Answer:
The relation is linear between [tex]ln(P_{SO_2Cl_2})[/tex] and time as given in the graph attached thus the reaction is first order wrt [tex]SO_2Cl_2[/tex].
Explanation:
As the reaction is given as
[tex]SO_2Cl_{2(g)}\rightarrow SO_{2(g)}+Cl_{2(g)}[/tex]
This indicates that 1 mole of [tex]SO_2Cl_{2(g)}[/tex] dissociates into exactly one mole of [tex]SO_{2(g)}[/tex] and [tex]Cl_{2(g)}[/tex].
By indicating the degree of dissociation as ζ and solving for the pressure gives
[tex]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[/tex]
Now by calculation of degree of dissociation ζ and thus pressure of [tex]SO_2Cl_{2(g)}[/tex] is that calculated as
[tex]P_{SO_2Cl_2}=(P_o-\zeta )[/tex]
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 [tex]ln(P_{SO_2Cl_2})[/tex] 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.
