Question

How many milliliters of $25\%$ (m/v) NaOH solution would contain 75 g of NaOH?

Answer 1

Hint: The mass by volume (m/v) percentage of a solution is the grams of solute present in the 100 mL volume of its solution. It is given as –
\[\text{(Mass by volume)}%=\dfrac{\text{mass of solute (in grams)}}{\text{volume of solution (in mL)}}\times 100\]

Complete answer: The solution’s concentration can be expressed in many ways in terms of solute and the solvent involved. One of the most commonly used ways of calculating the percentage composition of a solution is mass by volume percentage.
It is used when the mass of the solute and the volume of the solution are known to us. In general, it can be defined as the mass of solute dissolved in a 100 mL volume of solution.
Mathematically,
\[\text{(Mass by volume)} \%=\dfrac{\text{mass of solute (in grams)}}{\text{volume of solution (in mL)}}\times 100\]
Given values in the question are:
\[\begin{align}
  & \text{(Mass by volume)} \%=25\% \\
 & \text{Mass of solute}=75\text{ g} \\
 & \text{Volume of solution (in mL)}=?\text{ (To be calculated)} \\
\end{align}\]
According to the question, 25 g of NaOH is present in 100 mL of solution. Putting these values in the equation for mass by volume percent, we get:
\[\begin{align}
  & \text{25}=\left( \dfrac{75\text{ }}{\text{V}} \right)\times 100 \\
 & \Rightarrow \text{V}=\left( \dfrac{75\text{ }}{\text{25}} \right)\times 100 \\
 & \Rightarrow \text{V}=300\text{ mL} \\
\end{align}\]
hence, 300 milliliters of a $25\%$ (m/v) NaOH solution would contain 75 g of NaOH.

Additional information:
The mass by volume percent is often calculated to find the concentration of solutions in which a specific mass of solid solute is dissolved in a liquid solvent.

Note: During the calculation of mass by volume percent, the units in numerator and denominator are different and the overall unit of (m/v) percent is the same as the unit of density, that is, gram per milliliter. Since these two quantities are not the same, so the units are simply omitted while solving for mass by volume percent using the above-given equation.