Chemical kinetics is the study of how quickly chemical reactions occur, known as the reaction rate. This rate quantifies the change in the amount of a substance over a specific period. Since reactions involve reactants being consumed and products being formed, the rate can be tracked by monitoring either species. For reactants, the speed at which they are used up is termed the rate of disappearance. Understanding this consumption rate is the first step toward determining the overall speed of the chemical process.
What Rate of Disappearance Means
The rate of disappearance (RoD) formally defines how the concentration of a reactant changes over time as it is converted into products. Specifically, the RoD is calculated as the change in the reactant’s concentration divided by the time interval over which that change occurred. Because the concentration of a reactant is always decreasing during a reaction, the change in concentration, represented as \(\Delta[A]\), will be a negative number.
To ensure the rate is reported as a positive value, a standard convention is to place a negative sign in front of the concentration change term. This makes the overall rate of disappearance a positive quantity, reflecting the speed of the process. The units for any reaction rate are typically expressed as molarity per second (M/s), or moles per liter per second (mol L⁻¹ s⁻¹).
Calculating the Average Rate Over Time
The simplest method for calculating the rate of disappearance involves finding the average rate over a defined time interval. This calculation uses two distinct concentration measurements taken at two different times during the reaction. The formula for the average rate of disappearance of a reactant ‘A’ is given by \(Rate_{avg} = – (\Delta[A] / \Delta t)\).
Expanding this formula gives \(Rate_{avg} = – ([A]_2 – [A]_1) / (t_2 – t_1)\), where \([A]_1\) and \(t_1\) are the initial concentration and time, and \([A]_2\) and \(t_2\) are the final concentration and time. For instance, if the concentration of a reactant drops from 1.0 M to 0.5 M over 50 seconds, the concentration change is \(-0.5\) M and the time change is \(50\) s. The average rate is therefore \(-(-0.5 \text{ M} / 50 \text{ s})\), which simplifies to \(0.01\) M/s.
This calculation provides a broad estimate of the reaction speed across the entire measured interval. The actual speed of the reaction is constantly changing, usually slowing down as the reactant concentration decreases. Consequently, the average rate calculated is merely a mean speed and does not accurately represent the rate at any single point in time.
Finding the Instantaneous Rate
Since the speed of most reactions is not constant, finding the instantaneous rate provides a more precise measurement of the rate of disappearance at one exact moment in time. This requires a graphical approach, which involves plotting the reactant’s concentration on the y-axis against time on the x-axis. The resulting curve typically slopes downward, showing the concentration decreasing over time.
To determine the instantaneous rate at a given time point, a straight line must be drawn that touches the curve at that single point without crossing it; this line is known as the tangent. The slope of this tangent line precisely represents the rate of change of concentration with respect to time at that specific instant. Calculating the slope involves selecting two convenient points on the tangent line and applying the standard slope formula, \(\Delta y / \Delta x\).
In this context, the slope is \((\Delta[A] / \Delta t)\), and since the concentration is decreasing, the slope value will be negative. The instantaneous rate of disappearance is then taken as the negative of this slope to ensure the rate is reported as a positive value. For example, if the calculated slope of the tangent at \(t=15\) seconds is \(-0.03\) M/s, the instantaneous rate of disappearance is \(0.03\) M/s.
Using Stoichiometry to Find the Overall Reaction Rate
The final step in kinetics is to relate the rate of disappearance of a single reactant to the overall rate of the chemical reaction. The measured rate of disappearance is specific to that species, but the overall reaction rate must be the same regardless of which reactant or product is monitored. This connection is established through the stoichiometry of the balanced chemical equation.
The stoichiometric coefficients, which are the numbers in front of each chemical species, dictate the relative rates of consumption and formation. For a generic reaction like \(aA + bB \rightarrow cC\), ‘A’ disappears ‘a’ times faster than the overall reaction rate, and ‘B’ disappears ‘b’ times faster. To normalize these different rates, the rate of disappearance for each species must be divided by its corresponding stoichiometric coefficient.
The general expression for the overall reaction rate is \(Rate = -(1/a) \cdot (\Delta[A] / \Delta t) = -(1/b) \cdot (\Delta[B] / \Delta t)\). This normalization ensures the calculated reaction rate is consistent whether derived from the disappearance of reactant A or reactant B. Incorporating the stoichiometric factor converts the species-specific rate of disappearance into a single, standardized value for the overall chemical process.