Well, first we must remember that
[tex]pK_{a}+pK_{b}=14[/tex]
This is because
[tex]K_{a}*K_{b}=10^{-14}[/tex]
[tex]-log(K_{a}*K_{b})=-log(10^{-14})\\-logK_{a}+-logK_{b}=-log(10^{-14})\\pK_{a}+pK_{b}=14[/tex]
So then
[tex]pK_{b}=14-pK_{a}=14-3.2=1.8[/tex]
Answer : The value of [tex]pK_b[/tex] is, 10.8
Explanation :
First we have to calculate the value of [tex]K_a[/tex].
The expression used for the calculation of [tex]pK_a[/tex] is:
[tex]pK_a=-\log (K_a)[/tex]
Now put the value of [tex]pK_a[/tex] in this expression, we get:
[tex]3.2=-\log (K_a)[/tex]
[tex]K_a=6.3\times 10^{-4}[/tex]
Now we have to calculate the value of [tex]K_b[/tex].
Formula used :
[tex]K_a\times K_b=K_w[/tex]
[tex]K_b=\frac{K_w}{K_a}[/tex]
Now put the value of [tex]K_a[/tex] in this expression, we get:
[tex]K_b=\frac{1\times 10^{-14}}{6.3\times 10^{-4}}[/tex]
[tex]K_b=1.5\times 10^{-11}[/tex]
Now we have to calculate the value of [tex]pK_b[/tex].
The expression used for the calculation of [tex]pK_b[/tex] is:
[tex]pK_b=-\log (K_b)[/tex]
Now put the value of [tex]K_b[/tex] in this expression, we get:
[tex]pK_b=-\log (1.5\times 10^{-11})[/tex]
[tex]pK_b=10.8[/tex]
Therefore, the value of [tex]pK_b[/tex] is, 10.8
