Question

25 ml, 0.2M \[Ca{(OH)_2}\]is neutralized by 10 ml of 1M HCl. The pH of the resulting solution is
(A) 1.37
(B) 9
(C) 12
(D) 7

Answer 1

Hint: When acid and bases combine, acids will reduce the concentration of \[O{H^ - }\]and similarly bases will reduce the concentration of the \[{H^ + }\]ions. When no more ions are present then the solution is said to be neutralized.

Complete answer:
Before moving onto the problem, let us see what a Neutralization is. Neutralization is a process in which acid reacts with the base to form salt.
In the question, it is given that 0.2M solution of 25ml of \[Ca{(OH)_2}\], when added to 1M solution of 10ml of HCl, the solution will get neutralized. The pH of the resulting solution can be calculated from the concentration of \[{H^ + }\] or \[O{H^ - }\] ions dissociated. As \[Ca{(OH)_2}\] is a strong base, \[O{H^ - }\]will get ionized completely. HCl being a strong acid, it will ionize the \[{H^ + }\] ions completely.
As HCl is a strong acid, therefore
\[{\rm{number\, of\, moles\, of\, HCl = number\, of\, moles\, of\, }}{{\rm{H}}^{\rm{ + }}}\]
Number of millimoles of HCl or \[{H^ + }\] \[ = {N_1}{V_1} = 1 \times 10 = 10\]
As \[Ca{(OH)_2}\] is a strong base, therefore
\[{\rm{number\, of\, moles\, of\, Ca(OH}}{{\rm{)}}_2}{\rm{ = number\, of\, moles\, of\, O}}{{\rm{H}}^ - }\]
Number of millimoles of \[Ca{(OH)_2}\]or \[O{H^ - }\] \[ = {N_2}{V_2} = 2 \times 25 \times 0.2 = 10\]
As the number of millimoles of \[{H^ + }\]=number of millimoles of \[O{H^ - }\]=10.
Therefore, the acid will completely neutralize the base. Hence the pH is 7.

The correct answer is option(D) 7.

Additional information:
pH is used to measure the concentration of \[{H^ + }\]or \[O{H^ - }\]ion in a given aqueous solution. pH helps to determine how much acidic or basic a solution is. When the value of pH scale is below 7, then the solution is said to be acidic. If the pH is above 7, then the solution is said to be alkaline. When the pH is equal to 7, then the solution is neutral.

Note: Since we are using the strong base and strong acid, it will get dissociated completely. Hence the number of moles of acid will be equal to the number of moles of \[{H^ + }\]ions and number of moles of the strong base will be exactly equal to the number of moles of \[O{H^ - }\]ions.