# Question 1266e

Dec 19, 2014

The asnwer is 2.04% for the w/v solution and 1.94% for the v/v solution.

Let's start by clearly defining what our solutions look like.

A w/v solution is usually used when a dry chemical is mixed as a dry mass (grams) per volume (mL), where

$\frac{n u m b e r . o f . g r a m s}{100 m L}$ = percent concentration

So, a 5% w/v solution will have $5 g$ of a substance in $100 m L$ of ethanol.

A v/v solution is used when dealing with liquid reagents and it represents

$\frac{n u m b e r . o f . m L}{100 m L}$ = percent concentration

So, a 5% v/v solution will have $5 m L$ of a substance in $95 m L$ ethanol.

Now, let's start with the w/v solution. An initial 5% concentration is now brought to 0.1%; this means that the volume of the solution is now 50 times larger (since the concentration is 50 times smaller).
Therefore, the $5 g$ of the substance would now occupy

$50 \cdot 100 m L = 5000 m L$, out of which only the initial $100 m L$ would represent ethanol (since the initial solutions are diluted in saline). The percentage of ethanol in the final solution would be

(100mL)/((5000 - 100)mL) * 100% = 2.04%

The procedure is similar for the v/v solution; the initial 5% solution's volume will now be 50 times larger, which means that the $5 g$ of substance will now occupy

$50 \cdot 100 m L = 5000 m L$, out of which $95 m L$ would represent ethanol. The percentage of ethanol would now be

(95mL)/((5000 - 95)mL) * 100% = 1.94%#