Question

The data below show the concentration of ABversus time for the following reaction:
AB(g)→A(g)+B(g)

A.Determine the order of the reaction.

B.Determine the value of the rate constant.

C.Predict the concentration of AB at 20 s .

Time (s)	[AB] (M)
0	0.950
50	0.459
100	0.302
150	0.225
200	0.180
250	0.149
300	0.128
350	0.112
400	0.0994
450	0.0894
500	0.0812

Answer 1

Since concentration vs time data is given we wilL try to find the rate law using integrated rate law approach

That is assume the order and than plot concentration vs time curve and see whether the curve fits for that particular order or not.

Let us start with '0' order

case(1) : 'O' order reaction

As can be seen above, the graph is not linear hence, the given reaction cannot be 'o' order reaction

Case(2): 1st order reaction

Now we will plot (Cab/0.950) Vs t and see whether we are getting a straight line or not

Time (s)	[AB] (M)	Ln(Cab/0.950)
0	0.95	0
50	0.459	-0.727411775
100	0.302	-1.146034967
150	0.225	-1.440361582
200	0.18	-1.663505134
250	0.149	-1.852515679
300	0.128	-2.004431721
350	0.112	-2.137963113
400	0.0994	-2.257309871
450	0.0894	-2.363341302
500	0.0812	-2.459546737

We obatin a straight line with slope '- 0.009'

Equation that with slope from equation, - K =-0.009, Therefore K =0.009

Hence,

A)the given equation is a 1st order equation

B) Value of rate constant is 0.009

Rate equation will be

C_AB =0.950e^{-0.009 t}

C) Predicting the concentration at 20 sec

We will substitute 20 sec in the above equation

C_AB =0.950e^{-0.009 *20}

        = 0.7935 M

Concentration of AB at 20 sec is 0.7935 M