Answer : The pH of the solution is, 2.67
Explanation :
The equilibrium chemical reaction is:
![Al^(3+)+H_2O\rightarrow Al(OH)^(2+)+H^+](https://img.qammunity.org/2021/formulas/chemistry/high-school/q3dtpy70hy9j8vx2qu3uxdbf82f7o0kw3y.png)
Initial conc. 0.450 0 0
At eqm. (0.450-x) x x
As we are given:
![K_a=1.00* 10^(-5)](https://img.qammunity.org/2021/formulas/chemistry/high-school/7g6ta1y7zrb5yzrc9m1dq6akbxbatsqgg0.png)
The expression for equilibrium constant is:
![K_a=((x)* (x))/((0.450-x))](https://img.qammunity.org/2021/formulas/chemistry/high-school/grrlth8xv9bo2b1ixgn6c7eyc3m01e0ane.png)
Now put all the given values in this expression, we get:
![1.00* 10^(-5)=((x)* (x))/((0.450-x))](https://img.qammunity.org/2021/formulas/chemistry/high-school/m32udrbdnrilmpp7jinjywwbsoy50g0of1.png)
![x=0.00212M](https://img.qammunity.org/2021/formulas/chemistry/high-school/p63bwggzqjsbtbcwobbrznyn9ktl0qxq6d.png)
The concentration of
= x = 0.00212 M
Now we have to calculate the pH of solution.
![pH=-\log [H^+]](https://img.qammunity.org/2021/formulas/chemistry/high-school/rjo2yhb5oj9ry1fr4db1ujrazm6fh3vhke.png)
![pH=-\log (0.00212)](https://img.qammunity.org/2021/formulas/chemistry/high-school/svm2tfsakblhm67zbmll79vk977a0hcaqt.png)
![pH=2.67](https://img.qammunity.org/2021/formulas/chemistry/high-school/zsau6f5y5a1wveg0axa72yurv10rpnxqpv.png)
Therefore, the pH of the solution is, 2.67