Question

b. the rate constant (k) for the reaction Consider the equation for the decomposition of SO2Ch: 2. SO2CI2(8) S2(8)+ Cl2(8) The concentration of SO;Cla is monitored at a fixed temperature as a function of time during the decomposition reaction, and the following data are tabulated: (SO-Ch) (M) Time (s) Time (s) 0.0793 0.100 800 0.0770 100 0.0971 900 1000 0.0748 200 0.0944 0.0727 1100 300 0.0917 0.0706 0.0890 1200 400 0.0686 0.0865 1300 500 0.0666 1400 0.0840 600 1500 0.0647 0.0816 700

Answer 1

Since, the reaction involves decomposition of one molecule of SO₂Cl₂, it would follow first order kinetics.

In first order kinetics,

ln[SO₂Cl₂]_t = - k*t + ln[SO₂Cl₂]₀

where

[SO₂Cl₂]_t is the concentration of SO₂Cl₂ at time t

[SO₂Cl₂]₀ is the concentration of SO₂Cl₂ at time 0

k is the rate constant

Using the data given, we get

Time (s)	[SO2Cl2], M	ln[SO2Cl2]
0	0.1	-2.30259
100	0.0971	-2.33201
200	0.0944	-2.36021
300	0.0917	-2.38923
400	0.089	-2.41912
500	0.0865	-2.44761
600	0.084	-2.47694
700	0.0816	-2.50593
800	0.0793	-2.53452
900	0.077	-2.56395
1000	0.0748	-2.59294
1100	0.0727	-2.62141
1200	0.0706	-2.65073
1300	0.0686	-2.67946
1400	0.0666	-2.70905
1500	0.0647	-2.73799

Plotting this data, ln[SO₂Cl₂]_t vs t, we get

Time, s in 500 1000 1500 2000 Le w In[A] = -0.00029*time - 2.30262 R? = 1.00000 Series1 in u In(SO2Cl2] Linear (Series1) u Ou

The slope of the line gives -k.

Therefore

rate constant = 2.9 x 10^-4 s^-1