Answer to Question #128213 in Physical Chemistry for Asad Amin

Question

It is believed that humans first arrived in the Western Hemisphere during the last Ice Age, presumably by traveling over an exposed land bridge between Siberia and Alaska. Archaeologists have estimated that this occurred about 11,000 yr ago, but some argue that recent discoveries in several sites in North and South America suggest a much earlier arrival. Analysis of a sample of charcoal from a fire in one such site gave a 14C decay rate of 0.4 dpm/g of carbon. What is the approximate age of the sample?
Ethyl chloride decomposes to ethylene and HCl in a first-order reaction that has a rate constant of 1.6 × 10−6 s−1 at 650°C.
a. What is the half-life for the reaction under these conditions?
b. If a flask that originally contains 0.077 M ethyl chloride is heated at 650°C, what is the concentration of ethyl chloride after 4 half-lives?

Answer 1

 Analysis of a sample of charcoal from a fire in one such site gave a 14C decay rate of 0.4 dpm/g of carbon. approximate age of the sample is  30,000 yr .

a) Half Life = 2.303 log2 / k = 0.693 / k . = 0.693 /  1.6 × 10^-6 =  4.3 × 10⁵ s = 120 hr.

= 5 day.

b) concentration after 4 half-lives = initial concentration / ( 2 )⁴ = 0.077 M / 16 .

= 4.8 × 10⁻³ M .