Question

ammonia is a common constituent of many natural waters and wastewaters. when water containing ammonia is treated at a water treatment plant, the ammonia reacts with the disinfectant hypochlorous acid (HOCl) in solution to form monochloroamine (NH2Cl) as follows:

NH3 + HOCl > NH2Cl + H2O

The rate law for this reaction is:

d[NH3]/dt = -k[HOCl][NH3]

a) what is the reaction order with respect to NH3?

b) What order is this reaction overall?

c) If the HOCl concentration is held constant and equals10^-4 M, and the rate constant equals 5.1 x 10^6 L/moles-s, calculate the time required to reduce the concentration of NH3 to one half its original value.

Answer 1

(a): The given rate law for the reaction is

d[NH3]/dt = -k[HOCl]x[NH3]

The power of the concentration of NH3, [NH3] in the above rate law expression is 1. Hence the reaction order with respect to NH3 is 1.

(b): In the rate law expression, power of the concentration of NH3 is 1 and also the power of the concentration of HOCl is 1. Hence the overall order of the reaction is 1+1 = 2

(c): Given rate constant, k = 5.1x 10⁶ L/moles.s

Concentration of HOCl, [HOCl] = C = 10^-4 M which is kept constant through out the reaction.

Let Initial concentration of NH3, [NH3]_i = a M

Hence the final concentration of NH3,  [NH3]_f = (a - x) = (a - a/2) = a/2 M

Since the concentration of HOCl, C is kept constant, the integrated rate law for this reaction will be like that of a first order reaction with division by HOCl concentration, C.

t = (1 / kxC) x ln [a / (a - x)]

=> t = [1 / (5.1x 10⁶ L/moles.s x 10^-4 M)] x ln( a / a/2)

=> t = [1 / (5.1x 10⁶ L/moles.s x 10^-4 M)] x ln(2) = 0.00136 sec (answer)

Note: Please check given the value of rate constant, k, as i have doubt that might be wrong. If it is correct then no problem.