Answer :
(1) pH = 1.27
(2) pH = 13.35
(3) The given solution is not a buffer.
Explanation :
(1) 53.1 mM HCl
Concentration of HCl =
![53.1mM=53.1* 10^(-3)M](https://img.qammunity.org/2020/formulas/chemistry/college/t8ln0wq2vnft1q7pg8j5beyx7fhmlfj3i1.png)
As HCl is a strong acid. So, it dissociates completely to give hydrogen ion and chloride ion.
So, Concentration of hydrogen ion=
![53.1* 10^(-3)M](https://img.qammunity.org/2020/formulas/chemistry/college/qt0yzbs71lkf4viptzapsdcy2pi4bgqgii.png)
pH : It is defined as the negative logarithm of hydrogen ion concentration.
![pH=-\log [H^+]](https://img.qammunity.org/2020/formulas/chemistry/high-school/ipfjz05f4cfbguiwup37xvxa7furlbuapf.png)
![pH=-\log (53.1* 10^(-3))](https://img.qammunity.org/2020/formulas/chemistry/college/gt23w12ap98mdpydygcapthjluv2i8oz9a.png)
![pH=1.27](https://img.qammunity.org/2020/formulas/chemistry/college/66op1rq2p6ufptavuakabugj28qx0ubgt4.png)
(2) 0.223 M KOH
Concentration of KOH = 0.223 M
As KOH is a strong base. So, it dissociates completely to give hydroxide ion and potassium ion.
So, Concentration of hydroxide ion= 0.223 M
Now we have to calculate the pOH.
![pOH=-\log [OH^-]](https://img.qammunity.org/2020/formulas/chemistry/high-school/h1t4ubcsdqvqg0xpalkkvnwrun04y9pzd8.png)
![pOH=-\log (0.223)](https://img.qammunity.org/2020/formulas/chemistry/college/db4axva8y354jlfo57jjgv3pgmqcki6joz.png)
![pOH=0.65](https://img.qammunity.org/2020/formulas/chemistry/college/wuux24e6q5rtq1oy8106sf6ioulbqvnfm1.png)
Now we have to calculate the pH.
![pH+pOH=14\\\\pH=14-pOH\\\\pH=14-0.65=13.35](https://img.qammunity.org/2020/formulas/chemistry/college/a37fcquewx4dmuikexc3a47r1ryzk6aujt.png)
(3) 53.1 mM HCl + 0.223 M KOH
Buffer : It is defined as a solution that maintain the pH of the solution by adding the small amount of acid or a base.
It is not a buffer because HCl is a strong acid and KOH is a strong base. Both dissociates completely.
As we know that the pH of strong acid and strong base solution is always 7.
So, the given solution is not a buffer.