Question

A doctor orders $100mLof2.0\%(m/v)$ibuprofen. If you have $8.0\%(m/v)$ibuprofen on hand, how many milliliters do you need?

Short answer

The volume of Ibuprofen is$25mL$is need when you have$8.0\%(m/v)$ibuprofen.

Step-by-step solution

Given Information.

The following are the given information:

Mass per volume of ibuprofen is $2.0\%(m/v)$

To find the milliliters of Ibuprofen.

Find the Mass per Volume percent. 

Using the following, find the mass per volume percent,

$\text{Mass percent}(\mathrm{m}/\mathrm{v})=\frac{\text{Solute mass}}{\text{Solution volume}}\times 100\%$

Mass per volume percent of Ibuprofen is$2.0\%(m/v)$

Find the mass of Ibuprofen.

Volume of the solution is $100mL$

$$\begin{gathered} \text{Solute mass}=\frac{\text{Mass percent}(\mathrm{m}/\mathrm{v})\times \text{Solution volume}}{100\%} \\ =\frac{2.0\%\times 100\mathrm{mL}}{100\%} \\ =2.0g \end{gathered}$$

We know that,

Mass per volume of the solution is $8.0\%(m/v)$

Mass of Ibuprofen is$2g$

Find the volume of Ibuprofen.

$$\begin{gathered} \text{Solution volume}=\frac{\text{Solute mass}}{\text{Mass percent}(\mathrm{m}/\mathrm{v})}\times 100\% \\ =\frac{2.0\mathrm{g}}{8.0\%}\times 100\% \\ =25mL \end{gathered}$$

Therefore, the volume of Ibuprofen is $25mL$