The speed of a chemical reaction changes as reactants are consumed over time. The initial rate of reaction is the instantaneous speed measured at the very beginning of the process, specifically at time \(t=0\) seconds. Chemists focus on this measurement because the exact concentrations of all reactants are precisely known before any significant change occurs. This simplifies the complex mathematics of chemical kinetics before factors like reverse reactions or intermediate steps influence the speed. Determining the initial rate is the fundamental first step toward understanding the reaction’s complete mechanism.
Collecting Experimental Data
Finding the initial rate requires obtaining precise experimental data that tracks the change in concentration of a reactant or product over short, regular time intervals. The time resolution must be high enough to accurately capture the rapid changes that occur immediately after the reactants are mixed. The choice of monitoring technique depends on the physical properties of the chemicals involved in the reaction.
Monitoring Techniques
For reactions involving compounds that absorb light, spectrophotometry is an effective method. This technique measures the amount of light absorbed by the solution at a specific wavelength, which is directly proportional to the concentration of the colored substance. By taking absorbance measurements every few seconds, researchers generate a detailed profile of how concentration changes during the initial moments.
Reactions that produce or consume gases can be monitored by tracking changes in the total pressure within a sealed reaction vessel. As gas molecules are generated, the pressure increases, providing a measurable proxy for the reaction’s extent. Alternatively, reactions involving the formation or consumption of ions can be tracked using the electrical conductivity of the mixture.
Determining Rate Using Graphical Analysis
After the concentration versus time data is collected, the points are plotted on a graph. Concentration (molarity) is placed on the vertical Y-axis, and time (seconds) occupies the horizontal X-axis. This curve represents the decreasing concentration of a reactant or the increasing concentration of a product over time.
The speed of the reaction at any specific moment, known as the instantaneous rate, is equivalent to the slope of the concentration-time curve at that point. Since the rate changes continuously, taking the average rate over a large interval will not yield the precise initial rate. The instantaneous rate method is necessary because the decrease in reactant concentration is fastest at the beginning and slows down as the reaction progresses.
To find the instantaneous rate at \(t=0\), one must draw a tangent line to the curve precisely at the origin of the graph. A tangent line is a straight line that touches the curve at only one specific point. This line must be carefully aligned to match the direction and steepness of the reaction curve at the zero-time mark.
The final step involves calculating the slope of this constructed tangent line, which provides the numerical value for the initial rate. The slope is calculated using the standard formula: the change in the Y-axis value divided by the change in the X-axis value. Researchers select two distinct points on the drawn tangent line and calculate the difference in concentration divided by the corresponding difference in time. The resulting numerical value, typically expressed in units like Molarity per second (\(M/s\)), is the experimentally determined initial rate.
Using Initial Rates to Find the Rate Law
Calculating the initial rate from a single experiment is the first step toward determining the reaction’s rate law. The rate law mathematically expresses how the reaction rate depends on reactant concentrations, written as \(Rate = k[A]^x[B]^y\). Here, \([A]\) and \([B]\) are reactant concentrations, \(x\) and \(y\) are the reaction orders, and \(k\) is the rate constant. The exponents are determined experimentally and provide insight into the molecular mechanism.
Method of Initial Rates
To find the exponents, chemists employ the “Method of Initial Rates,” which requires performing multiple separate experiments. In this method, the initial concentration of one reactant is systematically varied while the concentrations of all other reactants are held constant. This isolation allows researchers to observe the change in the initial rate caused solely by the concentration change of the varied reactant.
By comparing the initial rates of two trials where only reactant \([A]\) was changed, the reaction order with respect to \([A]\) (\(x\)) can be calculated. For example, if doubling the concentration of \([A]\) causes the initial rate to quadruple, the reaction is second order. This comparison process is repeated for every reactant to find all the individual reaction orders.
Once all the individual exponents are determined, they are summed together to yield the overall order of the reaction. The completed rate law expression allows for the prediction of the reaction rate at any given initial concentration of reactants.
The final step involves calculating the specific numerical value of the rate constant, \(k\), which is unique for that reaction at a given temperature. This is achieved by substituting the experimentally determined initial rate, the initial concentrations, and the calculated reaction orders back into the rate law equation. The rate constant \(k\) is independent of concentration and serves as a direct measure of the reaction’s intrinsic speed.