Step 1: Meaning of order. The order of a reaction is the sum of the powers of the concentration terms in the experimental rate law. When that sum equals one, the reaction is first order.
Step 2: Rate expression. For a first order change \(A \rightarrow products\), doubling the concentration of \(A\) doubles the rate, because rate \(= k[A]\). A plot of \(\log[A]\) against time is a straight line of slope \(-k/2.303\).
Step 3: Useful relations. The concentration falls exponentially, \([A] = [A]_0 e^{-kt}\), and the half-life \(t_{1/2} = 0.693/k\) stays constant no matter how much reactant you start with, which is a signature test for first order behaviour.
Step 4: Illustration. Acidic hydrolysis of an ester, \(CH_3COOC_2H_5 + H_2O \rightarrow CH_3COOH + C_2H_5OH\), behaves as a pseudo first order reaction because water is in large excess, so rate \(= k[ester]\).
\[\boxed{\text{Rate}=k[A],\ \ k=s^{-1}}\]