# A 0.25*L volume of 0.010*mol*L^-1 concentration was obtained by diluting a WHAT volume of a mother solution of 0.50*mol*L^-1 concentrations?

Apr 11, 2017

We need a volume of.........$5.0 \cdot m L$

#### Explanation:

The product $\text{concentration"xx"volume}$ has units of $\text{moles per litre"xx"litre}$, i.e. clearly an answer in $\text{moles}$................

And thus, since we dilute a given molar quantity of solute...........

${C}_{1} {V}_{1} = {C}_{2} {V}_{2}$

We solve for ${V}_{1}$, and thus we solve..........

${V}_{1} = \frac{{C}_{2} {V}_{2}}{C} _ 1 = \frac{0.010 \cdot \cancel{m o l} \cdot \cancel{{L}^{-} 1} \times 0.25 \cdot \cancel{L}}{0.50 \cdot m o l \cdot {L}^{-} 1} = 0.0050 \cdot L \equiv 0.005 \left(\frac{1}{\frac{1}{L}}\right) = 5.0 \times {10}^{-} 3 L = 5.0 \cdot m L$.