# Question #27266

Mar 26, 2017

When diluting a solution with distilled water, ${M}_{1} {V}_{1} = {M}_{2} {V}_{2}$ where ${M}_{1}$ and ${V}_{1}$ are the molarity and volume of the concentrated solution and ${M}_{2}$ and ${V}_{2}$ are the molarity and volume of the dilute solution.
In this situation, ${M}_{1} = 1.0247 \text{M}$, ${V}_{1} = 25 \text{mL}$, and ${V}_{2} = 250. \text{mL}$. Rearranging the equation to solve for ${M}_{2}$ gives ${M}_{2} = \frac{{M}_{1} {V}_{1}}{V} _ 2$.
Plugging in the known values, we have ${M}_{2} = \left(\left(1.0247 \text{M")(25"mL"))/((250."mL}\right)\right)$, and solving that gives ${M}_{2} = 0.10247 \text{M}$