Question

Question #6a10d

Answer 1

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 `"B"` is said to be a `1:10` dilution of sample `"A"`. This means that the concentration of sample `"B"` is `10` times lower than the concentration of sample `"A"` because the volume of sample `"B"` is `10` times higher than the volume of sample `"A"`.

So, let's say that sample `"A"` has a concentration `c_"A"` and a volume `V_"A"`.

To get sample `"B"`, you must add enough solvent to make the volume of sample `"B"` equal to

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

If you start with the initial volume of sample `"A"`, then you must add a volume of `9V_"A"` of solvent to make solution `"B"`.

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

`c_"A" = n/V_"A" ->` for sample `"A"`

`c_"B" = n/V_"B" ->` for sample `"B"`

But you know that you can use `color(orange)("(*)")` to write

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

Since `n` is equal to

`n = c_"A" * V_"A"`

you will get that

`c_"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 `"B"` is `10` times lower than the concentration of solution `"A"`.