Question

percent ionization of a weak base

pH and Percent lonization of a Weak Base Ammonia, NH, is a weak base with a Ky, value of 1.8 x 105 The degree to which a weak base dissociates is given by the base ionization content K) For the generic weak base, B B(aq) + H2O(1) BH(aq) + OH (!) this constant is given by Pan A KDO What is the pH of a 0.165 Mammonia solution? Express your answer numerically to two decimal places. View Available Hints) Strong bases will have a higher Ky value. Similarly, strong bases will have a higher percent ionization value Percent ionization Co q uilibrium Initial X 100% Strong bases, for which is very large, lonce completely (1006). For weak bases, the percent ionization changes with concentration. The more diute the solution the greater the percent location Η ΑΣΦ Submit Part B What is the percentonization of ammonia at this concentration? Express your answer with the appropriate units. ► View Available Hints) MARO? lonization - Value Units Submit

Answer 1

A)

NH3 dissociates as:

NH3 +H2O -----> NH4+ + OH-

0.165 0 0

0.165-x x x

Kb = [NH4+][OH-]/[NH3]

Kb = x*x/(c-x)

Assuming x can be ignored as compared to c

So, above expression becomes

Kb = x*x/(c)

so, x = sqrt (Kb*c)

x = sqrt ((1.8*10^-5)*0.165) = 1.723*10^-3

since x is comparable c, our assumption is not correct

we need to solve this using Quadratic equation

Kb = x*x/(c-x)

1.8*10^-5 = x^2/(0.165-x)

2.97*10^-6 - 1.8*10^-5 *x = x^2

x^2 + 1.8*10^-5 *x-2.97*10^-6 = 0

This is quadratic equation (ax^2+bx+c=0)

a = 1

b = 1.8*10^-5

c = -2.97*10^-6

Roots can be found by

x = {-b + sqrt(b^2-4*a*c)}/2a

x = {-b - sqrt(b^2-4*a*c)}/2a

b^2-4*a*c = 1.188*10^-5

roots are :

x = 1.714*10^-3 and x = -1.732*10^-3

since x can't be negative, the possible value of x is

x = 1.714*10^-3

So, [OH-] = x = 1.714*10^-3 M

use:

pOH = -log [OH-]

= -log (1.714*10^-3)

= 2.7659

use:

PH = 14 - pOH

= 14 - 2.7659

= 11.2341

Answer: 11.23

B)

% dissociation = x * 100 / initial concentration

= (1.714*10^-3)*100 / 0.165

= 1.04 %

Answer: 1.04 %