Question

A 0.645 M solution of a weak base (B:) is made. The solution has a pH of 11.99. Calculate the Kb of this base. Report your answer in scientific notation with 3 sig figs.

Answer 1

Consider reaction, B (aq) + H2O (l) $1585336116692_blob.png$BH + (aq) + OH - (aq)

Equilibrium constant for above reaction is K b = [ BH + ] [ OH - ] / [ B ]

According to above reaction, [ BH + ] = [ OH - ]

We can calculate [ OH - ] from pH.

We have relation, pH = - log [ H3O + ]

[ H3O + ]= 10 -pH

[ H3O + ] = 10 - 11.99

[ H3O + ]=10.23 $1585336116633_blob.png$ 10 - 12 M

We have relation, [ H3O + ] [ OH - ​​​​​​​] = 1.00 $1585336116633_blob.png$ 10 -14

$\therefore$[ OH - ​​​​​​​] = 1.00 $1585336116633_blob.png$ 10 -14  / [ H3O + ]

$\therefore$[ OH - ​​​​​​​] = 1.00 $1585336116633_blob.png$ 10 -14  / 10.23 $1585336116633_blob.png$ 10 - 12

$\therefore$[ OH - ​​​​​​​] = 9.77 $1585336116633_blob.png$ 10 -03 M

Let's use ICE table.

Concentration (M)	B (aq) $1585336116692_blob.png$BH + (aq) + OH - (aq)
I	0.645
C	- 9.77 $1585336116633_blob.png$ 10 -03	+ 9.77 $1585336116633_blob.png$ 10 -03	+ 9.77 $1585336116633_blob.png$ 10 -03
E	0.645 - 9.77 $1585336116633_blob.png$ 10 -03	9.77 $1585336116633_blob.png$ 10 -03	9.77 $1585336116633_blob.png$ 10 -03

We have, K b = [ BH + ] [ OH - ] / [ B ]

$\therefore$  K b = ( 9.77 $1585336116633_blob.png$ 10 -03 ) ( 9.77 $1585336116633_blob.png$ 10 -03 ) / 0.645 - 9.77 $1585336116633_blob.png$ 10 -03

K b = 1.5026  $1585336116633_blob.png$ 10 -04

ANSWER :  K b = 1.50 $1585336116633_blob.png$ 10 -04