# If you take 10 mL of a 500 ppb solution, add sufficient water until the total volume is 250 mL,...

## Question:

If you take 10 mL of a 500 ppb solution, add sufficient water until the total volume is 250 mL, and mix thoroughly, what is the concentration of the final solution in ppb?

## Concentration:

The concentration of a solution refers to how much solute is dissolved per unit volume. Concentration is often measured in moles per liter (molarity) in chemistry, but can also be measured in parts-per notation. In our question, our concentration is measured in ppb, which stands for parts per billion.

## Answer and Explanation: 1

The question provides us with the initial volume (10 mL) and concentration (500 ppb) of a solution and asks us to determine the concentration if it is diluted to a final volume of 250 mL. To answer this question we can use the following formula:

{eq}\rm c_1V_1 = c_2V_2{/eq}

Where:

{eq}\rm
c_1{/eq} is the initial concentration

{eq}\rm V_1{/eq} is the initial volume

{eq}\rm c_2{/eq} is the final concentration

{eq}\rm V_2{/eq} is the final volume

Rearranging the formula to solve for {eq}\rm c_2{/eq} and substituting in the values:

{eq}\begin{align} \rm c_2 =& \rm \dfrac{c_1V_1}{V_2}\\ &= \rm \dfrac{(500\:ppb)(10\:mL)}{250\:mL}\\ &= \rm 20\:ppb \end{align} {/eq}

**The final concentration is 20 ppb.**

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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.