For example, is a 1:20 solution of acetic acid in water 5% acetic acid, or 4.76% acetic acid? I’m embarrassed to ask such a seemingly simple question, but I think one of my instructors is misusing the concept of ratio. This was a question on a recent examination:
How many milliliters of a 30% solution and water are needed to prepare 2.5 liters of a 1:20 solution?
The correct answer was 417 milliliters of the 30% solution, and 2083 milliliters of water. (.30) (417) = 125, which of course is 5% of 2500. But isn’t a 1:20 solution one part solute to twenty parts solution? In other words, I have 21 parts total, not 20, right? I should actually have 119 milliliters of total solute, not 125, right?
But if I’m looking into a room with 37 people in it, and 17 of those people are men and the rest are women, then the ratio of men to women in that room is 17:20, right? And since 17 and 20 have no common factors other than one, there has to be at least 37 people in the room for this statement to be true, right?
Or is the reason I’m having a problem with this is because I’m confusing two different concepts—the concept of one to twenty and one in twenty?
My immediate instinct is to say that the 1:1 solution is half water and half acetic acid. And to extrapolate on this, that a 1:2 solution is one-third acetic acid and two-thirds water.
So it’s just a form of shorthand which is unrelated to the mathematical concept of ratio? In other words, it looks like a ratio, but it’s really just an agreed-upon way of saying “you’ll find one of these in every twenty of those”?
Now that I think about it I only know this because I trained as a psychiatric nurse and learned it in pharmacology. Otherwise I guess I would assume it’s a ratio too.
I think I’ve sorted this out. It seems that 1:20 can be defined as “one part in twenty-one” (as I maintain) or it can also mean “one part in twenty.” It depends on whom you ask. So the statement I made in post # 7 is not true. Stating that a 5% solution is synonymous with a 1:20 ratio may be accurate. It’s not “shorthand”, as I suggested, but an actual ratio. Be sure to click the second-to-last link on the page to understand the complete explanation.
What you are getting hung up on here is that the chemical notation for concentration in a solution and the **mathematical **notation for a ratio are both expressed using two numbers separated by a colon.
They are not the same thing, and are not calculated in the same way. They just happen to look alike.
OK, but can somebody cough up a cite for this and nail it shut right now? So far we’ve got three possible explanations:
1). It’s just look-alike notation and the two are unrelated. 1:20 therefore means a 5% solution.
2). The expression “a 1:20 solution” does indicate an actual ratio, and therefore indicates a 4.76% (or 100/21) level of solute in solvent.
3). The expression “a 1:20 solution” does indicate an actual ratio, but indicates a 5% solution because that’s another acceptable definition of the word ratio.
The thing is, for a chemist, if the solution is expressed in these terms, then precise calculation is rarely important so the differene between the two notations is insignificant. If somebody asked for 1 liter of a 1:1 solution of acetic acid in water, you would add 0.5 liters of acetic acid to 0.5 liters of water. If the specific meaning of the notation is not indicated or obvious, then the differrence is insignificant. If you want a precise solution of something, you use a notation that isn’t ambiguous.
So bottom line—a chemist sees “100 ml. of a 1:20 solution of acetic acid in water.” He fills the beaker to the 5 ml. line with acetic acid, fills to the 100 ml. line with water, and then adds Parmesan and anchovy paste and heads off to lunch?
Only if the solution required parmesian and anchovy paste.
I’ve seen advanced chemists interpret it both ways depending on the circumstance. A 1:1 solution is pretty obviously 1 part on and 1 part the other. A 1:2 solution is most likely 1 part one and 2 parts another. At 1:3 the notation gets a bit iffy. The bottom line is, if you want to be clear, use units that aren’t ambiguous.
Frankly, I think if the instructor wasn’t clear on the intent, it wasn’t a fair question. Unfortunately, the instructor probably felt it was obvious and never bothered to spend time on it. You can make an argument using the 1:1 solution example and ask them where the definition is explicitly described in the coursework, but I wouldn’t expect to get your points back.
There are three things, solute, solvent, and solution. You could describe ratios between any of them. A 1:20 ratio can mean one part solute to 20 parts of solution, and it would match the convention several above describe, and would be a ratio in the classic mathematical sense.
It does seem, though, ambiguous, because the phrase “x:y solution” does not literally convey which two of the three things are in ratio.
Now, for a more complicated question, suppose you mix some number of liters of ethanol with another number of liters of water. Ethanol and water mix such that they occupy a little less space than they did before mixing. Maybe the molecules nestle well - maybe they’re spooning. So, there are four volumes - the volume of unmixed ethanol, the volume of unmixed water, the total volume of unmixed ethanol and water, and the volume of the mixture. What’s the convention in this case, if we insist on using volume measurement?
