# Question 63a58

Sep 29, 2015

You can use a simple dilution calculation.

#### Explanation:

I assume that by "concentration and volume of the concentration acid" you mean molar concentration and volume of the concentrated acid solution, right?

If you know the molar concentration and volume of the concentrated acid solution, and assuming that you know what the volume of the target solution must be, then you can say that

${C}_{1} \cdot {V}_{1} = {C}_{2} \cdot {V}_{2} \text{ }$, where

${C}_{1}$, ${V}_{1}$ - the molarity and volume of the stock solution;
${C}_{2}$, ${V}_{2}$ - the molarity and volume of the target solution.

So, if your concentrated acid solution has amolarity of ${C}_{1}$ and a volume of ${V}_{1}$, and your target solution has a volume of ${V}_{2}$, then you can say that

${C}_{2} = {V}_{1} / {V}_{2} \cdot {C}_{1}$

Now, if you know the volume and percent concentration by mass of the concentrated acid solution, then you must use its density to find the molarity of the stock solution.

Once you know the volume and molarity of the stock solution, you can use the formula for dilution calculations again.

For example, if you have one liter of a concentrated hydrochloric acid solution, which is about $\text{37% w/w}$ and has a density of about $\text{1.18 g/mL}$, you know that you have

1 * 10^3color(red)(cancel(color(black)("mL"))) * "1.18 g"/(1color(red)(cancel(color(black)("mL")))) = "1180 g"

The mass of hydrochloric acid in this solution will be

1180color(red)(cancel(color(black)("g solution"))) * "37 g HCl"/(100color(red)(cancel(color(black)("g solution")))) = "436.6 g"

Now use the compound's molar mass to get the number of moles you have in one liter of solution

436.6color(red)(cancel(color(black)("g"))) * "1 mole HCl"/(36.46color(red)(cancel(color(black)("g")))) ~= "12.0 moles HCl"

The molarity of the stock solution will be

${C}_{1} = \text{12 moles"/"1 L" = "12 M}$

So, if you dilute a $\text{100-mL}$ sample of this stock solution to $\text{500 mL}$, what will be the concentration of the target solution?

${C}_{2} = {V}_{1} / {V}_{2} \cdot {C}_{1}$

C_2 = (100color(red)(cancel(color(black)("mL"))))/(500color(red)(cancel(color(black)("mL")))) * "12 M" = "2.4 M"#