You need $500mL$of a $5.0\%(m/v)$glucose solution. If you have a $25\%(m/v)$glucose solution on hand, how many milliliters do you need?

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The following are the given information:

We have $500mL$of a $5.0\%(m/v)$glucose solution.

Find for$25\%(m/v)$glucose solution.

$\text{Mass / Volume percent}(\mathrm{m}/\mathrm{v})=\left(\text{Mass of solute / Volume of solution}\right)\times 100\%$

$\text{Mass / Volume percent of the glucose solution to be prepared}=5.0\%(\mathrm{m}/\mathrm{v})$

Volume of the solution is $500mL.$

Mass of the glucose is,

$$\begin{gathered} =(\text{Mass}/\text{Volume percent}\times \text{Volume of the solution})/100\% \\ =(5.0\%\times 500)/100\% \\ =25g \end{gathered}$$

Mass of the glucose is $25g$

$\text{Mass / Volume percent of the stock solution}=25\%(\mathrm{m}/\mathrm{v})$

Therefore,

The volume of the glucose is,

$$\begin{gathered} =\left(\text{Mass of glucose in the solution / Mass / Volume percent of the solution}\right)\times 100\% \\ =(25/25\%)\times 100\%mL \\ =100mL \\ =1.0\times {10}^{2}mL \end{gathered}$$

Hence the volume of the glucose is$1.0\times {10}^{2}mL$