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

Given reaction is A ----> Products

Rate=k[A]x

where k=rate constant, x=order of reaction.

The rate laws are

The zero-order rate law is [A]=-kt+[A]0

If the plot of [A] vs time gives a straight line then the order of the reaction is zero-order and the slope of the line is equal to rate constant.

First-order rate law is ln[A]=-kt+ln[A]0

If the plot of ln [A] vs time gives a straight line then the order of the reaction is first-order and the slope of the line is equal to rate constant.

The second-order rate law is 1/[A]=kt+1/[A]0

If the plot of 1/[A] vs time gives a straight line then the order of the reaction is second-order and the slope of the line is equal to rate constant.

Where [A]0=initial concentration of A,

k=rate constant and [A]=concentration of A at time t.

The calculations are shown below the table

Time(s)	[A](M)	ln[[A]	1/[A]
0	0.75	-0.287682072	1.333333333
0.5	0.665	-0.407968238	1.503759398
1	0.575	-0.553385238	1.739130435
1.5	0.49	-0.713349888	2.040816327
2	0.41	-0.891598119	2.43902439
2.5	0.32	-1.139434283	3.125
3	0.235	-1.448169765	4.255319149
3.5	0.15	-1.897119985	6.666666667
4	0.06	-2.813410717	16.66666667

The Zero-order plot is

The first order plot is

The second-order plot is

From the above plots, the plot [A] vs time gives a straight line with R2=0.9999.

Therefore the order of the reaction is zero order.

The rate law is

Rate=k[A]0

Rate=k

The slope of the line=-k=-0.17183 M s-1.

rate constant=k=0.172 M s-1.

Please let me know if you have any doubt. Thanks