Rate of Reaction
A chemical reaction results in the formation of one or more substances (called products) from one or more starting materials (called reactant). For instance, the “equation”
indicates that two molecules of hydrogen and one molecule of oxygen form two molecules of water. Let’s consider the reaction
The concentration of a reactant A is the number of moles (6.022 x 1023 molecules) per liters and is denoted by [A]. Then concentration varies during a reaction, so [A], [B], [C] are all functions of time t. The average rate of reaction of the product C over a time interval from t1 to t2 is
The instant rate of reaction is
Since the concentration of product increases as the reaction proceeds, the derivative will be nonnegative. The concentrations of reactants, however, decreases during reaction, so, to make the rates of reaction of A and B positive numbers, we put minus signs in front of the derivatives and . Since each decreases at the same rate that [C] increases, we have
More generally, if a reaction is given by
we have
The data in the following table concern the lactonization of hydroxyvaleric acid at 25。C. They give the concentration C(t) of this acid in moles per liter after t minutes.
T / 0 / 2 / 4 / 6 / 8C(t) / 0.0800 / 0.0570 / 0.0408 / 0.0295 / 0.0210
Here is a plot of the data :
The average rate of reaction for the following time intervals:
(i)
(ii)
(iii)
We can find a smooth curve to fit the data by applying the least square method. The red curve in the following graph is given by the equation
We can use the tangent at t = 2 to estimate the instantaneous rate of reaction when t = 2.
So we get
which is the instantaneous rate of reaction when t = 2.
⇦Current / ⇨Marginal Cost