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Question: The pH of the solution produced when an aqueous solution of strong acid pH 5 is mixed with equal vol...

The pH of the solution produced when an aqueous solution of strong acid pH 5 is mixed with equal volume of an aqueous solution of a strong acid of pH 3 is:
A.3.33.3
B.3.53.5
C.4.54.5
D.4.04.0

Explanation

Solution

This problem can be solved from the knowledge of the pH of the solution which can be defined as the negative logarithm to the base 10 of the hydronium ion concentration of the solution. We shall calculate the concentration of the solutions from their pH and add it and then calculate the pH of the resultant concentration.
Formula Used:
pH=−log10[H + ]{\text{pH}} = - {\text{lo}}{{\text{g}}_{{\text{10}}}}\left[ {{{\text{H}}^{\text{ + }}}} \right]

Complete step by step answer:
According to formula of pH, H+{{\text{H}}^ + }ion concentration of solution with pH 5 is,
−log10[H + ]=5- {\text{lo}}{{\text{g}}_{{\text{10}}}}\left[ {{{\text{H}}^{\text{ + }}}} \right] = 5
⇒[H+]=10−5\Rightarrow \left[ {{{\text{H}}^ + }} \right] = {10^{ - 5}} Mole /litre
And that with pH 3 has H+{{\text{H}}^ + }ion concentration,
−log10[H + ]=3- {\text{lo}}{{\text{g}}_{{\text{10}}}}\left[ {{{\text{H}}^{\text{ + }}}} \right] = 3
⇒[H+]=10−3\Rightarrow \left[ {{{\text{H}}^ + }} \right] = {10^{ - 3}} Mole/litre
When the two solutions are mixed, the resultant H+{{\text{H}}^ + }ion concentration will be,
(1×10−5)+(1×10−3)2\dfrac{{\left( {1 \times {{10}^{ - 5}}} \right) + \left( {1 \times {{10}^{ - 3}}} \right)}}{2}=5×10−4 M5 \times {10^{ - 4}}{\text{ M}}
Therefore the pH of the resultant solution will be,
=−log⁡10[5×10−4]= - \log 10\left[ {5 \times {{10}^{ - 4}}} \right]
⇒−log⁡10[5]−4log⁡1010=3.2967\Rightarrow - {\log _{10}}\left[ 5 \right] - 4{\log _{10}}10 = 3.2967 = 3.33.3 (approx.)

So, the correct answer is option A.

Note:
-The pH of the solution is a measure of the molar concentration of the hydronium ions present in the solution and as such a measure of the acidity or the basicity of the solution.
-The letters in “pH” stand for “power of hydrogen”.
-The usual range of the pH of the solution can range from 0-14, with 0 being the pH value for the most acidic solutions while 14 being the pH for the most basic solution.
-Deionized water has a neutral pH value of 7, which means the hydronium ion concentration of the solution is 10−7{10^{ - 7}}mole/litre.
-The pH of human blood is 7.47.4 and any change in the value of this pH can prove to be fatal.