Question #23db6

1 Answer
Jun 9, 2016

If this is a kinetics problem, you need to know the order of the reaction, the integrated rate law, and the rate constant at 420 °C

Since you don’t state the specific problem, let's arbitrarily assume that the reaction is first order, the initial concentration of "SO"_2"Cl"_2SO2Cl2 is 0.0225 mol/L and that the rate constant is 2.90 × 10^"-4"color(white)(l) "s"^"-1"2.90×10-4ls-1 at 420 °C.

Whenever a question asks, "How much is left after an amount of time?", that is a clue for you to use an integrated rate law.

The integrated rate law for a first order reaction is

color(blue)(|bar(ul(color(white)(a/a) ln(A_0/A_t) = kt color(white)(a/a)|)))" "

where

"A"_0 = "concentration at time 0"
"A"_t = "concentration at time"color(white)(l) t
k = "rate constant"
t = "time"

t = 16.2 color(red)(cancel(color(black)("h"))) × (60 color(red)(cancel(color(black)("min"))))/(1 color(red)(cancel(color(black)("h")))) × "60 s"/(1 color(red)(cancel(color(black)("min")))) = "58 320 s"

Then,

ln("0.0225 mol/L"/"A"_t) = 2.90 × 10^"-4" color(red)(cancel(color(black)("s"^"-1"))) × "58 320" color(red)(cancel(color(black)("s"))) = 16.91

"0.0225 mol/L"/"A"_t= e^16.91 = 2.21× 10^7

"A"_t = "0.0225 mol/L"/(2.21× 10^7) = 1.02 × 10^"-9" color(white)(l)"mol/L"