Question

If $250mL$ of $0.25\left( M \right)NaCl$ solution is diluted with water to a volume of 500 mL, the new concentration of solution is:
A. $0.167M$
B. $0.0167M$
C. $0.125M$
D. $0.0833M$

Answer 1

Hint: The initial and final concentration of the $NaCl$ solution plays the most important role in this process. The concentration of the $NaCl$ solution is very important because the changes in volume cause change in the concentration if equal volumes of solute and solvent are not added.

Complete step by step answer:
Here there are two conditions in the given $NaCl$ solution as the sample.
The initial state of the solution is defined by two specific characters of the solution.
The molarity of the $NaCl$ solution can be written as ${S_1} = 0.25\left( M \right)$
The initial volume of the solution can be written as ${V_1} = 250mL$
The final state of the solution has one character which is given here. The final volume of the solution can be written as ${V_2} = 500mL$
The molarity of the final $NaCl$ solution is not known here which can be considered as ${S_2}$.
Therefore, from the given formula, ${V_1}{S_1} = {V_2}{S_2}$ the value of ${S_2}$ can be calculated. This ${S_2}$ value is the molarity of the final solution. The other variables are already defined here.
${V_1}{S_1} = {V_2}{S_2}$
$250 \times 0.25 = 500 \times {S_2}$
${S_2} = \dfrac{{250 \times 0.25}}{{500}}$
${S_2} = 0.125\left( M \right)$
The molarity of the final solution as found after dilution till $500mL$ of the $NaCl$ solution is $0.125\left( M \right)$. This reduction in the molarity is because the solvent volume changed but the solute level remained the same in the solution.

So, the correct answer is Option C.

Note: Molarity is directly associated with the volume and mass level in the specific solution. Therefore, the changes in the strength of the solution depend on the changing level of these physical characters in the solution. Volume change is very important in this case as the changes in the components of the solution were defined previously.