Question

The decomposition reaction: SO,Cl, SO2 + Cl2, has a first order rate constant of 2.2 x 10's at 320 °C. If the initial concentration of SO2Cl2 is 0.0040 M, what will be its concentration be (a) after 1.00 hr and (b) after 1.00 day?

Answer 1

Answer :

(a) The concentration of $SO_2Cl_2$ after 1.00 hr will be 0.0037 M

(b) The concentration of $SO_2Cl_2$ after 1.00 day will be 0.00060 M

Explanation :

(a) The expression for first order reaction is:

$[C_t]=[C_o]e^{-kt}$

where,

$[C_t]$ = concentration of $SO_2Cl_2$ at time 't'  = ?

$[C_o]$ = concentration of $SO_2Cl_2$ at time '0' = 0.0040 M

k = rate constant = $2.2\times 10^{-5}s^{-1}$ (assuming the power of 10 from the correct source)

t = time = 1.00 hr = 3600 s (1 hr = 3600 s)

Now put all the given values in the above expression, we get:

$[C_t]=(0.0040)\times e^{-(2.2\times 10^{-5})\times (3600)}$

$[C_t]=0.0037M$

Thus, the concentration of $SO_2Cl_2$ after 1.00 hr will be 0.0037 M

(b) The expression for first order reaction is:

$[C_t]=[C_o]e^{-kt}$

where,

$[C_t]$ = concentration of $SO_2Cl_2$ at time 't'  = ?

$[C_o]$ = concentration of $SO_2Cl_2$ at time '0' = 0.0040 M

k = rate constant = $2.2\times 10^{-5}s^{-1}$

t = time = 1.00 day = 86400 s (1 day = 86400 s)

Now put all the given values in the above expression, we get:

$[C_t]=(0.0040)\times e^{-(2.2\times 10^{-5})\times (86400)}$

$[C_t]=0.00060M$

Thus, the concentration of $SO_2Cl_2$ after 1.00 day will be 0.00060 M