CEE 670 Fall 2011

# Kinetics Problem Set #1

Problem 26. A glass vial contains 0.5% potassium by weight.  The natural abundance of 40K, which decays by β-emission is 0.00118%, and its half-life is 1.28x109 years.  If the vial weighs 15g, calculate the expected rate of β- production by the vial in disintegrations per minute or dpm.  (problem 1 in Chapter 2 of Brezonik; pg.102).

Problem 27. Using the kinetic plot and data for the hydrolysis of Benzyl Chloride as presented in class (refer to posted slides on website[1]), determine the following:

a.       The expected concentration of benzyl chloride after 72 hours (@25°C), when the initial concentration was 33µg/L.

b.      The expected concentration of benzyl chloride after 72 hours (@25°C), when the initial concentration was 7.9µg/L.

c.       The expected concentration of benzyl chloride after 72 hours (@0.1°C), when the initial concentration was 33µg/L.

Problem 28. It has been known for some time that concentrated solutions of aqueous chlorine lose strength with time.  Accompanying this is the accumulation of chlorate ion.  Early chemical studies have determined this to be a second order reaction in hypochlorite.  The stoichiometry is as follows:

Bolyard and co-workers [1992, Env. Sci. Technol. 26(8)1663-1665] found that chlorate is being inadvertently added to drinking water when aqueous chlorine is used as a disinfectant.  Data collected at 14 sites showed that raw water chlorate levels were 0.02 mg/L or below.  However, finished water levels were as high as 0.66 mg/L, apparently due to contamination from the chlorine stocks.  Gordon and Adam [Water Disinfection News, 5:1, Novatek] have subsequently studied this reaction.  They determined that a 2.776 M chlorine stock solution (15.89% FAC, d=1.239 g/mL) has a 61.7 day half-life at 25°C and pH 13.  Based on this information answer the following questions.

a.       What is the 2nd order rate constant for this reaction in units of M-1s-1?

b.      Calculate the concentration of chlorate in the stock after 40 days holding time at 25°C

c.       What is the dosed concentration (mg/L) of chlorate if sufficient stock (aged 40 days at 25°C) is added to a finished drinking water to achieve a free chlorine dose of 2.5 mg/L?

d.      Repeat "c", but assume that the chlorine stock was diluted by a factor of 4 prior to holding for 40 days.  Assume that dilution does not change the value of the rate constant [we will find out later that it will change a bit due to the change in ionic strength].

e.       Consider an MCLG (maximum contaminant level goal) of 0.2 mg/L for chlorate.  Determine the amount of dilution of the chlorine stock, which will just allow compliance after 40 days holding time at 25°C.

Assigned: 17 Nov 11

Due: 29 Nov 11

[1] http://www.ecs.umass.edu/cee/reckhow/courses/670/