Question

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?

Answer 1

Answer:

The relation is linear between $ln(P_{SO_2Cl_2})$ and time as given in the graph attached thus the reaction is first order  wrt $SO_2Cl_2$.

Explanation:

As the reaction is given as

$SO_2Cl_{2(g)}\rightarrow SO_{2(g)}+Cl_{2(g)}$

This indicates that 1 mole of $SO_2Cl_{2(g)}$ dissociates into exactly one mole of $SO_{2(g)}$ and $Cl_{2(g)}$.

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

$P_{total}=P_{SO_2Cl_2}+P_{SO_2}+P_{Cl_2}\\P_{total}=(P_o-\zeta )+\zeta+\zeta\\P_{total}=P_o-\zeta +\zeta+\zeta\\P_{total}=P_o+\zeta\\P_{total}-P_o=\zeta$

Now by calculation of degree of dissociation ζ and thus pressure of $SO_2Cl_{2(g)}$ is that calculated as

$P_{SO_2Cl_2}=(P_o-\zeta )$

For the data given the calculation is as below

t P(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 $ln(P_{SO_2Cl_2})$  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.