Experimental Measurement of Reaction Rates

Watch a beaker of hydrogen peroxide slowly fizz as it decomposes into water and oxygen gas. To turn that fizz into a rate constant, a chemist needs numbers, not just bubbles. Every kinetics experiment ultimately answers one question: how does concentration change with time? This matters because the rate law, the reaction order, and the rate constant are all inferred from concentration-versus-time data. No theory can substitute for a clean, well-chosen measurement. Building on the definitions of rate covered earlier, this article surveys the laboratory techniques chemists use to track reactant or product concentration as a reaction proceeds. You will see how light absorption, electrical conductivity, gas pressure, and chemical quenching each convert an invisible molecular event into a readable signal. You will learn which method suits which reaction. Finally, you will see how these raw traces feed forward into determining reaction order.

Key takeaways

Kinetics experiments measure a physical property that changes predictably with concentration, then convert that signal into concentration versus time.
Spectrophotometry uses the Beer–Lambert law to track colored or UV-absorbing species continuously and non-destructively.
Conductivity monitoring suits reactions that change the number or mobility of ions in solution.
Manometric (pressure) methods work for reactions producing or consuming gas at constant volume.
Quenching-and-titration methods stop the reaction at fixed times, allowing off-line analysis of otherwise fast reactions.
Key idea: choosing the right monitoring technique means matching a measurable physical property to the chemistry, so that signal changes in direct, known proportion to concentration.

The core insight

Every method for measuring reaction rate rests on the same logic: find a physical observable, such as absorbance, conductance, pressure, or the amount of unreacted material trapped by quenching, that is linearly or otherwise predictably related to concentration, then record that observable as a function of time to reconstruct the concentration profile.

The physical picture

A rate law such as

\text{rate} = k[\mathrm{A}]^m[\mathrm{B}]^n

is meaningless without a way to measure $[\mathrm{A}]$ or $[\mathrm{B}]$ at various times. Chemists rarely measure concentration directly. Instead, they measure some proxy property linked to concentration by a known physical law, then invert that law to recover concentration. Four properties dominate teaching and research laboratories. Spectrophotometry exploits the fact that many reactants, products, or added indicators absorb light at characteristic wavelengths, with absorbance proportional to concentration through the Beer–Lambert law. Conductivity exploits the fact that ions carry current, and conductivity changes when a neutral species ionizes, when a highly mobile ion (such as H⁺ or OH⁻) is consumed, or when ion identities swap during a reaction. Manometry (pressure measurement) exploits the ideal gas law for reactions that change the number of moles of gas at fixed volume and temperature. Quenching methods stop the reaction abruptly, in a chemical sense freezing a clock, then use classical wet-chemistry analysis such as titration on the frozen sample. The technique determines the time resolution achievable. Spectrophotometry and conductivity can sample continuously, once per second or faster, making them ideal for reactions with half-lives of seconds to hours. Quenching methods are limited by how quickly an aliquot can be withdrawn and analyzed, typically seconds at best, but they can be applied to reactions monitored by methods (like titration) that are inherently destructive and slow.

Figure

Four monitoring strategies mapped onto a single reaction coordinate

Figure

Beer–Lambert calibration line used to convert absorbance to concentration

The core relations

A = \varepsilon\, c\, l

where: $A$ is absorbance (dimensionless), $\varepsilon$ is the molar absorption coefficient (dm³ mol⁻¹ cm⁻¹), $c$ is concentration (mol dm⁻³), $l$ is path length (cm).

\kappa = \sum_i \lambda_i c_i

where: $\kappa$ is solution conductivity, $\lambda_i$ is the molar conductivity of ion $i$ , $c_i$ is its concentration.

PV = n_{\text{gas}}RT \quad\Rightarrow\quad n_{\text{gas}} = \frac{PV}{RT}

where: $P$ is total gas pressure, $V$ is fixed reaction vessel volume, $T$ is absolute temperature, $R$ is the gas constant.

[\mathrm{A}]_t = [\mathrm{A}]_0 - \frac{(\text{titre})_t}{(\text{titre factor})}

where: (titre) $_t$ is the volume of titrant needed to react with unreacted species at time $t$ , after the reaction in that aliquot has been quenched.

The core relations — worked derivation

Derivation AFrom absorbance trace to rate constant for a first-order decay

Goal. Show how a spectrophotometric absorbance-time trace for A → products, monitored where only A absorbs, yields the first-order rate constant $k$ .

Step 1. Because only A absorbs at the chosen wavelength, and path length and cell are fixed, Beer–Lambert gives

A_t = \varepsilon l [\mathrm{A}]_t .

The proportionality constant $\varepsilon l$ is the same at every time, since neither $\varepsilon$ (fixed wavelength, fixed compound) nor $l$ (fixed cell) changes during the run.

Step 2. For a first-order process, integrated rate law theory (established when rate laws were introduced) gives

[\mathrm{A}]_t = [\mathrm{A}]_0\, e^{-kt}.

Step 3. Substitute Step 2 into Step 1:

A_t = \varepsilon l [\mathrm{A}]_0 e^{-kt} = A_0 e^{-kt},

since $A_0 = \varepsilon l [\mathrm{A}]_0$ is just the initial absorbance, itself measurable before reaction starts.

Step 4. Take natural logarithms of both sides:

\ln A_t = \ln A_0 - kt.

This says a plot of $\ln A_t$ against $t$ is a straight line, with slope $-k$ and intercept $\ln A_0$ , without ever needing to know $\varepsilon$ .

Step 5. Because $\varepsilon l$ cancels exactly between numerator and reference value, the method works even if $\varepsilon$ is unknown, provided only that absorbance remains linear in concentration (Beer–Lambert holds) across the concentration range explored.

Boxed result.

\boxed{\ln A_t = \ln A_0 - kt \quad\Longrightarrow\quad k = -\,\text{slope of } \ln A_t \text{ vs } t}

Worked examples

Example 1 — Spectrophotometric first-order decay (foundational). A dye A decomposes by a first-order reaction, A → products, monitored at 500 nm in a 1.00 cm cell. The measured absorbances are:

$t$ / s	0	60	120	180	240
$A_t$	0.800	0.593	0.440	0.326	0.242

Step 1: check linearity of $\ln A_t$ vs $t$ .

\ln(0.800) = -0.223,\quad \ln(0.593) = -0.523,\quad \ln(0.440) = -0.821,

\ln(0.326) = -1.121,\quad \ln(0.242) = -1.418.

Step 2: compute the slope. Using the first and last points as a check (a full least-squares fit would use all five):

\text{slope} = \frac{-1.418-(-0.223)}{240-0\ \text{s}} = \frac{-1.195}{240\ \text{s}} = -4.98\times10^{-3}\ \text{s}^{-1}.

Step 3: identify $k$ .

k = 4.98\times10^{-3}\ \text{s}^{-1}.

Step 4: sanity check via half-life.

t_{1/2} = \frac{\ln 2}{k} = \frac{0.693}{4.98\times10^{-3}\ \text{s}^{-1}} = 139\ \text{s}.

Since $A_0 = 0.800$ , half of that is $0.400$ ; the data show $A \approx 0.440$ at 120 s and $0.326$ at 180 s, bracketing $A=0.400$ near $t \approx 139$ s — consistent with the fitted $t_{1/2}$ . The method is self-consistent.

Example 2 — Manometric monitoring of a gas-evolving decomposition (applied, harder). Hydrogen peroxide decomposes catalytically:

2\,\mathrm{H_2O_2(aq)} \rightarrow 2\,\mathrm{H_2O(l)} + \mathrm{O_2(g)}.

The reaction is run in a sealed rigid vessel of volume $V = 250\ \text{cm}^3 = 0.250\ \text{dm}^3$ at $T = 298\ \text{K}$ , and the pressure rise above the initial (baseline) pressure is recorded, since only O₂ escapes into the gas phase. Initial concentration of H₂O₂ in solution: $[\mathrm{H_2O_2}]_0 = 0.500\ \text{mol dm}^{-3}$ , in a solution volume of $0.0500\ \text{dm}^3$ (50.0 cm³), giving

n_0(\mathrm{H_2O_2}) = 0.500\ \text{mol dm}^{-3} \times 0.0500\ \text{dm}^3 = 0.0250\ \text{mol}.

At $t = 600\ \text{s}$ , the measured excess pressure of O₂ is $\Delta P = 1.85\times10^4\ \text{Pa}$ . The gas-phase volume (headspace) is $V_{\text{gas}} = 0.250\ \text{dm}^3 - 0.0500\ \text{dm}^3 = 0.200\ \text{dm}^3 = 2.00\times10^{-4}\ \text{m}^3$ . Step 1: moles of O₂ produced by $t=600$ s, via ideal gas law.

n(\mathrm{O_2}) = \frac{\Delta P\, V_{\text{gas}}}{RT} = \frac{(1.85\times10^4\ \text{Pa})(2.00\times10^{-4}\ \text{m}^3)}{(8.314\ \text{J K}^{-1}\text{mol}^{-1})(298\ \text{K})}.

n(\mathrm{O_2}) = \frac{3.70}{2478} = 1.494\times10^{-3}\ \text{mol}.

Step 2: relate O₂ formed to H₂O₂ consumed via stoichiometry (2:1).

n(\mathrm{H_2O_2}\ \text{consumed}) = 2 \times n(\mathrm{O_2}) = 2.99\times10^{-3}\ \text{mol}.

Step 3: remaining H₂O₂ and concentration.

n_t(\mathrm{H_2O_2}) = 0.0250 - 0.00299 = 0.02201\ \text{mol},

[\mathrm{H_2O_2}]_{600\text{s}} = \frac{0.02201\ \text{mol}}{0.0500\ \text{dm}^3} = 0.440\ \text{mol dm}^{-3}.

Step 4: sanity check. Only 12% of the peroxide has decomposed after 10 minutes, plausible for a mild catalyst at room temperature; the pressure rise corresponds to a very small amount of gas (1.49 mmol), consistent with a modest concentration drop. If this experiment is repeated at several times, $\ln[\mathrm{H_2O_2}]_t$ plotted against $t$ tests for first-order kinetics — precisely the question the next stage of kinetics analysis addresses.

Limiting cases & common traps

Technique	Best suited to	Common trap
Spectrophotometry	Colored/UV-active species; fast continuous sampling	Assuming Beer–Lambert linearity holds outside the calibrated range; stray light or turbidity causes deviations
Conductivity	Reactions changing ionic strength or ion mobility (e.g., ester hydrolysis by base)	Forgetting that conductivity is not linear in concentration at high ionic strength; temperature must be tightly controlled since conductivity is strongly $T$ -dependent
Manometry	Gas-evolving or gas-consuming reactions at constant $V,T$	Ignoring dissolved gas or vapor pressure of solvent, which adds a constant offset to measured pressure
Quenching + titration	Slow reactions, or where no continuous physical signal exists	Quenching too slowly relative to the reaction rate, so the "instant" sample keeps reacting during work-up

The chemist behind it

Physical organic chemists in the early twentieth century pioneered quenching and titration methods for studying ester hydrolysis and inversion reactions long before electronic spectrophotometers existed. Among them, Christopher Kelk Ingold systematically combined kinetic measurement (often via titration of quenched aliquots) with mechanistic reasoning, helping establish the SN1/SN2 framework that rests entirely on rate data gathered by exactly the techniques surveyed here.

Origins · 1 minChristopher Kelk Ingold and how this was discovered

Christopher Kelk Ingold

1893–1970 · British chemist who linked reaction mechanism to quantitative kinetic measurement, pioneering conductimetric and titrimetric rate studies of nucleophilic substitution

Ask the tutor: How do we use these concentration-time traces to actually determine whether a reaction is zero, first, or second order?

Why can't we just measure concentration directly with a balance or a ruler?

Concentration is a bulk property of dissolved or gaseous species, not something a balance can isolate mid-reaction without disturbing the system. Any physical extraction step (like weighing a precipitate) risks perturbing the ongoing reaction, and most reacting species cannot be separated fast enough for meaningful time resolution. Instead, chemists measure an indirect but precisely calibrated physical signal, absorbance, conductance, or pressure, that responds instantaneously and non-invasively to concentration changes, then convert that signal mathematically using the appropriate physical law.

How do chemists choose between spectrophotometry and conductivity for the same reaction?

The choice depends on which species changes in a convenient, measurable way. If a reactant or product has a strong, distinct absorption band, ideally where nothing else absorbs, spectrophotometry gives fast, continuous, non-destructive data. If instead the reaction changes the number, charge, or mobility of ions, such as neutral ester converting to charged carboxylate and alcohol, conductivity is often simpler and cheaper, though it requires tight temperature control since ionic mobility is temperature sensitive.

Why is temperature control so critical in these measurements, beyond its effect on the rate constant?

Nearly every monitoring technique's calibration is itself temperature dependent. Molar absorption coefficients shift slightly with temperature, conductivity is strongly temperature sensitive because ion mobility increases with temperature, and the ideal gas law explicitly contains $T$ . If temperature drifts during a run, the measured signal reflects both the concentration change and instrumental drift, contaminating the rate constant extracted from the data.

Can more than one monitoring technique be applied to the same reaction?

Yes, and doing so is good practice for validating a rate constant. If spectrophotometric and conductimetric measurements of the same reaction under the same conditions agree on $k$ , that agreement strongly supports both the proposed mechanism and the calibration of each instrument. Discrepancies often reveal a secondary process, such as a colored intermediate absorbing at the monitored wavelength, or an ionic side reaction.

How does this connect to determining reaction order?

Once a technique yields a reliable concentration-time trace, that data is exactly what's needed to test candidate rate laws. Plotting concentration, its natural log, or its reciprocal against time and checking for linearity distinguishes zero-, first-, and second-order kinetics. This procedure is the direct next step in the study of chemical kinetics.