers

Problem

A zero-order disappearance process starts at 0.100 mol/L with k = 0.00200 mol/(L·s). Find the concentration after 20.0 s, before depletion.

Given

C_{0} = 0.100 mol L^{- 1}

k = 0.00200 mol L^{- 1} s^{- 1}

t = 20.0 s

Solution

C_{t} = C_{0} - k t

C_{t} = 0.100 mol L^{- 1} - (0.00200 mol L^{- 1} s^{- 1}) (20.0 s)

C_{t} \approx 0.06 mol L^{- 1}

Final Answer

C_{t} \approx 0.06 mol L^{- 1}

Formula Guide

Info

DifficultyIntermediate

Read Time3 min

PrerequisitesAlgebra, logarithms, and molar quantities

Tools

Source & review

StatusNeeds review

Last reviewedPending

Source

OpenStax, Chemistry 2e, §12.4

Adapted from Teng-Jui Lin’s CHEM 155 equation sheet. The linked textbook reference was used to check the equation and its physical context. Pending editorial review.

Adapted from Teng-Jui Lin, Equation Sheets, under CC BY 4.0.

Assumptions

• Use a constant-volume system at fixed temperature with the stated disappearance-rate law and constant rate coefficient.
• Use consistent concentration and time units; apply the model only while the reactant remains present.
• Here k is defined by −dC/dt = k; include any stoichiometric factor if using a normalized reaction-rate convention.
• Use nonnegative initial concentration, rate constant, and elapsed time, with kt no greater than the initial concentration.

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