Question

A teacher instructed three students A, B and C respectively to prepare a 50%(mass by volume)solution of sodium hydroxide (NaOH). A dissolved 50g of NaOH in 100 mL of water, B dissolved 50g of NaOH in 100g of water while C dissolved 50g of NaOH in water to make 100 mL of solution. Which one of these has made the desired solution?
(A) A
(B) B
(C) C
(D) All of the above

Answer 1

Hint: 50% mass by volume means 50g of solute for every 100mL of solution.
Formula Used: Mass by volume % =\[\dfrac{{{\text{mass of solute(g)}}}}{{{\text{volume of solution(mL)}}}}{\text{ x 100}}\]

Complete step by step answer:
Student C has made the desired solution.
We know that Mass by volume % can be calculated from the formula,
Mass by volume % =\[\dfrac{{{\text{mass of solute(g)}}}}{{{\text{volume of solution(mL)}}}}{\text{ x 100}}\]
For 50% mass by volume solution,
Mass of solute = \[\dfrac{{{\text{mass by volume % x volume of solution}}}}{{100}} = \dfrac{{50{\text{ x 100}}}}{{100}} = 50g\]
Thus, 50g of NaOH must be dissolved in water to make the volume of solution 100mL.
Correct option: C
In case of student A, 50g dissolved in 100mL of water where water is a solvent therefore volume of solvent is 100 mL which is not 50% mass by volume %. Hence, option A is not correct.
In case of student B, 100g of water does not make 50% mass by volume solution since 50g of NaOH dissolved in 100g of water literally equal to 100mL again here water is a solvent. Hence, option B is not correct.
So, the correct option is C.

Additional Information: Mass by volume % can also be denoted as m/v %. Using this value, we can find the mass of solute or volume of solution easily.

Note: The point to be noted is that the volume of solution should be 100mL not the volume of solvent.
Useful conversions:
> 1 litre = 1000mL.
> Density of water = 1g/mL thus 1g water = 1 mL