Question

How many times a $0.1M$ strong monobasic acid solution should be diluted so that $pH$ of the resulting solution is tripled?
(A) $50$
(B) $10$
(C) $25$
(D) $100$
(E) $1000$

Answer 1

Hint : We know that the basicity of an acid is the number of hydrogen ions which can be produced by one molecule of acid or it can be defined as the capacity of an acid to react with a base, measured by the number of hydrogen atoms that can be replaced by a base. A monobasic acid is an acid that has only one hydrogen ion to donate to a base in an acid-base reaction. Therefore, a monobasic molecule has only one replaceable hydrogen atom.

Complete Step By Step Answer:
The solution is divided into several types based on the dissolved solute. A solution is called as concentrated when a fixed amount of solute is dissolved in the minimum amount of solvent. It is referred to as dilute when more solvent is present in the solution than the amount required to dissolve the solute. The dilution of a solution is achieved by adding more solvent to the solution. Upon dilution the solute molecules go far apart from each other. Hence the distance between two solute molecules increases and also the interaction between them decreases.
Here we know that the Monobasic acid $=0.1M$
Let consider the acid is $HCl$ then, ${{H}^{+}}=0.1$ and $pH=-log\left( 0.1 \right)=1$
According to question the resulting pH after dilution should be tripled which means $pH=3$
$\therefore \left[ {{H}^{+}} \right]={{10}^{-3}}$ now by assuming if V ml of $0.1M$ solution were taken initially then, volume required to get $0.001M$ concentration
${{M}_{1}}{{V}_{1}}={{M}_{2}}{{V}_{2}}~\Rightarrow 0.1\left( V \right)=0.001\left( {{V}_{2}}\text{ } \right)$
$\Rightarrow {{V}_{2}}=100V$
Hence, $0.1M$ strong monobasic acid solution should be diluted $100$ times, so that $pH$ of the resulting solution is tripled.
Therefore, the correct answer is option D i.e. $100$ times dilution is required.

Additional Information:
Stronger acids have a larger ${{K}_{a}}$ and a smaller logarithmic constant $\left( p{{K}_{a}}=-\log {{K}_{a}} \right)$ than weaker acids. The stronger an acid is, the more easily it loses a proton $\left( {{H}^{+}} \right).$ Two key factors that contribute to the ease of deprotonation are the polarity of the $H-A$ bond and the size of atom A, which determine the strength of the $H-A$ bond. Strength of acid also depends on the stability of the conjugate base.

Note :
Note that the dilution is the process of decreasing the concentration of a solute in a solution. To dilute a solution means to add more solvent without the addition of more solute. For example, if there are $10$ grams of salt (the solute) dissolved in $1$ litre of water (the solvent), this solution has a certain salt concentration (molarity).