# Question 509f4

Jul 11, 2017

The volume of the 40 molar solution required is $\text{0.005 mL}$ or $\text{5 mL}$.

Refer to the explanation for the process.

#### Explanation:

The symbol $\text{M}$ represents molarity, which is $\text{moles of solute"/"liters of solution}$.

A $\text{0.10 M}$ solution is said to be $0.10$ molar.

When diluting a solution, use the following equation:

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

where ${M}_{1}$ and ${M}_{2}$ are the initial and final molarity, and ${V}_{1}$ and ${V}_{2}$ are the initial and final volume.

When calculating dilutions involving molarity, the volume must be in liters, so $\text{100 mL}$ will be converted into liters.

Known

${M}_{1} = \text{40 M}$

${M}_{2} = \text{2 M}$
V_2=100 color(red)cancel(color(black)("mL"))xx(1"L")/(1000color(red)cancel(color(black)("mL")))="0.1 L"

Unknown

${V}_{1}$

Solution

Rearrange the equation to isolate ${V}_{1}$. Insert your data into the equation and solve.

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

V_1=(2color(red)cancel(color(black)("M"))xx0.1"L")/(40color(red)cancel(color(black)("M")))="0.005 L"# or $\text{5 mL}$