# Question 6a10d

Oct 20, 2016

See explanation.

#### Explanation:

The underlying principle of a dilution is that the number of moles of solute remains unchanged.

In this regard, a dilution reduces the concentration of a solution by increasing its volume while keeping the number of moles of solute constant.

In this case, sample $\text{B}$ is said to be a $1 : 10$ dilution of sample $\text{A}$. This means that the concentration of sample $\text{B}$ is $10$ times lower than the concentration of sample $\text{A}$ because the volume of sample $\text{B}$ is $10$ times higher than the volume of sample $\text{A}$.

So, let's say that sample $\text{A}$ has a concentration ${c}_{\text{A}}$ and a volume ${V}_{\text{A}}$.

To get sample $\text{B}$, you must add enough solvent to make the volume of sample $\text{B}$ equal to

V_"B" = 10 * V_"A"" " " "color(orange)("(*)")

If you start with the initial volume of sample $\text{A}$, then you must add a volume of $9 {V}_{\text{A}}$ of solvent to make solution $\text{B}$.

Since the number of moles of solute is constant, you will have

${c}_{\text{A" = n/V_"A}} \to$ for sample $\text{A}$

${c}_{\text{B" = n/V_"B}} \to$ for sample $\text{B}$

But you know that you can use $\textcolor{\mathmr{and} a n \ge}{\text{(*)}}$ to write

c_"B" = n/(10 * V_"A")#

Since $n$ is equal to

$n = {c}_{\text{A" * V_"A}}$

you will get that

${c}_{\text{B" = (c_"A" * color(red)(cancel(color(black)(V_"A"))))/(10 * color(red)(cancel(color(black)(V_"A")))) = c_"A}} / 10$

Therefore, you can say that the concentration of solution $\text{B}$ is $10$ times lower than the concentration of solution $\text{A}$.