M.4—Curves, models, logarithms and core chemical formulae

A tangent gradient gives an instantaneous rate of change; an area under a curve represents an accumulated quantity only when the axes and units make that interpretation valid. Log transforms can linearise relationships, but every model has a range of validity.

Estimate orders of magnitude before calculating, use log₁₀ or ln consistently, and calculate core quantities such as n = m/Mr, c = n/V and ρ = m/V with compatible units.

The initial gradient of a concentration–time curve is an initial rate. If ln k is plotted against 1/T, a straight line can test an Arrhenius model within the measured range.

A tangent slope is not the same as the total change, and a straight transformed graph does not prove the underlying model is universally true.