# What is the new concentration of a solution that is prepared in the lab by diluting 200 mL of a...

## Question:

What is the new concentration of a solution that is prepared in the lab by diluting {eq}\displaystyle \rm 200 \ mL {/eq} of a {eq}\displaystyle \rm 2.0 \ M {/eq} solution to a final volume of {eq}\displaystyle \rm 0.800 \ L {/eq}?

(a) 0.50 M

(b) 0.40 M

(c) 0.80 M

(d) 8.00 M

(e) 0.20 M

## Creating Dilutions:

To create a dilution we often use volumetric flasks. Volumetric flasks measure one specific volume very accurately, which allows you to create solutions with lower uncertainty and higher accuracy. The volume of solution to be diluted is often added to the volumetric flask using a volumetric or graduated pipette. When diluting, we always use distilled water instead of tap water to avoid any contamination from dissolved compounds in the tap water.

We are told that 200 mL of a 2.0 M solution is diluted to a final volume of 0.800 L. To determine the new concentration, 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

As the question gives us the volumes in two different units, we must convert one of them to the same units as the other. I will choose to convert liters to mL:

{eq}\rm 0.800\:L \times \dfrac{1000\:mL}{1\:L} = 800\:mL{/eq}

Now we rearrange the formula to solve for {eq}\rm c_2{/eq} and substitute in the values:

{eq}\begin{align} \rm c_2 =& \rm \dfrac{c_1V_1}{V_2}\\ &= \rm \dfrac{(2.0\:M)(200\:mL)}{800\:mL}\\ &= \rm 0.50\:M \end{align} {/eq}

Therefore option (a) is the correct answer.