Q. 9.62 - An Introduction to General, Organic, and Biological Chemistry

Question

A doctor orders $100 mL of 2.0\% (m/v)$ ibuprofen. If you have $8.0\% (m/v)$ ibuprofen on hand, how many milliliters do you need?

Step-by-Step Solution

Answer

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

Step 1: Given Information.

The following are the given information:

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

To find the milliliters of Ibuprofen.

Step 2: 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 $2.0\% (m/v)$

Step 3: Find the mass of Ibuprofen.

Volume of the solution is $100mL$

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

We know that,

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

Mass of Ibuprofen is $2 g$

Step 4: Find the volume of Ibuprofen.

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

Therefore, the volume of Ibuprofen is $25 mL$