Question

Question #a3b28

Answer 1

`"75.22 mL"`

Explanation:

I'll stat with a quick rundown of what dilution something actually means.

As you know, the molarity of a solution tells you how many moles of solute you get per liter of solution.

In simple terms, molarity is a measure of how concentrated a solution is in terms of the amount of solute it contains per liter of solution.

When your aim is to dilute a solution, you're essentially keeping the amount of solute constant while increasing the volume of the solution.

This can be written as

`color(blue)( overbrace(c_1 xx V_1)^(color(purple)("moles of solute in initial solution")) = overbrace(c_2 xx V_2)^(color(purple)("moles of solute in target solution")))`

Here

`c_1`, `V_1` - the concentration and volume of the initial solution
`c_2`, `V_2` - the concentration and volume of the target solution

Notice that you can rewrite this equation as

`c_1/c_2 = V_2/V_1`

The ratio between the volume of the target solution and the volume of the initial solution gives you the dilution factor.

`color(blue)("D.F". = V_"final"/V_"initial")`

For example, in order to perform a `1:2` dilution, which implies that the concentration of the target solution is `1/2` times that of the initial solution, you would use a dilution factor of `2`, since

`c_2 = 1/2 * c_1`

will give you

`V_2/V_1 = (color(red)(cancel(color(black)(c_1))))/(1/2 * color(red)(cancel(color(black)(c_1)))) = 2`

Notice that you don't need concentration values to find the dilution factor of a solution, as is the case with your example.

In your case, you want to perform a `1:64` dilution, which means that the dilution factor will be equal to `64`

`"D.F." = 64 = V_2/V_1`

This tells you that the volume of the target solution must be

`64 = V_2/V_1 implies V_2 = 64 * V_1`

Plug in your value for the volume of the aliquot to get

`V_2 = 64 * "1.194 mL" = "76.416 mL"`

Since the volume of the target solution will be equal to

`V_2 = V_1 + V_"saline"`

it follows that you will need to add

`V_"saline" = "76.416 mL" - "1.194 mL" = color(green)(color(green)("75.22 mL")`

of sterile saline solution to your anti-cancer drug to perform a `1:64` dilution.