Answer : The pH of the solution is, 2.67
Explanation :
The equilibrium chemical reaction is:
[tex]Al^{3+}+H_2O\rightarrow Al(OH)^{2+}+H^+[/tex]
Initial conc. 0.450 0 0
At eqm. (0.450-x) x x
As we are given:
[tex]K_a=1.00\times 10^{-5}[/tex]
The expression for equilibrium constant is:
[tex]K_a=\frac{(x)\times (x)}{(0.450-x)}[/tex]
Now put all the given values in this expression, we get:
[tex]1.00\times 10^{-5}=\frac{(x)\times (x)}{(0.450-x)}[/tex]
[tex]x=0.00212M[/tex]
The concentration of [tex]H^+[/tex] = x = 0.00212 M
Now we have to calculate the pH of solution.
[tex]pH=-\log [H^+][/tex]
[tex]pH=-\log (0.00212)[/tex]
[tex]pH=2.67[/tex]
Therefore, the pH of the solution is, 2.67