# Question d35f2

Feb 18, 2015

The student should use 1.0 × 10³ µL of clarified yeast extract.

The first question is, How much 100 % ethanol is needed to make 1.3 mL of 26 % ethanol?

This is a standard dilution calculation.

$\text{Volume" = "1.3 mL" × "26 %"/"100 %" = "0.34 mL}$

So you need to add enough clarified extract to make a total of 1.3 mL of solution.

How much extract is needed?

If there is no change of volume on mixing,

${V}_{\text{extract" = V_"total" – V_"ethanol" = "1.3 mL" – "0.34 mL" = "1.0 mL" = 1.0 × 10^3"µL}}$

Note: The answer can have only 2 significant figures, because that is all you gave for the volume of the sample. If you need more precision, you will have to recalculate.

Feb 18, 2015

You would need $962$ $\mu L$ of clarified yeast extract.

Here's how you'd go about solving this problem. You know that you must mix ethanol and clarified yeast extract together to get a $\text{1.3-mL}$ sample that is $\text{26%}$ ethanol.

Now, I'm assuming you're dealing with a $\text{26% v/v}$ solution, which is defined as

"% volume" = V_("solute")/V_("solution") * 100

If ethanol is your solute, a $\text{26% v/v}$ solution would imply that every $\text{100 mL}$ of solution contain $\text{26 mL}$ of ethanol. As a result, your sample will contain

$\text{1.3 mL solution" * ("26 mL ethanol")/("100 mL solution") = "0.338 mL ethanol}$

This means that the volume of clarified yeast extract must be

${V}_{\text{solution") = V_("ethanol") + V_("yeast") => V_("yeast") = V_("solution") - V_("ethanol}}$

V_("yeast") = "1.3 mL" - "0.338 mL" = "0.962 mL", or

$\text{0.962 mL" * (1000 muL)/("1 mL") = "962}$ $\mu L$

Rounded to two sig figs, the answer should be

V_("yeast") = "960# $\mu L$