Zero-order kinetics are identified when reactant disappears at a constant rate, independent of its concentration. In an isothermal batch reactor, measure (C_A) at known times and test whether (C_A) decreases linearly with time: (C_A=C_{A0}-kt). The slope of the linear fit gives the rate constant (k), while the concentration-dependent half-life provides an additional diagnostic.

Core takeaway: A straight-line plot of (C_A) versus (t), or equivalently (C_{A0}-C_A) versus (t), supports zero-order behavior. The conclusion is strongest when the fitted rate is constant, the residuals show no systematic curvature, and runs with different initial concentrations produce half-lives proportional to (C_{A0}).

What Zero-Order Kinetics Mean

The defining rate law

For a reactant (A), zero-order kinetics are represented by

[ -r_A=-\frac{dC_A}{dt}=k ]

The reaction rate is therefore independent of (C_A) over the tested operating range.

The rate constant (k) has concentration-per-time units, such as (\mathrm{mol,L^{-1},s^{-1}}), rather than the first-order units of inverse time.

Why zero-order behavior occurs

In educational pilot plants, zero-order behavior is often associated with a saturated catalytic surface. Once the active sites are fully occupied, increasing reactant concentration or partial pressure does not significantly increase the reaction rate.

Examples include certain heterogeneous catalytic reactions, such as decomposition reactions on hot metal surfaces. However, the observed zero-order response is valid only within the experimental range where the surface remains saturated and other effects do not control the rate.

How to Collect Suitable Pilot-Plant Data

Control the reactor conditions

For a batch-reactor kinetics experiment, maintain approximately constant temperature, mixing, and sampling conditions. Temperature control is particularly important because even small temperature changes can alter (k) substantially.

Record the initial concentration (C_{A0}), each sampling time (t), and the corresponding concentration (C_A). The sampling method must not significantly change reactor volume or composition.

Check the reactor assumptions

The standard integrated expression assumes a well-mixed batch reactor and a constant-volume or otherwise correctly modeled concentration basis. Poor mixing, evaporation, leaks, or changing volume can create apparent deviations from zero-order behavior.

If the reactor operates at constant pressure with a changing volume, concentration-time data must be corrected for that volume change before applying the constant-volume equation.

The Primary Identification Method

Plot concentration against time

Integrating the zero-order rate law gives

[ C_A=C_{A0}-kt ]

Therefore, plot either:

[ C_A \text{ versus } t ]

[ C_{A0}-C_A \text{ versus } t ]

A zero-order reaction should produce a straight line.

For a plot of (C_A) versus (t):

Slope: (-k)
Intercept: ideally (C_{A0})

For a plot of (C_{A0}-C_A) versus (t):

Slope: (k)
Intercept: ideally zero

The second form directly displays the amount of concentration consumed and is often convenient for educational laboratory analysis.

Determine the rate constant

Using linear regression on the (C_A) versus (t) data,

[ k=-\text{slope} ]

Alternatively, for the (C_{A0}-C_A) plot,

[ k=\text{slope} ]

Use the fitted slope rather than a single pair of measurements because regression reduces the influence of sampling and analytical noise.

Examine more than the correlation coefficient

A high (R^2) value supports linearity but does not by itself establish the correct reaction order. Examine the residuals—the differences between measured and fitted concentrations.

For zero-order behavior, residuals should be scattered around zero without a systematic curve. A curved residual pattern indicates that the reaction rate changes with concentration or that another experimental effect is present.

Comparing Zero-Order Behavior with Other Orders

Use integrated rate-law plots

The integral method tests several possible reaction orders using the same concentration-time data:

Assumed order	Linearized quantity	Expected slope
Zero order	(C_A) versus (t)	(-k)
First order	(\ln(C_{A0}/C_A)) versus (t)	(k)
Second order	(1/C_A) versus (t)	(k)

The transformation that gives the most credible straight line, with random residuals and physically reasonable parameters, is the better kinetic model.

This comparison is more reliable than selecting a model solely because one plot has the largest (R^2), particularly when the concentration range is narrow.

Use differential analysis as a supporting test

Estimate the instantaneous reaction rate from concentration-time data:

[ -r_A\approx-\frac{\Delta C_A}{\Delta t} ]

Central differences, forward differences, backward differences, or a fitted smooth curve can be used. Because numerical differentiation amplifies measurement noise, the result should be treated carefully.

For a power-law model,

[ -r_A=kC_A^\alpha ]

taking logarithms gives

[ \ln(-r_A)=\ln k+\alpha\ln C_A ]

Plotting (\ln(-r_A)) against (\ln C_A) gives:

Slope: reaction order (\alpha)
Intercept: (\ln k)

Zero-order behavior corresponds to a slope near zero. In practice, differential analysis is best used to support the integrated analysis rather than replace it.

Use nonlinear regression when appropriate

Nonlinear regression can fit the untransformed concentration-time data directly to

[ C_A=C_{A0}-kt ]

and compare this model with first- or second-order alternatives. This avoids some distortion introduced by logarithmic or reciprocal transformations.

It is especially useful when the reactor involves changing volume, heterogeneous catalysis, multiple reactions, or additional parameters.

The Half-Life Diagnostic

Calculate the zero-order half-life

At the half-life, (C_A=C_{A0}/2). Substituting into the integrated zero-order equation gives

[ t_{1/2}=\frac{C_{A0}}{2k} ]

Unlike a first-order reaction, the zero-order half-life is not constant.

Vary the initial concentration

Conduct otherwise comparable batch runs with different initial concentrations. For genuine zero-order behavior, the half-life should increase directly with (C_{A0}):

[ t_{1/2}\propto C_{A0} ]

This is a powerful educational demonstration because it distinguishes reaction orders:

Zero order: (t_{1/2}) increases with (C_{A0})
First order: (t_{1/2}) remains constant
Second order: (t_{1/2}) decreases as (C_{A0}) increases

The relationship should be tested over a concentration range where the catalyst remains saturated and the reactor remains otherwise comparable.

Special Considerations for Pilot-Plant Reactors

Variable-volume batch operation

If pressure is constant and the reaction changes the total number of moles, reactor volume may change during the run. In that case, a simple (C_A)-versus-(t) plot can give misleading results if volume effects are ignored.

For the variable-volume formulation provided, zero-order behavior can be tested using

[ \ln\left(\frac{V}{V_0}\right)

\frac{k\varepsilon_A}{C_{A0}}t ]

A straight-line plot of (\ln(V/V_0)) against (t) supports the model, with slope

[ \frac{k\varepsilon_A}{C_{A0}} ]

The volume relationship and the definition of (\varepsilon_A) must match the actual stoichiometry and reactor configuration.

Catalytic reactors

In packed-bed or fixed-bed experiments, rate data may be affected by catalyst loading, residence-time distribution, external mass transfer, internal diffusion, adsorption, and deactivation.

A nearly zero reaction order with respect to a reactant may indicate saturated active sites, but it can also arise from an incorrectly chosen rate region or transport limitation. Varying reactant partial pressure and checking temperature and flow-rate effects helps distinguish intrinsic kinetics from reactor artifacts.

Understanding the Trade-offs

Linear plots are simple but can distort errors

Integral plots are easy for students to construct and interpret, but transformations can change the distribution of experimental errors. Reciprocal and logarithmic plots are particularly sensitive to small concentrations and measurement noise.

Whenever possible, use linearized plots for initial diagnosis and confirm the result with regression on the original concentration data.

Complete depletion is not always experimentally usable

The zero-order model predicts

[ C_A=0 \quad \text{when} \quad t=\frac{C_{A0}}{k} ]

Near depletion, concentration measurements may approach the detection limit, and the rate may no longer remain zero order. Do not treat the final few data points as automatically reliable evidence for or against the model.

A zero slope can be a measurement problem

If (C_A) appears nearly constant, the reaction may be slow, the analytical method may lack sensitivity, or the reactor may not have reached the intended temperature.

Confirm that measurable conversion occurs and that the concentration changes are larger than the analytical uncertainty.

How to Apply This to Your Experiment

Use the following workflow to evaluate zero-order kinetics systematically:

If your primary focus is identifying reaction order: Plot (C_A) versus (t), compare it with the first- and second-order integrated plots, and inspect residuals rather than relying only on (R^2).
If your primary focus is calculating the rate constant: Fit (C_A=C_{A0}-kt) by linear regression and take the negative slope as (k).
If your primary focus is validating the model: Repeat runs at different (C_{A0}) values and verify that (t_{1/2}=C_{A0}/(2k)).
If your primary focus is catalytic pilot-plant behavior: Vary reactant concentration or partial pressure and confirm that the rate remains approximately constant while checking for mass-transfer and catalyst-deactivation effects.
If your primary focus is a variable-volume reactor: Apply the volume-corrected integrated balance and plot (\ln(V/V_0)) against time instead of using an uncorrected concentration plot.

A defensible zero-order conclusion combines a linear integrated plot, a concentration-independent measured rate, consistent half-life behavior, and evidence that reactor or transport effects are not controlling the result.

Summary Table:

Evaluation method	Expected result for zero-order kinetics	Purpose
Concentration-time plot	Straight line for `C_A` versus `t`	Identify zero-order behavior
Linear regression	Slope equals `-k`	Calculate the rate constant
Residual analysis	Random scatter without curvature	Check model reliability
Reaction-order comparison	`C_A` versus `t` fits best among tested models	Distinguish zero-, first-, and second-order kinetics
Half-life test	`t₁/₂ = C_A0/(2k)` and increases with `C_A0`	Validate zero-order behavior
Variable-volume correction	Linear `ln(V/V₀)` versus `t` relationship	Account for changing reactor volume
Catalytic reactor checks	Rate remains stable as concentration or pressure changes	Detect saturation and transport effects

Planning a reliable kinetics experiment? Contact LABPARK to discuss Educational and Vocational Unit Operations Pilot Plants for chemical engineering, bioprocess and biotech, and environmental and water treatment applications. LABPARK helps universities, research institutes, and enterprises select practical reactor systems that support reaction-order analysis, rate-constant measurement, variable-volume studies, and catalytic process evaluation. Our team can help you match reactor configuration, instrumentation, teaching objectives, and scale to your laboratory or training program.