# Question #d755f

Feb 17, 2016

375 mL of water is needed.

#### Explanation:

Using the dilution formula, calculate first for the amount of 2.0 M NaOH needed to prepare 500 mL of 0.5M NaOH solution:

let:
${C}_{1}$= initial concentration of NaOH solution
${C}_{2}$= final concentration of NaOH solution
${V}_{1}$ = volume needed
${V}_{2}$ = total volume of resulting solution

So then:

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

${V}_{1} = \frac{\textcolor{b l u e}{\cancel{0.5 M}} \left(500 m L\right)}{\textcolor{b l u e}{\cancel{2.0 M}}}$

${V}_{1} = 125$ $m L$

Then to calculate for the volume of water needed, subtract the volume of the final solution with the computed volume of 2.0 M NaOH needed:

${V}_{w a t e r} = 500 m L - 125 m L$
${V}_{w a t e r} = 375 m L$