

Percent by Weight and Volume
Name: D. D.
Status: student
Grade: 912
Country: USA
Date: March 2009
Question:
What is v/v? How do you calculate it? How do you
calculate a concentration base on percent by volume and percent by
weight? On some msds' it is listed that a certain compound has a
concentration of 35% by weight, and on others it is listed that a
certain compound has a concentration of 35% by volume.
Replies:
Hello,
This is a question that I remember being confusing myself because there are
so many combinations, w/w, v/v, w/v etc. Take the amount of alcohol in beer,
for example. In the US, it is generally indicated as abv (alcohol by volume),
but in the UK it is generally indicated as abw (alcohol by weight). For
ethanol, the abv is a larger number than abw and after I explain how each is
calculated, you should understand why. I will use ethanol and water as the
two parts of a mixture for the examples below.
So before we begin, I expect you to be able to convert from grams to moles and
vise verse. Let's list out some physical properties of ethanol and water.
Ethanol: FW = 46, d = 0.798 (at 20C)
Water: FW = 18, d = 0.998 (at 20C)
d=0.914
v/v: To make a v/v solution, you simply take equal volumes of the two components
and mix them together. One caveat however, mixing ethanol and water makes a funny
thing occurs. The volume of the mixture will be less than the sum of the volume of
water and ethanol. For example, if you have 1 liter of water and 1 liter of
ethanol, then mix the two, what you end up with is only 1.92 liters of a 50/50
mixture (by volume). The reason for this is in the arrangement of the molecules.
When water freezes, the arrangement of the water molecules take up more space than
in liquid form, hence why ice becomes less dense than water and floats. When
combined with ethanol, the mixture contracts and the molecules take up less space
than the individual parts.
So if you need to make a 30/70 v/v solution of ethanol in water, you can multiply
0.3 times the final volume you wish to achieve to figure out how much ethanol to
add and do the same with 0.7 times the final volume to figure out how much water
to add. Combine the two and viola, you have your mixture, which is almost the final
volume you want. To compensate for this volume discrepancy, you can simply adjust
your desired volume upward by 510%.
The other situation is that you are given a unknown premixed solution and you wish
to figure out the v/v ratio. I am not aware of a way that one can (simply) calculate
this so the best option is then to look up empirical (experimentally derived) data on
the Internet, the CRC Handbook or other reference texts. There are ways to calculate
it, but this would require that you know the total number of moles of each component,
or at least the mole ratio of the two. I will get more into this with w/w below.
w/w: This is the other most commonly used ratio (w/v is not used much). To make a
35 w/w% solution, one simply weighs out the two components and mixes them together.
This sounds like you are looking up concentrated hydrochloric acid, but I will stick to
ethanol and water. If you want 1 kg of final solution, then 350 g of ethanol mixed with
650 g of water would give you a 35 wt/wt% solution of ethanol in water. Conversely,
if you are given the w/w and a total mass, then calculating simply back calculate by
multiplying the w/w% (35% in this example) by the total mass of the mixture and you
will obtain the mass of ethanol (or component 1).
But if you wish to calculate the wt/wt% of a unknown premixed solution, this gets a bit
more tricky. The advantage to using w/w is that it is independent of the volume, and
hence the contraction or expansion of the mixture due to molecular rearrangement, as
noted above with v/v. Here you must know at a minimum the mole ratio between the two
components, or the moles of one component and the total mass of the mixture
Example 1: You have 1 mole of ethanol and the mass of the mixture is 100g. Since the
FW of ethanol is 46, then 1 mole weighs 46 grams and you have a 46/100 = 46 w/w%
mixture.
Example 2: you have a mole ratio of 1:1 ethanol:water. In this case, even if you do
not know the mass of the final mixture you can still figure out the w/w%. 1 mole of
ethanol weighs 46 grams and 1 mole of water weighs 18 grams, so if you have equamolar
amounts, then the total mass could be 64 grams, which would make this a
46/64 = 71.9 w/w% ethanol/water solution.
I hope this helps!
Matt Voss
D. D.,
Percent by volume (v/v) is simply the volume of solute divided by the sum of the
volume of solute and volume of solvent  prior to be mixed together  times 100.
It is important to note that while the numbers may be close Vsolute/Vsolution is not
equal to Vsolute/(Vsolute + Vsolvent) since Vsolution is not always equal to Vsolute +
Vsolvent (since substances that mix well will interact and change the volumes upon
mixing).
Equivalently, percent by weight (w/w) is mass of solute/mass of solution * 100. In this
case, since mass is not affected by mixing, mass of solution is always equal to mass of
solute + mass of solvent.
To convert between the two, you would need to go through a conversion factor of density.
Remembering that density is mass/volume, you should be able to do the math.
Greg (Roberto Gregorius)
Hello D.D.
%v/v = percent volume/volume; for example: 1 / 100 X 100% is 1%,
therefore,
1mL / 100mL X 100% = 1% mL/mL, or, properly stated: 1% v/v
%w/v = percent weight/volume; for example: 1g / 100mL is 1% w/v
%w/w = percent weight/weight; for example: 1g / 100g is 1% w/w
Hope this helps,
Joel Jadus
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Update: June 2012

