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Question: If \(250mL\) of \(0.25\left( M \right)NaCl\) solution is diluted with water to a volume of 500 mL, t...

If 250mL250mL of 0.25(M)NaCl0.25\left( M \right)NaCl solution is diluted with water to a volume of 500 mL, the new concentration of solution is:
A. 0.167M0.167M
B. 0.0167M0.0167M
C. 0.125M0.125M
D. 0.0833M0.0833M

Explanation

Solution

The initial and final concentration of the NaClNaCl solution plays the most important role in this process. The concentration of the NaClNaCl 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 NaClNaCl solution as the sample.
The initial state of the solution is defined by two specific characters of the solution.
The molarity of the NaClNaCl solution can be written as S1=0.25(M){S_1} = 0.25\left( M \right)
The initial volume of the solution can be written as V1=250mL{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 V2=500mL{V_2} = 500mL
The molarity of the final NaClNaCl solution is not known here which can be considered as S2{S_2}.
Therefore, from the given formula, V1S1=V2S2{V_1}{S_1} = {V_2}{S_2} the value of S2{S_2} can be calculated. This S2{S_2} value is the molarity of the final solution. The other variables are already defined here.
V1S1=V2S2{V_1}{S_1} = {V_2}{S_2}
250×0.25=500×S2250 \times 0.25 = 500 \times {S_2}
S2=250×0.25500{S_2} = \dfrac{{250 \times 0.25}}{{500}}
S2=0.125(M){S_2} = 0.125\left( M \right)
The molarity of the final solution as found after dilution till 500mL500mL of the NaClNaCl solution is 0.125(M)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.