As discussed in the text, the total system pressure can be used to monitor the progress of a chemical reaction. Consider the following reaction: SO2Cl2(g)→SO2(g)+Cl2(g). The reaction is initiated, and the following data are obtained:

Time (h) 0 3 6 9 12 15
PTotal (kPa) 11.07 14.79 17.26 18.90 19.99 20.71

Is the reaction first or second order with respect to SO2Cl2?

The relation is linear between and time as given in the graph attached thus the reaction is first order  wrt .

Explanation:

As the reaction is given as

This indicates that 1 mole of dissociates into exactly one mole of and .

By indicating the degree of dissociation as ζ  and solving for the pressure gives

Now by calculation of degree of dissociation ζ and thus pressure of is that calculated as

For the data given the calculation is as below

tP(total)Dissociation(ζ)P(SO2CL2)ln(P(SO2CL2))            

                          P(total)-11.07    11.07-ζ              

0  11.07            0                      11.07              2.4042

3  14.79         3.72                      7.35              1.9947

6  17.26         6.19                     4.88              1.5851

9   18.9         7.83                      3.24              1.1756

12   19.99         8.92              2.15              0.7655

15   20.71         9.64               1.43              0.3577

For the estimation of the degree the relation between  vs time is to be plotted, if the relation is linear it is a first order reaction, if the relation is not linear than it is a higher order reaction. The relation is linear as given in the graph attached thus the reaction is first order  wrt SO2Cl2.

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years

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