Introduction to Rate Law

Zero-Order Reactions: The rate is independent of the reactant concentration. Doubling the concentration has no effect on the rate, and the rate law is simply $Rate = k$.

First-Order Reactions: The rate is directly proportional to the concentration of one reactant. If the concentration of that reactant doubles, the reaction rate also doubles ($Rate = k[A]$).

Second-Order Reactions: The rate is proportional to the square of a reactant's concentration or the product of two different concentrations. Doubling the concentration of a second-order reactant increases the rate by a factor of four ($Rate = k[A]^2$).

It is a fundamental principle that reaction orders cannot be determined from the stoichiometric coefficients of a balanced chemical equation; they must be determined experimentally.

The Method of Initial Rates involves conducting multiple trials of a reaction where the starting concentrations of reactants are varied systematically.

By comparing two trials where only one reactant's concentration changes, the order for that specific reactant can be isolated. The ratio of the rates is set equal to the ratio of the concentrations raised to the power of the order: $\frac{Rate_2}{Rate_1} = (\frac{[A]_2}{[A]_1})^m$

Once all individual orders are found, the rate constant $k$ is calculated by substituting the data from any single trial into the completed rate law expression.

This experimental approach ensures that the rate law reflects the actual kinetic behavior of the molecules rather than theoretical stoichiometry.

Differential rate laws express the rate as a function of concentration at a specific moment, while integrated rate laws express concentration as a function of elapsed time.

The linear plots are essential for identifying reaction order from experimental data; the slope of the resulting straight line is used to determine the value of the rate constant $k$.

Check Units of $k$: This is the fastest way to verify reaction order. For zero order, units are $M \cdot s^{-1}$; for first order, $s^{-1}$; and for second order, $M^{-1} \cdot s^{-1}$.

Half-Life Patterns: Remember that for a first-order reaction, the half-life ($t_{1/2}$) is constant and independent of the initial concentration. If you see a graph where the time to reach half-concentration is always the same, it is first-order.

Stoichiometry Trap: Never use the coefficients from the balanced equation as exponents in the rate law unless the problem explicitly states the reaction is an 'elementary step'.

Logarithmic Relationships: In first-order reactions, a plot of $\ln[A]$ vs. time yields a negative slope equal to $-k$. Ensure you distinguish between natural log ($\ln$) and base-10 log ($\log$).