Question: Volume occupied by 10% alcohol, 20%, 30%, 40%

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  • Thread starter Thread starter Bryan Parry
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    Alcohol Volume
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Discussion Overview

The discussion revolves around determining the volume occupied by various concentrations of alcohol solutions (10%, 20%, 30%, 40%, etc.) based on a given mass. Participants explore the relationships between mass, volume, and density, particularly focusing on the relative density of alcohol and water.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in finding a comprehensive list of volumes for different alcohol concentrations and requests assistance.
  • Another participant suggests using the International Critical Tables or library resources for relevant data.
  • A participant proposes a formula to calculate the volume of alcohol solutions based on mass fraction, but notes the need for unit clarification.
  • There is a discussion about the assumptions regarding whether the percentages refer to weight or volume, with a common assumption being that they refer to volume.
  • Participants outline equations to solve for the volumes of water and alcohol in a solution, given a specific mass.
  • One participant questions the assumption that volume is conserved when mixing alcohol and water, indicating potential complications in the calculations.

Areas of Agreement / Disagreement

Participants generally agree on the approach to calculate volumes using density and mass, but there is uncertainty regarding the conservation of volume when mixing alcohol and water, indicating a lack of consensus on this assumption.

Contextual Notes

The discussion highlights the importance of clarifying whether the percentages refer to mass or volume, as this distinction significantly affects the calculations. Additionally, the assumption of volume conservation when mixing solutions remains unresolved.

Bryan Parry
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I have looked for months in handbooks, online, in encyclopaedias and so on, tried piecing things together fro mvarious sources, and I still cannot find this. What I basically wish for is a list that tells me what volume a certain mass of a solution of alcohol occupies at 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 100%. The mass can be a kilogramme or a pound or a gramme or whatever. I know that the relative density of 100% alcohol is 0.79, but do not know of the rest.

Please could somebody help me, as this information is relatively important to me. Thank you and cheers for any help offered :)

-Bryan
 
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International Critical Tables (old, but no less accurate than today's measurements); failing that, hit whatever abstract/citation indices are available in the library for "systems: water-_____ol."
 
With the info you have, you can build yourself that table in Excel in about 30 seconds. Don't use units, but assuming you mean alcohol percentage mass vs volume, the (unitless) equation is (someone check me):

volume = .79*(mass fraction of alcohol) + (1-mass fraction of alcohol)
 
Originally posted by russ_watters
With the info you have, you can build yourself that table in Excel in about 30 seconds. Don't use units, but assuming you mean alcohol percentage mass vs volume, the (unitless) equation is (someone check me):

volume = .79*(mass fraction of alcohol) + (1-mass fraction of alcohol)

I am not quite sure I follow what you are saying. Could you give this to me referring to measuring units so I can get this point. Thank you :)
 
Failing Excel, you could try doing the arithmetic yourself!

You have already told us that you know that alcohol has a relative density of 0.79. Okay, a 30% solution of alcohol consists of 0.3 alcohol and 0.7 water. (Although you didn't say if that was 50% by weight or by volume-those are two completely different things. I'll assume "by volume" which is more common.)

You are seeking the volume of this solution that will have a mass of 1 (kg, say). Let X be the volume of Water and Y the volume of alchol. This is a 30% solution so Y/(X+Y)= 0.30. Since the density of alcohol is 0.79 times the density of water, the mass of the solution is (0.79Y+ X)times the density of water= 1. If I recall correctly the density of water is 1 gram/cm3 so 1 kg/liter. Using that: 0.79Y+ X= 1.

Now solve the two equation: Y/(X+Y)= 0.30 (which is the same as
Y= 0.3X+ 0.3Y or 0.7Y= 0.3X) and 0.79Y+ X= 1.

For a general percentage of alcohol, P, the same analysis gives the two equations as (1-P)Y= PX and 0.79Y+ X= 1. Solve those two equations for X and Y.
 
Originally posted by HallsofIvy
Failing Excel, you could try doing the arithmetic yourself!

You have already told us that you know that alcohol has a relative density of 0.79. Okay, a 30% solution of alcohol consists of 0.3 alcohol and 0.7 water. (Although you didn't say if that was 50% by weight or by volume-those are two completely different things. I'll assume "by volume" which is more common.)

You are seeking the volume of this solution that will have a mass of 1 (kg, say). Let X be the volume of Water and Y the volume of alchol. This is a 30% solution so Y/(X+Y)= 0.30. Since the density of alcohol is 0.79 times the density of water, the mass of the solution is (0.79Y+ X)times the density of water= 1. If I recall correctly the density of water is 1 gram/cm3 so 1 kg/liter. Using that: 0.79Y+ X= 1.

Now solve the two equation: Y/(X+Y)= 0.30 (which is the same as
Y= 0.3X+ 0.3Y or 0.7Y= 0.3X) and 0.79Y+ X= 1.

For a general percentage of alcohol, P, the same analysis gives the two equations as (1-P)Y= PX and 0.79Y+ X= 1. Solve those two equations for X and Y.

Oh my God. A very interesting and informative response. Physics, maths etc are not really my strong point- I am an English student. Regardless I shall attempt this as I need the info...

Are you saying to me that the volume occupied by 1 kilogramme of a solution that is 30% alcohol is equal to 1080 millilitres? That is my figure, anyway.
Erm, that is, pure alcohol would be 1/0.79 * 1000ml = 1266ml. This 266ml difference then * 0.3 = 80ml (plus the original 1000ml)

Is this right?


So a 75% alcohol solution, for instance, which weighs a kilogramme, will have a volume of 1200ml.
So a 40proof solution which weighs a pound will have a volume of 29.15cuin.


[?] [?] [?]
 
Originally posted by Bryan Parry
I am not quite sure I follow what you are saying. Could you give this to me referring to measuring units so I can get this point. Thank you :)
Halls (the math wiz) gave a great explanation of the derivation, but for the units thing, apply whatever units you want using the appropriate conversion. Metric is easiest, since 1cc of water is 1g.

And yeah - looks like you understand the equations.
 
Last edited:
Are you guys sure of the assumption that volume is conserved when alcohol and water are mixed?
 
Originally posted by NateTG
Are you guys sure of the assumption that volume is conserved when alcohol and water are mixed?

Oh dear... so what is the problem now? :D
 

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