How many grams of NaOH are needed to make 450 mL of a 2.5%(m/v) NaOH solution?

Question:

How many grams of {eq}\rm NaOH {/eq} are needed to make {eq}\rm 450\ mL {/eq} of a {eq}\rm 2.5\%\ (m/v)\ NaOH {/eq} solution?

Mass/Volume Percentage:

We can express the solute concentration in terms of the mass/volume percentage, or {eq}\displaystyle \%\ m/v {/eq}. This is done by dividing the mass of the solute, in grams, by the total volume of the solution, in milliliters, and then multiply the result to a hundred percent.

Determine the mass of {eq}\displaystyle NaOH {/eq}, {eq}\displaystyle m_{NaOH} {/eq}, contained in the given amount of solution by multiplying the volume, {eq}\displaystyle V = 450\ mL {/eq}, to the mass/volume percentage (2.5{eq}\displaystyle \% {/eq}). This yields the mass of {eq}\displaystyle NaOH {/eq} in grams. We proceed with the solution.

{eq}\begin{align} \displaystyle m_{NaOH} &= V \times 2.5\%\\ &= 450\ mL \times 0.025\ \rm{g/mL}\\ &\approx \boxed{\rm{11.25\ g\ NaOH}} \end{align} {/eq}