Question

Consider the table of data collected for the reaction A → Products. Determine the magnitude (value) of the reaction rate constant by graphing the data appropriately.

Answer 1

Firstly the given data must be plotted in different ways using manual or computerized software. In this solution, MS Excel was used. The shapes of the graphs obtained will confirm whether the reaction is a first- or second- or zero-order reaction. Then using the equations that are derived from the integrated rate laws, the value of reaction rate constant, k, can be found. The given data and Ln[A] values are presented below:

Plotting [A] versus T, the following graph is obtained.

The shape of the graph is characteristic of a first-or second-order reaction

The plot of Ln[A] versus T is shown below:

The shape of Ln[A] versus T graph (presented above) confirms that the given data is a first-order reaction whose rate law will be of the form:

Rate = k[A]; where k is the rate constant and the units of a first-order rate constant will be s^-1

[Units can also be derived using units of rate as molL^-1s^-1 and units of [A] as molL^-1]

and the equation is: In[A] = -kt +In[A]₀

The slope of the above graph = -k

=> k = -(slope)

Slope can be found by taking any two points on the above graph. The values of Ln[A] corresponding to times 2.00 and 3.00 s are chosen for the calculation below: