Question

100ml of \[0.1M\] \[HCl\] is mixed with $100ml$ of \[0.01M\]\[HCl\] .The \[pH\] of the resulting solution is:
A. \[2.0\]
B. \[1.0\]
C. \[1.26\]
D. None of these

Answer 1

Hint: The term “\[pH\]” is an abbreviation for the “potential of hydrogen.” \[pH\] is a unit of measurement which represents the concentration of hydrogen ions in a solution.

Complete step by step answer:
To calculate the \[pH\] of an aqueous solution you need to know the concentration of the hydronium ion in moles per liter (molarity). The \[pH\] is then calculated using the expression:
\[pH = - \log {[{H_3}O]^ + }\]
Calculating the Hydronium Ion Concentration from \[pH\]
The hydronium ion concentration can be found from the pH by the reverse of the mathematical operation employed to find the \[pH\] .
\[{[{H_3}O]^ + } = {10^{ - pH}}\]
Or
\[{[{H_3}O]^ + } = anti{\log ^{( - pH)}}\]
Calculating \[pOH\]
To calculate the \[pOH\] of a solution you need to know the concentration of the hydroxide ion in moles per liter (molarity). The \[pOH\] is then calculated using the expression:
\[pOH = - \log {[OH]^ - }\]
Calculating the Hydroxide Ion Concentration from \[pOH\]
The hydroxide ion concentration can be found from the \[pOH\] by the reverse mathematical operation employed to find the \[pOH\] .
\[{[OH]^ - } = {10^{ - pOH}}\]
Or
\[{[OH]^ - } = anti\log ( - pOH)\]
Relationship Between and \[pOH\] .
The \[pH\] and \[pOH\] of a water solution at 25$^\circ $C are related by the following equation.
\[pH + pOH = 14\]
Step by step solution: When you add two different concentrations of the same strong acid, the pH contribution will be from both concentrations.
$
  M_1 = 0.1M \\
  V_1 = 100ml \\
  M_2 = 0.01M \\
  V_2 = 100ml
$
Final volume of solution is \[100 + 100 = 200ml\]
The final concentration of mixture will be calculated as
\[MV = M_1V_1 + M_2V_2\]
= \[M(100 + 100) = 0.1 \times 100 + 0.01 \times 100M\]
\[M = 200(10 + 1) = 0.055M\]
\[pH = - \log [{H^ + }]\]
=\[ - \log (0.055)\]
=\[1.259 \sim 1.26\]

So, the correct answer is Option C.

Note: The \[pH\] scale describes the acidity of the solution: acidic, neutral, or basic A solution with a \[pH\] less than 7 is an acid, exactly 7 is a neutral solution, and above 7 is a base. Bases have less hydrogen ions but more hydroxide ions, represented by the \[pOH\] or “potential of hydroxide ions.”

Acidic	Neutral	Basic
Less than 7	7	Greater than 7