Chemical reactions occur at varying speeds, and the study of these speeds is known as chemical kinetics. Measuring the rate of a reaction is fundamental to understanding how and why a chemical process happens. Calculating the reaction rate is essential for practical applications, such as optimizing manufacturing processes or determining the efficacy and shelf life of a new drug.
Defining Reaction Rate and Units
The reaction rate is defined as the change in the concentration of reactants or products over a specific period of time. Concentration is typically measured in Molarity (M), which represents moles of solute per liter of solution. Time is most often measured in seconds (s) when discussing reaction kinetics. Combining these standard units results in the standard unit for reaction rate, which is Molarity per second (M/s). This unit can also be expressed as moles per liter per second (mol L⁻¹ s⁻¹).
Calculating Rate Using Experimental Data
Calculating Average Rate
The most direct way to determine a reaction rate is by measuring the concentration of a reactant or product at different time points during an experiment. This yields the average rate of reaction over that measured time interval, calculated by dividing the change in concentration by the change in time. For reactants, concentration decreases, resulting in a negative change. Since the reaction rate must be a positive value, a negative sign is placed in the calculation: Rate = – \(\Delta\)[Reactant] / \(\Delta\)t. Conversely, product concentrations increase over time, so the calculation is Rate = + \(\Delta\)[Product] / \(\Delta\)t.
Adjusting for Stoichiometry
The balanced chemical equation is necessary because the rates of disappearance and appearance for different species are related by their stoichiometric coefficients. For example, if a reaction consumes two moles of A for every one mole of B produced, A disappears twice as fast as B appears. To define a single, consistent rate for the entire reaction, the change in concentration for each species is divided by its coefficient. For a generalized reaction \(a\)A \(\to\) \(b\)B, the overall reaction rate is expressed as Rate = \(-(1/a) \cdot \Delta[A] / \Delta t = +(1/b) \cdot \Delta[B] / \Delta t\). This adjustment ensures the calculated rate value remains the same regardless of which species is monitored.
Average vs. Instantaneous Rate
The average rate calculation provides a snapshot of the reaction’s speed over a specific interval. Reactions typically slow down as reactant concentrations drop. Therefore, the rate calculated over the initial seconds will be faster than the rate calculated over a later time period. This difference highlights the distinction between the average rate and the instantaneous rate, which is the rate at a single moment in time.
Modeling Rate Using the Rate Law
The Rate Law Equation
The rate law provides a mathematical model to predict the reaction rate based on the current concentrations of the reactants. This relationship is expressed by the general equation: Rate = \(k\)[A]\(^x\)[B]\(^y\), where [A] and [B] are the molar concentrations of the reactants.
Rate Constant (\(k\))
The term \(k\) is the rate constant, a proportionality factor unique to a specific reaction at a specific temperature. The value of \(k\) must be determined experimentally and reflects the inherent speed of the reaction under defined conditions. The rate constant changes significantly with temperature, generally increasing as temperature rises, a relationship described by the Arrhenius concept.
Reaction Orders (\(x\) and \(y\))
The exponents \(x\) and \(y\) are the reaction orders with respect to reactants A and B. These exponents indicate how sensitive the reaction rate is to changes in the concentration of each reactant. The sum of all the exponents gives the overall reaction order. The values for the reaction orders are not derived from the stoichiometric coefficients; they must be determined through experimentation.
Determining Orders Experimentally
The primary method used to find these exponents is the Method of Initial Rates. This technique involves running the reaction multiple times, systematically changing the initial concentration of one reactant while keeping the others constant. By observing how the initial rate changes, the reaction order for that reactant can be deduced. For instance, if doubling the concentration of reactant A causes the rate to quadruple, the reaction is second order (\(x=2\)). Once the exponents are determined, the rate constant \(k\) can be calculated using the concentration and rate data from any experimental trial.