Rate of reaction Knowledge-Based Study

Study notes

1. In chemical kinetics, the rate of reaction describes the speed at which reactants are transformed into products. It is defined quantitatively as the change in the concentration of a reactant or product per unit of time.

   For any species involved in an aqueous solution or gas phase, concentration is typically measured in molarity ($\text{mol}\cdot\text{L}^{-1}$ or $\text{M}$), and time is measured in seconds ($\text{s}$), minutes, or hours. Consequently, the standard unit of reaction rate is $\text{mol}\cdot\text{L}^{-1}\cdot\text{s}^{-1}$ (or $\text{M}\cdot\text{s}^{-1}$).

   Because reactant concentrations decrease as the reaction proceeds, their changes are mathematically negative. By convention, reaction rates are defined as positive quantities. Therefore, a negative sign is added when expressing the rate with respect to a reactant:

   • Rate of consumption of reactant: $\text{Rate} = -\frac{\Delta[\text{Reactant}]}{\Delta t}$
   • Rate of formation of product: $\text{Rate} = +\frac{\Delta[\text{Product}]}{\Delta t}$

   The rates at which different substances in a reaction are consumed or produced are directly related through their stoichiometric coefficients in the balanced chemical equation.

   Consider a general balanced reaction:

   $a\text{A} + b\text{B} \rightarrow c\text{C} + d\text{D}$

   To obtain a single, unambiguous value for the overall reaction rate, each individual rate of change is divided by its corresponding stoichiometric coefficient:

   $$\text{Rate} = -\frac{1}{a}\frac{\Delta[\text{A}]}{\Delta t} = -\frac{1}{b}\frac{\Delta[\text{B}]}{\Delta t} = \frac{1}{c}\frac{\Delta[\text{C}]}{\Delta t} = \frac{1}{d}\frac{\Delta[\text{D}]}{\Delta t}$$

   Example: In the decomposition of dinitrogen pentoxide,

   $2\text{N}_2\text{O}_5(g) \rightarrow 4\text{NO}_2(g) + \text{O}_2(g)$

   Because four moles of $\text{NO}_2$ form for every one mole of $\text{O}_2$ produced, $\text{NO}_2$ forms four times as fast as $\text{O}_2$. The overall rate is expressed as:

   $$\text{Rate} = -\frac{1}{2}\frac{\Delta[\text{N}_2\text{O}_5]}{\Delta t} = \frac{1}{4}\frac{\Delta[\text{NO}_2]}{\Delta t} = \frac{\Delta[\text{O}_2]}{\Delta t}$$

   Because reactant concentrations decrease over time, the rate of most chemical reactions is not constant; it slows down as reactants are consumed. We distinguish between three types of rates:

   • Average Rate: The rate calculated over a measurable, finite time interval ($\Delta t$). On a concentration-versus-time graph, the average rate between two points corresponds to the slope of the secant line connecting those points.
   • Instantaneous Rate: The rate at one specific moment in time. It is determined from the slope of the tangent line drawn to the concentration-versus-time curve at that exact time ($t$). In differential calculus notation, it is represented as $-\frac{d[\text{Reactant}]}{dt}$ or $\frac{d[\text{Product}]}{dt}$.
   • Initial Rate: The instantaneous rate at the very start of the reaction ($t = 0$). The initial rate is often measured to study reaction kinetics before reverse reactions or catalyst poisoning can interfere.

   To determine reaction rates experimentally, chemists continuously monitor a measurable physical property that changes as reactants convert to products.

   Common experimental methods include:

   • Gas Volume or Pressure: When a gas is evolved (e.g., $\text{CO}_2$ or $\text{H}_2$), a gas syringe or manometer measures the increase in volume or pressure over time.
   • Mass Loss: If a light gas escapes from an open reaction vessel on an electronic balance, continuous mass loss corresponds directly to the rate of gas production.
   • Spectrophotometry (Colorimetry): If a reactant or product absorbs visible light, the intensity of transmitted or absorbed light is monitored; absorbance is directly proportional to concentration according to Beer's Law.
   • Electrical Conductivity: If the total number or nature of ions changes during the reaction, conductivity probes track the rate of ion change.
   • pH Monitoring: If hydrogen ions ($\text{H}^+$) or hydroxide ions ($\text{OH}^-$) are consumed or produced, a pH meter provides continuous concentration data.