gen-define-reaction-rate-and-rate-laws-and-give-one-short-worked-98cb

Define reaction rate and rate laws and give one short worked example.

# Reaction Rate and Rate Laws ## **Reaction Rate** The **reaction rate** is the change in concentration of a reactant or product per unit time. **Mathematical definition:** $$\text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt}$$ For the general reaction: aA + bB → cC + dD - Negative sign for reactants (concentration decreases) - Positive sign for products (concentration increases) - Units: typically mol/(L·s) or M/s ## **Rate Laws** A **rate law** is an equation that relates the reaction rate to the concentrations of reactants raised to powers (orders). **General form:** $$\text{Rate} = k[A]^m[B]^n$$ Where: - k = rate constant - m, n = reaction orders (determined experimentally) - Overall order = m + n --- ## **Worked Example** **Given:** For the reaction 2NO₂(g) + F₂(g) → 2NO₂F(g) The rate law is: Rate = k[NO₂][F₂] If k = 0.025 M⁻¹s⁻¹, [NO₂] = 0.30 M, and [F₂] = 0.50 M, find the rate. **Solution:** $$\text{Rate} = k[NO₂][F₂]$$ $$\text{Rate} = (0.025)(0.30)(0.50)$$ $$\text{Rate} = 3.75 \times 10^{-3} \text{ M/s}$$ The reaction is **first order** in NO₂, **first order** in F₂, and **second order overall**.