Question

How many liters of water must be added to 1 liter of an aqueous solution of $HCl$ with a pH of 1 to create an aqueous solution with a pH of 2?
A. 0.1 L
B. 0.9 L
C. 2.0 L
D. 9.0 L

Answer 1

Hint: pH is defined as the potential of hydrogen which can also be considered as power of hydrogen ions. pH is basically used to detect that the given aqueous solution is of what nature i.e. whether is of basic nature or acidic nature.

Complete step by step answer:
pH scale is logarithmic in nature because it inversely indicates the concentration of hydrogen ions in the solution. Formula used to calculate pH is the negative of the base 10 logarithmic to the molar concentration.
- At pH 1, concentration of $[{{H}^{+}}]$ will be equal to ${{10}^{-1}}$M i.e. 0.1 M
And at pH 2, concentration of $[{{H}^{+}}]$ will be equal to ${{10}^{-2}}$M i.e. 0.01 M
Now we know that ${{M}_{1}}{{V}_{1}} = {{M}_{2}}{{V}_{2}}$ and we know that ${{M}_{1}}$= 0.1 M, ${{M}_{2}}$ = 0.01 M, ${{V}_{1}}$ = 1 L now by substituting all the values in the equation we can find the value of ${{V}_{2}}$
$0.1\times 1 = 0.01\times {{V}_{2}}$, ${{V}_{2}} = 10L$
This corresponds to the final volume is 10 L so 9 liters of water must be added to 1 liter of an aqueous solution of $HCl$ with a pH of 1 to create an aqueous solution with a pH of 2.
The correct answer is option “D” .

Note: pH can be detected with the help of pH scale this scale ranges from 0 to 14 which describes that the solution having value less than 7 are acidic in nature while those solutions which have value greater than 7 are basic in nature and if any solution have value exactly equals to 7 then this is said to be neutral.