Question

If 10 mL of 0.1 M aqueous solution of NaCl is divided into 1000 drops of equal volume, what will be the concentration of one drop?
(A) 0.10 M
(B) 0.01 M
(C) 0.001 M
(D) 0.0001 M

Answer 1

Hint:We can use the following formula in order to solve this problem.
     \[{{M}_{1}}{{V}_{1}}={{M}_{2}}{{V}_{2}}\]
We can divide initial volume by 1000 in order to find volume of one drop which will be useful in finding concentration of drop.

Complete step by step answer:
Let’s know about dilution first.
- Dilution is when we have a solution of a certain concentration and we add more solvent to decrease the concentration. We should note that, if we are adding more solvent, the volume of the whole solution is going to increase as the concentration of the solution decreases. We can solve for the concentration or volume of the concentrated or dilute solution using the following equation:
     \[{{M}_{1}}{{V}_{1}}={{M}_{2}}{{V}_{2}}\] .........(1)
${{M}_{1}}$ : It is the concentration in molarity (moles per Litre) of the solution in initial state,
${{V}_{1}}$ : It is the volume of the solution in initial state
${{M}_{2}}$ : It is the concentration in molarity of the drop
${{V}_{2}}$ : It is the volume of one drop
Now, learning from the above concept we will now try to solve our question.
Following things are given in question:
Initial volume of NaCl solution: 10 mL
Initial concentration of NaCl solution: 0.1 M
So, we can write that $\text{Volume of one drop of NaCl solution =}\dfrac{\text{Total volume of NaCl solution}}{\text{Number of drops produced}}$
So, $\text{Volume of one drop of NaCl solution =}\dfrac{10mL}{1000}$
Hence, we found that Volume of one drop of NaCl solution = 0.01mL
Note that we have divided this solution into 1000 drops, so we will get equation (1) modified for this case as
     \[{{M}_{1}}{{V}_{1}}=1000{{M}_{2}}{{V}_{2}}\]
So, we will put all available values in above equation,
     \[0.1\times 10=1000\times M\times 0.01\]
     \[M=\dfrac{0.1\times 10}{0.01\times 1000}\]
     \[M=0.1M\]
From the above calculation, we can say that concentration is intensive and the property remains the same if a solution is divided into n equal parts.

The correct option is A.

Note:
There is an alternative method available to solve this problem in which we will first calculate the number of moles in initial condition and then we will find the concentration of one drop. So initially, number of moles of NaCl present in 10mL of solution will be: $\text{Concentration }\times \text{ Volume (in L)}$
So, we will get the number of moles of NaCl equal to $0.1\times 0.010$ = 0.001moles
Now, 0.001 moles is divided into 1000 parts i.e. drops. So, one drop will have $\dfrac{0.001}{1000}$ =${{10}^{-6}}$ moles of NaCl. Then we can find out the concentration by following way:
     \[\text{Concentration of one drop of NaCl = }\dfrac{\text{Number of moles}}{\text{Volume in L}}\]
     \[\text{Concentration of one drop of NaCl = }\dfrac{{{10}^{-6}}moles}{0.00001L}\]
     \[\text{Concentration of one drop of NaCl = 0}\text{.1M}\]