The rate of a chemical reaction, central to chemical kinetics, is the speed at which reactants are converted into products. This rate is measured by observing how quickly the concentration of a starting material decreases or how rapidly the concentration of a product increases over time. Measuring this rate allows scientists and engineers to predict how long a reaction will take and to optimize conditions for industrial processes, such as manufacturing pharmaceuticals or fuels.
Defining Change in Concentration Over Time
The fundamental mathematical basis for calculating a reaction rate involves measuring the change in concentration of a substance divided by the time interval over which that change occurred. This relationship is expressed as: Rate = Change in Concentration / Change in Time. Concentration is measured in Molarity (M), which represents moles per liter, and time is measured in seconds (s). The standard unit for the rate of a chemical reaction is Molarity per second (M/s), or mol/L·s.
When monitoring a reactant, its concentration decreases over time, resulting in a negative change. Since reaction rates are reported as positive values, a negative sign must be placed in front of the reactant’s concentration change term to ensure the calculated rate is positive. Conversely, a product’s concentration increases, leading to a positive change, so no sign adjustment is necessary when calculating the rate based on product formation.
Calculating Average Reaction Rate
The average reaction rate measures how quickly a reaction proceeded over a specific period of time. This straightforward calculation requires only two data points of concentration and time. The calculation involves finding the slope of the straight line, known as the secant line, that connects these two points on a concentration-time graph.
The formula for the average rate over a time interval is: Average Rate = – Change in Reactant Concentration / Change in Time. For example, consider a reactant A that decreases from an initial concentration of 0.80 M at time 1 (t1) to a final concentration of 0.30 M at time 2 (t2) = 50 s.
To calculate the average rate over this 50-second interval, determine the change in concentration: \(0.30 \text{ M} – 0.80 \text{ M} = -0.50 \text{ M}\). The change in time is \(50 \text{ s}\). Plugging these values into the formula gives: Average Rate = \(-(-0.50 \text{ M}) / 50 \text{ s} = 0.010 \text{ M/s}\). This result represents the overall speed of the reaction during that entire time period.
Determining Instantaneous Reaction Rate
The instantaneous reaction rate is the speed of the reaction at one exact moment in time, unlike an average over an interval. Since the rate of most reactions slows down as reactants are consumed, the instantaneous rate provides a more accurate picture of the reaction’s speed. This rate is determined graphically by plotting the concentration of a reactant or product against time, which results in a curved line.
To find the instantaneous rate at a specific time, a straight line, called a tangent line, is drawn to touch the curve at only that single point of interest. The slope of this tangent line is the instantaneous rate at that moment. Calculating the slope involves selecting two distinct points on the tangent line itself—not on the curve—and applying the standard slope formula: Slope = Change in Y / Change in X, where Y is the change in concentration and X is the change in time.
For instance, if the tangent line passes through (10 s, 0.60 M) and (30 s, 0.20 M), the slope calculation is \((0.20 \text{ M} – 0.60 \text{ M}) / (30 \text{ s} – 10 \text{ s}) = -0.020 \text{ M/s}\). Since the instantaneous rate must be a positive value, the result is reported as \(0.020 \text{ M/s}\). This method contrasts with the average rate, which uses the slope of the secant line.
Understanding the Rate Law Expression
The rate law expression shifts the focus from measuring concentration changes over time to modeling how the initial concentrations of reactants influence the reaction speed. This mathematical model, often called the differential rate law, takes the general form: Rate = k[A]^x[B]^y. This equation states that the reaction rate is proportional to the concentration of each reactant, [A] and [B], raised to a specific power.
The term \(k\) is the rate constant, a proportionality factor that is specific to a particular reaction and changes only with temperature. The exponents, \(x\) and \(y\), are the reaction orders with respect to reactants A and B, respectively. These orders indicate how sensitive the reaction rate is to a change in that reactant’s concentration. These reaction orders must be found through experimentation and cannot be determined simply by looking at the coefficients in the balanced chemical equation.