# What volume of a 10% stock solution is required to prepare 200 mL of a 1.5% solution?

## Question:

What volume of a 10% stock solution is required to prepare 200 mL of a 1.5% solution?

## Diluting Solutions:

The dilution of solutions is a process that allows us to change a parameter of a solution in order to make it a working solution for an experiment. In particular, diluting solutions entails decreasing the concentration by having to increase the volume of the solution. This can be achieved by adding more volume of solvent to the solution.

## Answer and Explanation:

Determine the volume of the concentrated solution, {eq}\displaystyle V_1 {/eq}, that can be diluted to yield the desired solution. We do this by applying the dilution equation,

{eq}\displaystyle M_1V_1 = M_2V_2 {/eq}

where *M* is the concentration in terms of percentage, *V* is the volume, and the subscripts indicate the concentrated and diluted solutions. Now, we use the values of the variables:

- {eq}\displaystyle M_1 = 10\% = 0.1 {/eq}

- {eq}\displaystyle M_2 = 1.5\% = 0.015 {/eq}

- {eq}\displaystyle V_2 = 200\ mL {/eq}

We proceed with the solution.

{eq}\begin{align} \displaystyle M_1V_1 &= M_2V_2 \\[0.3cm] V_1 &= \frac{M_2V_2}{M_1} \\[0.3cm] &= \frac{( 0.015)(200\ mL)}{0.1} \\[0.3cm] &= \boxed{\rm 30\ mL} \end{align} {/eq}

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Chapter 8 / Lesson 5Learn what a solution is and how to properly dilute a new solution from a stock solution. Learn the dilution equation that combines molarity, the volume of stock solution and desired solution to determine how much stock solution is needed for the new solution.