# To what volume should you dilute 55 mL of a 11 M stock HNO_3 solution to obtain a 0.137 M HNO_3 solution?

May 19, 2016

You need to dilute the given volume of stock solution to $\text{4.4 L}$.

#### Explanation:

Molarity $\left(\text{M}\right)$ represents the concentration of a solution in moles of solute/liters of solution.

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

${M}_{1} = \text{11 M"="11 mol/L}$
${V}_{1} = \text{55 mL"="0.055 L}$
${M}_{2} = \text{0.137 M"="0.137 mol/L}$
V_2="???

Solution
Rearrange the equation to isolate ${V}_{2}$, then substitute the given values into the equation and solve.

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

V_2=(11cancel"mol/L" * 0.055"L")/(0.137cancel"mol/L")="4.4 L" (rounded to two significant figures)