Calculating Fraction of Alcohol in Water-Alcohol Mixtures

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Discussion Overview

The discussion revolves around calculating the fraction of alcohol in a mixture of water and alcohol solutions. Participants explore the implications of mass ratios and how they relate to the total mass of the solution, focusing on two specific solutions with different ratios of water to alcohol.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant questions why the mass of alcohol in the 8-gram solution is calculated using 1/4 instead of 1/3, expressing confusion over the ratios.
  • Another participant explains that the mass ratio of alcohol to water is 1:3, but when considering the total solution, the ratio becomes 1:4, suggesting the use of 1/(3+1) for calculations.
  • A participant expresses difficulty in understanding the change in ratios when calculating the amount of alcohol in the 8-gram solution, indicating a struggle with the concept of ratios.
  • Clarification is sought regarding the difference between the ratio of alcohol to water and the ratio of alcohol to the total solution.
  • One participant confirms that the solution is the sum of the masses of alcohol and water, leading to the conclusion that the total mass is 4 for the ratio calculation.
  • A simple example is provided to illustrate the concept, showing that 1 gram of alcohol in 4 grams of solution corresponds to a 1:4 ratio.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the application of ratios in this context. While some clarify the relationship between the ratios, others still express confusion, indicating that the discussion remains unresolved in terms of full comprehension.

Contextual Notes

Participants are navigating through the complexities of mass ratios and their implications for solution calculations, with some assumptions about the clarity of ratio definitions and their applications in problem-solving.

lLovePhysics
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In an 8-gram solution of water and alcohol, the ratio by mass of water to alcohol is 3 to 1. If 12 grams of a solution consisting of 2 grams water for each gram of alcohol is added to the 8-gram solution, what fraction by mass of the new solution is alcohol?

-- I know that the first thing you should do is try to find the mass of alcohol in both the 8-gram and the 12-gram solution. However, to find the amount of alcohol in the 8-gram solution why would you multiply it by 1/4 and not 1/3? Its just confusing how the ratios can be written like 1:3 and then 1/4?
 
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The mass of the alcohol to water is 1:3, but the mass of the alcohol to the original 8 grammes solution is 1:4, hence multiply by 1/(3+1), hope this clears up the confusion.
 
bel said:
The mass of the alcohol to water is 1:3, but the mass of the alcohol to the original 8 grammes solution is 1:4, hence multiply by 1/(3+1), hope this clears up the confusion.

Lol, I still don't get it. I know that for every 1 gram of alcohol there are 3 grams of water. I can solve it by doing it that way. But I can't seem to get why it changes when you find the amount of alcohol in the 8-gram solution. Mabye I'm dumb or something. I just suck at ratios.
 
Do you understand the difference between

"The ratio of alchohol to water is 1:3" and
"The ratio of alchohol to solution is 1:4"?
 
HallsofIvy said:
Do you understand the difference between

"The ratio of alchohol to water is 1:3" and
"The ratio of alchohol to solution is 1:4"?

Well kind of. Solution would be the water + alcohol right? So you just add the msas of alcohol and the mass of water to get 4. Am I doing it correct?
 
lLovePhysics said:
Well kind of. Solution would be the water + alcohol right? So you just add the msas of alcohol and the mass of water to get 4. Am I doing it correct?

Yes. Why don't you imagine a really simple example. Say you added one gram of alcohol to 3 grams of water. You now have a total of 4 grams solution of which one gram is alcohol. It's not exactly rocket science as they say. :)
 
I see! Thanks! :smile:
 

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