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

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`.

Step-by-step 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.