Acetone is one of the most important solvents in organic chemistry. It is used t
ID: 485239 • Letter: A
Question
Acetone is one of the most important solvents in organic chemistry. It is used to dissolve everything from fats and waxes to airplane glue and nail polish. At high temperatures, it decomposes in a first-order process to methane and ketene. At 600 degree C, the rate constant is 8.7 times 10^-3 s^-1. (a) What is the half-life of the reaction? Give your answer in scientific notation. (b) How long docs it take for 36% of a sample of acetone to decompose? (c) How long docs it take for 83% of a sample of acetone to decompose? Give your answer in scientific notation.Explanation / Answer
a) Half life of first order reaction is
t1/2 = 0.693/k
where k is rate constant , 8.7×10^-3 /s
t1/2 = 0.693/8.7×10^-3s^-1
= 79.65 seconds
b)Integrated form of first law is
ln[A]t = -kt + ln[A]0
Where, [A]t is concentration at time t, 64%
[A]0 is initial concentration, 100
k is rate constant , 8.7×10^-3s^-1
t is time ?
ln(64) = - 8.7×10^-3s^-1× t +ln(100)
2.303 log (64) = - 8.7 × 10^-3 × t + 2.303log(100)
t = 0.447/8.7×10^-3s^-1
= 51.38 seconds
C) Applying the integrated first order equation as above
ln(17)= -8.7 × 10^-3 × t + ln (100)
2.303 log (17) = - 8.7 × 10^-3 × t + 2.303log (100)
t = 203.8 seconds