# 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.

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.

Calculating Dilution of Solutions

from

Chapter 8 / Lesson 5
69K

Learn 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.