# If you dilute a stock solution that has a molarity of "14.8 M" and a volume of "25 mL" by adding "100 mL" of water, what will be the molarity of the resulting solution?

Jan 26, 2016

Here's what I got.

#### Explanation:

You can actually use different approaches to figure out the molarity of the new solution.

As you know, a solution's molarity tells you how many moles of solute you get per liter of solution.

$\textcolor{b l u e}{\text{molarity" = "moles of solute"/"liter of solution}}$

The important thing to notice here is that you can decrease the concentration of a solution by keeping the number of moles of solute constant and increasing the volume of the solution.

This is exactly what is happening here. The volume of the solution will go from $\text{25 mL}$ to

${V}_{\text{total" = "25 mL" + "100 mL" = "125 mL}}$

The volume of the solution increases by a factor of

$\left(125 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{mL"))))/(25color(red)(cancel(color(black)("mL}}}}\right) = 5$

which means that the molarity of the resulting solution will decrease by a factor of $5$. Keep in mind, the number of moles of solute are unchanged, since you only added water to the stock solution.

Therefore,

c_2 = c_1/5 = "14.8 M"/5 = color(green)("2.96 M")

Essentially, you have diluted the stock solution by a factor of $5$.

As you know, diluting a solution implies keeping the number of moles of solute constant while increasing the total volume of the solution.

color(blue)(overbrace(c_1V_1)^(color(purple)("moles of solute in tock solution")) = overbrace(c_2V_2)^(color(orange)("moles of solute in target solution")))" ", where

${c}_{1}$, ${V}_{1}$ - the molarity and volume of the stock solution
${c}_{2}$, ${V}_{2}$ - the molarity and volume of the target solution

Once again, the molarity of the diluted solution will come out to be

${c}_{1} {V}_{1} = {c}_{2} {V}_{2} \implies {c}_{2} = {V}_{1} / {V}_{2} \cdot {c}_{1}$

c_2 = (25 color(red)(cancel(color(black)("mL"))))/((25 + 100)color(red)(cancel(color(black)("mL")))) * "14.8 M" = color(green)("2.96 M")

I'll leave the answer rounded to three sig figs, despite the fact that your values only justify one sig fig.