1. Example Question 18.01 [18.02 Rate Laws | Integrated Rate Laws ] [Answer: (a)
ID: 908431 • Letter: 1
Question
1. Example Question 18.01 [18.02 Rate Laws | Integrated Rate Laws ] [Answer: (a) t1/2 = |247 min; (b) t = 819 min; (c) 10.9 g.] Sulfuryl chloride, SO2Cl2, decomposes by first-order kinetics, and k = 2.81 x 10^-3 min^-1 at a certain temperature. (a) Determine the half-life for the reaction. (b) Determine the time needed for the concentration of SO2Cl2 to decrease to 10 % of its initial concentration. (c) 14.0 g of SO2Cl2 is sealed in a 2500.-L reaction vessel and heated to the specified temperature, what mass will remain after 1.5 h?Explanation / Answer
(a) For a first order reaction,
t1/2 = 0.693/k = 0.693/2.81 x 10^-3 = 247 min
(b) For a first order reaction,
ln([A]/[Ao]) = - kt
Where,
[A] = substrate concentration remaining after t time
[Ao] = initial substrate concentration
[A]/[Ao] = 1/10
k = 2.81 x 10^-3 min-1
Feed values,
ln(1/10) = -2.81 x 10^-3 x t
So the time needed to reduce the concentration to 10%,
t = 819.42 min
(c) [Ao] = 14.0 g
t = 1.5 h = 1.5 x 60 = 90 min
Feed values,
ln[A] = ln[Ao] - kt
= ln(14) - 2.81 x 10^-3 x 90
Mass remaining after 1.5 h would be,
[A] = 10.90 g
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