How To Calculate Initial Rate Of Reaction

Kinetics is the branch of physical chemistry that studies the rate of chemical reactions. In contrast, thermodynamics tells us which direction of the reaction is favored, without revealing its reaction rate. Some reactions can be thermodynamically favored but kinetically unfavored.

For example, in the conversion of diamond to graphite, graphite has a lower free energy than diamond, so the conversion is thermodynamically favored. However, there is a large activation barrier for diamond to break and reform all the bonds to the more stable graphite configuration, thus this reaction is kinetically unfavored and will not actually occur.

The rate of reaction is a measure of how fast the products are formed and the reactants are consumed, so you can determine it by measuring the change in the concentration of products or reactants, over a period of time. Consider a general chemical reaction:

aA + bB ———————–> cC + dD

The rate of reaction can be written as:

Modified from https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_Physical_and_Theoretical_Chemistry/Kinetics/Reaction_Rates/Experimental_Determination_of_Kinetcs/Measuring_Reaction_Rates

For example the rate of reaction for:

2 NO(g) + 2 H₂ (g) ———————> N₂(g) + 2 H₂O(g)

is given by

Adapted from https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_Physical_and_Theoretical_Chemistry/Kinetics/Reaction_Rates/Experimental_Determination_of_Kinetcs/Measuring_Reaction_Rates

To determine the rate of this reaction by experiment, you can measure the concentration of H₂ at different times of the reaction, and plot it against time as follows:

Modified from https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_Physical_and_Theoretical_Chemistry/Kinetics/Reaction_Rates/Experimental_Determination_of_Kinetcs/Measuring_Reaction_Rates

Modified from https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_Physical_and_Theoretical_Chemistry/Kinetics/Reaction_Rates/Experimental_Determination_of_Kinetcs/Measuring_Reaction_Rates

The average rate of reaction is an approximation of the reaction rate in a time interval and can be denoted by:

Modified from https://www.chem.purdue.edu/gchelp/howtosolveit/Kinetics/CalculatingRates.html#InitialRate

The instantaneous rate of reaction is defined as the rate of reaction at some instant in time. It is a differential rate and can be expressed by:

Modified from https://www.chem.purdue.edu/gchelp/howtosolveit/Kinetics/CalculatingRates.html#InitialRate

Where d[H₂]/dt is the slope for the curve of concentration of H₂ versus time at time t.

The initial rate of reaction is the instantaneous rate at the start of the reaction, when t = 0. In this case, the unit for average, instantaneous and initial rate of reaction is M/s.

In most cases, the reaction rate is dependent on the concentration of the various reactants at time t. For instance, in a higher concentration of all reactants, reactants collide more frequently and result in a faster reaction. The relationship between reaction rate ν(t) and the concentrations is defined as the rate law. And the rate law for the general chemical reaction aA + bB —————> cC + dD is:

Modified from https://chem.libretexts.org/Bookshelves/Ancillary_Materials/Laboratory_Experiments/Wet_Lab_Experiments/General_Chemistry_Labs/Online_Chemistry_Lab_Manual/Chem_12_Experiments/01%3A_Chemical_Kinetics_-_The_Method_of_Initial_Rates_Experiment

Where k is the rate constant, and the power x and y is the order of the reaction with respect to reactant A and B. The rate law must be determined experimentally and cannot be deduced from just the stoichiometry of a balanced chemical reaction.

The rate law can be determined by the method of initial rates. In this method, the experiment is performed multiple times, only changing the concentration of one reactant for each run while keeping other variables constant. The rate of the reaction is measured for each run to determine the order of each reactant in the rate law.

For example, consider the following initial rate data for the reaction:

2 NO(g) + 2 H₂ (g) ———————> N₂(g) + 2 H₂O(g)

Adapted from https://www.chemteam.info/Kinetics/WS-Kinetics-method-of-initial-rates.html

For trial 1 and 3, the concentration of NO is kept constant while the concentration of H₂ is doubled. As a result, the initial rate of reaction also doubled (think of it as 2¹), so you can conclude y = 1. For trial 1 and 2, the concentration of NO is doubled while the concentration of H₂ remains constant. The result of this change is that the initial rate quadrupled (think of it as 2²). You can therefore conclude x = 2.

The rate law for this reaction is therefore:

Adapted from https://www.chemteam.info/Kinetics/WS-Kinetics-method-of-initial-rates.html

And the reaction is first order in H₂ and second order in NO.