Question

The reaction SO₂Cl_2(g)----->SO_2(g) + Cl_2(g) is first order inSO₂Cl₂. Using the following kineticdata, determine the magnitude of the first-order rateconstant?

Time(s)                       Pressure SO₂Cl₂ (atm)

0                                          1.00

2,500                                   0.947

5,000                                   0.895

7,500                                   0.848

10,000                                 0.803

Answer 1

Graph between time and pressure can be plotted as follows,
                                
This is the graph for the first order reaction. Equationcorresponding to the graph is y = - 2.0 x 10^-5 x-0.0001
Here slope is nothing but rate constant. ∴K =2.0 x 10^-5 s^-1

Answer 2

A = A0*exp(-kt)

ln(A) = ln(A0) - kt

Plot ln(A) vs t, slope of line is -k

plot

t	ln(Pressure)
0	0
2500	-0.05
5000	-0.11
7500	-0.16
10000	-0.22

slope = -2.20e-5

Thus, k = 2.20 x 10^-5

Answer 3

            SO₂Cl_2(g)-----> SO_2(g) +Cl_2(g)

          Theintigrated form of rate law for the first order reactionis

          ln [A]_t = -kt + ln[A]_o

     

          This equation can also be written for the pressures.

           from the given data t = 2500 s

          Initial presure of SO2Cl2 is = 1.00 atm

           pressure after 2500 s is 0.947 atm

    

                ∴ ln 0.947 atm = - k * 2500 sec + ln1 atm

                ∴ rate constant k = 2.178 x 10^-5s^-1