Reaction Rates and How They Are Measured

Take the concentration of a species at two times and divide the change by the elapsed time. The result has units of molarity per second. Because a reactant is being used up, its concentration change is negative, so a minus sign is placed in front to make the reported rate positive.

For A → products, a fall from 0.250 M at 10.0 s to 0.190 M at 40.0 s gives Δ[A]/Δt = (0.190 − 0.250)/(40.0 − 10.0) = −0.00200 M/s. The disappearance rate is the positive magnitude, 0.00200 M/s. Use the elapsed interval, not the final clock reading. If the balanced reaction consumes 2 A per reaction event, the normalized reaction rate is half that disappearance rate. A question asking for “rate of disappearance of A” and one asking for “rate of reaction” can therefore require different numbers.

An average rate is the slope of a straight line joining two points on a concentration-time curve. An instantaneous rate is the slope of the tangent at a single point. Because a typical curve is steepest at the start and flattens later, for a monotonically slowing reaction, the average over a long interval understates the initial rate.

On a graph, draw a secant through the two specified measured points for an average, and a tangent at the requested instant for an instantaneous rate. Use widely separated points on the tangent to estimate its slope; they need not lie on the concentration curve itself. An initial rate is the tangent near the start of the run, often estimated from a short early interval. This estimate is more sensitive to mixing delays and measurement noise than a long-run average.

At constant temperature and medium, a positive-order reactant's falling concentration commonly reduces rate. Zero-order behavior can remain nearly constant while a catalyst is saturated, and autocatalysis can make the rate rise initially. A flat concentration curve can also indicate equilibrium: forward and reverse reactions continue at equal rates, giving zero net concentration change.

The initial rate is the instantaneous rate near the start, after mixing is complete. Measuring early can reduce complications from accumulated products and reverse reaction, and controlled initial concentrations make it useful for comparing experiments.

It is not automatically error-free: mixing takes time, a reaction mixture may contain products initially, and a mechanism can show induction or changing catalytic activity. In an initial-rates experiment, vary one initial concentration at a time where possible and compare the measured early slopes.

Anything that tracks concentration works: colour change followed with a spectrophotometer, gas volume or pressure for a reaction producing gas, mass loss on a balance, pH for reactions producing or consuming hydrogen ions, or conductivity when ion counts change.

An instrument records a signal, which must be related to the requested amount. With absorbance A = εbc and fixed ε and b, dc/dt = (1/εb)dA/dt. For a gas at fixed T and V, P = nRT/V makes pressure slope proportional to the gas's mole-production slope. A total-pressure change depends on the net change in gas moles, so it need not follow one product alone. Calibrate the signal and control temperature, path length or vessel volume before interpreting its slope as a concentration rate.