The decomposition of sulfuryl chloride (SO2Cl2) is a first-order process. The ra

Question

The decomposition of sulfuryl chloride (SO2Cl2) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 10-2 s-1.

(a) If we begin with an initial SO2Cl2 pressure of 325 torr, what is the pressure of this substance after 62 s? torr

(b) At what time will the pressure of SO2Cl2 decline to one half its initial value? s

By what factor will the pressure of sulfuryl chloride decrease after 4 half lives? Note: The answer wants this value: (325 torr)/value = final pressure after decay value

Explanation / Answer

The decomposition of sulfuryl chloride (SO2Cl2) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 10-2 s-1.

For first-order rate constant we use following expression:

ln[A] = - k t + ln[Ao],

here [A] is the pressure after time = t,

k is the rate constant, 4.5 10-2 s-1

[Ao] is the original pressure .,

ln(p) = ln(325 torr) - (4.5 10-2 s-1) (62 s);

ln(p) = ln(325 torr) - (2..79);

ln(p) = 5.78-2.79

ln(p) =3.00

p = 20.1 torr.

(b) At what time will the pressure of SO2Cl2 decline to one half its initial value? s

For first-order rate constant we use following expression:

ln[A] = - k t + ln[Ao],

here [A] is the pressure after time = t ½ 325 torr/2

k is the rate constant, 4.5 10-2 s-1

[Ao] is the original pressure ., 325 torr

ln(325 torr/2) = ln(325 torr) - (4.5 10-2 s-1) (t);

(4.5 10-2 s-1) (t)= ln(2)

0.693 = 4.5 10-2 s-1) (t)

t=15.4 s

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