Whiskey and Water

More whisky In Claire's water by a small percentage.

The classical answer is: Same amount.

However, when alcohol and water mix, the resulting volume is slightly less than before. But when Claire puts a full spoon back into Alan's glass, he winds up with slightly more total mixture.

So your answer is?

I don't remember just how much the mixture volume reduces from the sum of individual volumes. It depends on the alcohol proof, for one thing, which has not been given.

For sake of illustration, say 100 mL pure water and 100 mL pure ethanol combine to make 196 mL of mixture (i.e., 2% reduction). For good Scotch, say 50% alcohol, the reduction would be 1%, giving 198 mL total.

We don't know whether a spoonful is a tablespoonful, a teaspoonful, or a cokespoonful, so just say 10 mL.

Now, if Alan starts with 100 mL of Scotch and and gives 10 mL to Claire, he has 90 mL of Scotch left, and Claire has 109.9 mL of mixture, because of the reduction. Her mixture is divided into 100/110 parts water and 10/110 parts Scotch.

When she transfers 10 mL back to Alan, he gets 10 mL x 10/110 of Scotch back, the total reducing to about 99.99 mL of mixture. (The reduction is less because only about 90% water.) This gives him about 90 + 10 x 100/110 ≈ 90.9 mL Scotch and ≈ 9. 09 mL water.

Meanwhile, Claire is left with 99.9 mL of mixture. 99.9 x 100/110 ≅ 90.8 mL water and 99.9 x 10/100 ≈ 9.08 mL Scotch.

In short, Alan winds up with a wee deoch and doris more Scotch than Claire winds up with water. (Thanks to Harry Lauder, from those who remember.)

It seems your figures are based on a 50/50 mix of alcohol and water...the 50/50 mix is the peak of the bell curve of viscosity...here we are dealing with such a small amount of water to alcohol ratio I don't think the difference if any, would be measurable....this is why whiskey tastes better when mixed with alcohol to water in a 50/50 ratio ....or the equivalent in ice calculated to melt maintaining a 35% - 65% ratio during consumption...so a little bit of water and a couple cubes of ice makes the perfect whiskey drink...

https://www.facebook.com/WhiskyMolecules/posts/815756101809693:0

This is not about viscosity; it's about volume.

I already explicitly stipulated the 50/50 ratio as a good Scotch.

More viscosity = less volume

Wrong. No particular relation.

OK so if you are mixing alcohol and water and the volume decreases is the viscosity increasing, or decreasing, or does it stay the same?

https://www.researchgate.net/figure/a-Measured-mass-density-and-b-viscosity-of-commercial-beverages-as-a-function-of_fig5_229017093

It doesn't matter; this is not about about viscosity.

Well the whole point of adding water is to improve the taste, and an increase in viscosity is the result of adding water...so it not only matters, it's the whole point....

Baloney. This exercise is not about improving the taste of the whisky; it is about auditing the shifting of volumes. Viscosity has absolutely f nothing to do with it.

Not viscosity, density.

And if its a 1 litre glass and a tea spoon?
And "for good Scotch...50%" hmmm never heard of that. I forget how the US does it but say 80% proof, and here we'd say 40%avi, alcohol per volume. SO a Glenmorangie would be 40%.
Anyway, the point being that with "pure" water and "pure" ethanol with defined glass sizes and a defined measuring device a.k.a. spoon, you get a scientific answer.
The question doesn't state ethanol, pure water, or even the spoon size - so a correct answer is impossible.
For eggs - A cooking spoon from a shot glass would be about two thirds of the glass so the second glass must over flow if they start with the same contents

I will try here to calculate the effect of volume reduction when mixing alcohol (ethanol) with water. I will use the following initial data:

- Each glass contains initially 100 ml of liquid

- The spoon contains 10 ml of liquid

- Whiskey contains 40% ethanol and 60% water (in volume) – as most brands do. I will neglect any additional ingredient (which gives the color, for example).

- I will use the graph from #18, so I need the molar mass and the density of ethanol and water:

- Ethanol’s molar mass is 46.06844 g/mol and water’s molar mass is 18.01528 g/mol.

- Ethanol’s density is 0.7893 g/cm³ and water’s density is 1 g/cm³ (neglecting any additional salts).

First I will try to calculate how many ethanol and how many water I have in 100 ml (or cm³) of whiskey. If I mix 40 ml of ethanol with 60 ml of water, I will have the proper ratio but not 100 ml of whiskey, because:

- In 40 ml of ethanol I have 40x0.7893=31.572 g, which means 31.572/46.06844 =0.685 mol

- In 60 ml of water I have 60 g, which means 60/18.01528=3.331 mol

- So, the mol ratio of ethanol is 0.685/(0.685+3.331)=0.685/4.016=0.17 mol/mol

- Using the graph, gives a volume reduction of 0.9 ml/mol – so, the total reduction will be 0.9x4.016=3.61 cm³ (or ml)

- So, the resulting amount of whiskey will be of 100-3.61=96.39 ml. To have 100 ml, I need to use 100/96.39=1.037 of the initial quantities (41.498 ml of ethanol and 62.247 ml of water) – this corresponds to 0.711 mol of ethanol and 3.456 mol of water. So, this is what Alan has initially in his glass.

For Claire’s glass, it’s easier: 100 ml of water is 100 g, which means 100/18.01529 =5.551 mol.

Now, Alan moves 10 ml of whiskey to Claire’s glass, which means he moves 0.0711 mol of ethanol and 0.3456 mol of water. Now, the quantities are:

- In Alan’s glass: 0.64 mol of ethanol and 3.11 mol of water (=90 ml of whiskey)

- In Claire’s glass: 0.0711 mol of ethanol and 5.897 mol of water. This gives a reduction corresponding to a mol ratio of ethanol of 0.0711/(0.0711+5.897)=0.012. For this ratio is hard to read the graph, as the value is too close to the origin – I will consider 0.015 cm³/mol, which gives a reduction of 0.09 cm³ (or ml), which means that in Claire’s glass there is a volume of liquid of 109.91 ml.

Now, Claire moves 10 ml of liquid in Alan’s glass, which means 0.000647 mol of ethanol and 0.53653 mol of water. As a result, the final quantities are:

- In Alan’s glass: 0.64+0.00647=0.6465 mol of ethanol and 3.11+0.53653=3.64653 mol of water. This corresponds to a mol ratio of ethanol of 0.15, which gives a reduction ratio of 0.85 cm³/mol, so a total reduction of 3.65 cm³ (or ml). If we could separate ethanol from water we would have:

o Ethanol: 0.6465 mol, corresponding to 29.78 g and to 37.73 ml

o Water: 3.6465 mol, corresponding to 65.69 g and to 65.69 ml

Without reduction we would have 37.73+65.69=103.42 ml but we must reduce this with 3.65 ml, which gives a final value of 99.77 ml of liquid in Alan’s glass.

- In Claire’s glass: 0.0646 mol of ethanol and 5.36 mol of water, with a liquid volume of 99.91 ml.

So, in Claire’s glass there is more liquid than in Alan’s glass – the difference is 99.91-99.77=0.14 ml. Also, note that in each glass there is less than the initial 100 ml quantity!

Finally, calculating if Alan has less or more water in whiskey than Claire has whiskey in water is not possible, because we don't know how much reduction is associated to ethanol and how much to water, so we cannot calculate which quantity of water (in volume) corresponds to whiskey and which to the added water (the graph curve is not symmetrical, so for sure the reduction doesn't apply fifty-fifty).

Impeccable logic...

No, Claire has now got 110cc and she gives Alan 10cc of mixture. So both have 100cc but Alan's is 90.9cc since the 10cc from Claire's comes from 110cc.

No, Claire does not have 110 mL, because of the slight reduction of volume when the liquids are mixed.

You’re correct,.. sure, Alcohol is less dense that water,... they problem I see is you’re too focused and tripping over on the molecular size and can’t get over it.

and to confuse you even more,... I forgot what Einstein calls it, but this is more like a thought experiment... it may help if you let your mind go blank and start over.

I had a similar question like this posed in my physics class in college, why back when...

Actually, a more exact answer is:

Both start with 100 cc. Alan gives Claire 10cc of his whiskey. Now, Clair has 110cc of mix (90.(90)% water and 9.(09)% whiskey). When Claire returns the 10cc, it contains 9.(09)cc water and 0.(90)cc whiskey. Alan has now 90.(90)cc whiskey and Claire has 90.(90)cc water.

Of course, I didn’t consider the small volume reduction – I will do it later (as it is more complicated to calculate). I suppose anyhow that this was the desired answer when the challenge was created.

More water in Alan's whisky....

Because most whisky is over 50% water to begin with. So even if Alan's glass was only 2 spoonfuls (something about Scottish cheapne$$!), it would still become more watered than the water was whiskied!

I think you are confusing the ingredients with the product...

Scottish cheapness??

Back in the 1980s, there were many local pubs besides the big chains. You could tell the Scottish owners as they served 1/4 gill measures. The big chains used 1/6 gill, and others 1/5.

https://en.m.wikipedia.org/wiki/Gill_(unit)

Technically, that is like saying water is only partially hydrogen.

Whiskey is not whiskey unless you create a mixture of water and ethanol.

Nicely put. The spoon returning to Alan has 'x' quantity of water (or 'non-whisky), so need to faff with quantities and see the result. Fair game on CR4 to debate volume change when mixing the two liquids - it wouldn't be CR4 without such.

The classic puzzle is you have 2 urns, one red and one blue. The red one has 100 red balls in it and the blue one 100 blue balls. You move, say, a dozen balls from the red one to the blue one, stir them up, and then move a dozen from the blue urn to the red.

Does the red urn have more blue balls or the blue urn have more red balls or are they the same?

Both urns still each have 100 balls, so the blue balls in the red urn have displaced red balls, which are now in the blue urn. So they are the same.

The key to the logic is that both urns have 100 balls.

It works for liquids provided that both glasses end up with the same volume and the total volume doesn't change when you mix the liquids.

Alcohol and water are mutually soluble and a mixture of alcohol and water occupies less volume than the total volume of each.

http://butane.chem.uiuc.edu/pshapley/genchem1/l21/1.html

When 1 tsp of Whiskey is transferred from Alan to Clair, Clair's total volume is slightly less than 1 glass + 1 tsp. When 1 tsp of Clair's mixture is moved back, both more water and more whiskey are moved to Alan than would have been if Clair's mixture had not decreased in volume. Therefore, Alan has slightly more water and Claire has less whiskey.

...But are you talking volume or quantity?

...But are you talking volume or quantity?

I'm talking quantity (or moles), but I'm thinking it doesn't make any difference.

How do you figure the volume of water and alcohol in a solution, maybe by apportioning the solution volume in a ratio of the original volumes? Then if you have 1 oz of alcohol, you add 1 oz of water, and it shrinks to 90% volume, you now only have 0.9 oz of alcohol and 0.9 oz of water.

If Alan and Claire had exchanged molar volumes, it would have balanced out and Alan would have the same number of moles of water as Claire had moles of whiskey, just like the red and blue balls in the urns.

Since the volume was shrunk when Claire received the whiskey, more water and more whiskey (by weight) were returned to Alan because the amount transferred was by volume (1 tsp). Claire ends up with less whiskey and Alan with more water. So Alan ends up with more water than Claire ends up whiskey.

We are, of course, talking about a minuscule amount. There are 48 teaspoons in an 8-ounce glass, so 1/48 whiskey is not going to affect the volume very much.

It's the volume that shrinks, not the weight. If this whole problem had been cast in terms of weight, the classical answer would apply. But because of volume changes, the classical answer is no longer exact, although the deviation is very small.

Exactly!

...."to make sure they have exactly the same amount to drink."...

amount def...

..."a quantity of something, especially the total of a thing or things in number, size, value, or extent."...

..."Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value in terms of a unit of measurement. Wikipedia"...

Alan and Claire are in overthink mode.

They need to drink the damned whiskey, get naked, and watch Netflix and chill.

Jimmy Buffett put it a little differently.

kram, did you escape, or have you been released?

They were already spooning... did you miss that, the whiskey and water were secondary to confuse the readers.

Alan and Claire have a whiskey size glass each, which hold two spoons full of whiskey for a double serving, so, when Alan has a single whiskey,(one spoon full), and Claire has the same of water, then when a spoonful is added to Claire's glass, the mixture is 50/50 and when Alan has a spoonful back they have an even mixture of whiskey and water each.

What a waste of Scotch.

"I never drink water because of all the disgusting things that fish do in it"

"Work! The bane of the drinking man."

"Scotch needs water like a fish needs a bicycle"

All above quotes :_WC Fields

Alan puts neat whisky into Clair's glass which is then diluted with the water. Clair returns the same volume of diluted whisky to Alan's glass. The residual neat whisky in Alan,s glass increases the concentration of the diluted component so Alan always ends up with a stronger concentration unless the spoon transfers all of the whisky in which case both would have equal concentrations.

The question asks for the relative ratios of "whisky in water" to "water in whisky".

And for 64,000 dollars and all the marbles,.....

What is the name of the Mississippi River?

Big Muddy

Claire then grabs Alans glass, dumps it in her glass and then slams it down and asks,

What was the question again?

This clearly needs a scientific approach.

1. bottle of Glen Morangie Quinta Ruban 14 - 750ml
1. bottle of water - 250ml
24. Ice cubes ~ 550ml (they lose a bit in the melting)

Method - Add GM to glass, + 2 ice cubes + bit of water ~25ml (This is science so gotta be accurate). Repeat until all GM and water has been tested (Science after all)
Result - My missus isn't Claire
Cheers

I'm not following the logic here, but I am intrigued by your method....

The 24 ice cubes is a gross overestimate. The Glenmorangie isn't bad, though. How about Laphroig?

Melting factor mate ... bloody hot here.
Laphroig? Who am I to disagree with a man of your immutable wisdom?
Tomorrows experiment shall be rewritten, accordingly...I also think we should look at the possibility that the results could be different with an Irish Whiskey

Interesting debate, but has anyone considered the accuracy of the measurement tools. A spoon and two glasses are not sufficiently accurate to account for the tiny deviation in volume caused by the mixing.

but the time the test has been rerun with different glass sizes and different spoon sizes, everyone will be happy. I will use a lot glass,, Glenfiddich and a teaspoon.

Sliante.

and then, the cat died.

Clearly this could go either way....Factors include crudeness of measurement, unsteadiness of hand, especially late in the evening, number of transfers performed...Claire perhaps taking more than one teaspoon full as the evening progresses...

And there you go.
Proving,
a. Claire isn't my wife;

b. ice cubes melt (note the slightly deformed shape); and

c. that lovely old centenarian has certainly got more than a teaspoon of the nectar in her glass - going by colour

Claire may have been using progressively larger spoons...

I purchased a crate of whiskey and some shot glasses to run tests on this. After tests, including repeated swapping between 2 glasses, I am happy to report that there is no need to worry about whiskey dilution compared to water contamination. All possibilities have been tried. No problems with viscosity and volume change etc. Wife, less practised than myself, will be able to confirm when she wakes up. haPE U AawL apexiates muy Dudixacatioshun to sulvin probylumss bi praktikul mothed....kat trannned 2 hyt entur rettunses n cas of inkapasitashun

Well scientifically, those tests need to be repeatable.

You found the right way to manage COVID (Completely Objective View on Idiotic Debate) with Active Larynx Cleaning Original Heavenly Organic Liquid.

Only the doctors don't seem to agree - don't ask now... WHO's on first, since Tedros is followed by the rest of the of the St Louis (and aptly called) Wolves Team - "What" ? "I Don't Know", "Why", "Because", "Tomorrow", "Today".... and anyway it would end up, as it should "I/we don't give a darn" - as clearly (?) explained in the Naughty Nineteens.

What I say might un-disappoint you but this experiment result can't be relied upon. It is not done under controlled condition. How we can assume that after some time you haven't taken advantage of the blurry vision of the opponent and the spoon (supposed to be carrying whiskey from your glass) was not upside down?

This experiment to be repeated at least several times, in line with the applicable medical standards and there has to be an observer - who even if as blind as bat, should strictly be without glass. I always have a suspicion towards creatures that are small and quick , and to top it, who can rely on squirrels and nuts?

Get an observer and also get the whole procedure recorded on camera. Ensure that there are no other glasses than those two mandated by the experiment - not even in the Camera Lens.

After sufficient number of replications, you can forward the paper and the findings to Tedros.

It's all a horrible mess - they may have both started with a glass filled to the brim. Alan might put up with mild spillage when spoon is dipped, but Claire's coaster would be soaked. Mixing levels would be unknown without Tom Cruise or Bryan Brown to hand.

Next time you ask this question I sugest that Alan and Claire start with a glass of red and a glass of white wine which happen to be exactly the same strength: they both decide they would prefer rosé.

It beggars the question of what colour grape they like their wine made from.

Initial state Glass 1 V*S1 Glass2 V*S2

Step 1 Glass1 (V-v)*S1 Glass2 V*S2+v*S1 = (V+v)*S12→S12=(V*S2+v*S1)/(V+v)

Step 2 Glass1 (V-v)*S1+v*S12 = (V-v)*S1+v*(V*S2+v*S1)/(V+v)

Glass1 (V-v)*S1+v^2/(V+v)*S1+ v*V*S2/(V+v)

Glass 1 S1*((V^2-v^2)+v^2)/(V+v)) +S2*v*V/(V+v)

Glass 1 S1*(V^2/(V+v)) +S2*v*V/(V+v)

Glass2 V*S12 = S1*v*V/(V+v)+S2*V^2/(V+v)

R1=(V^2/(V+v))/(v*V/(V+v) = V/v >1 Glass 1 more S1 than Glass2

R2= v/V <1 Glass 2 has more S2 than Glass1

Let us follow pure mathematics... Let us assume that each glass has X amount of initial liquids and the spoon has Y capacity

Assumption 1 : where Y<X

Assumption 2: The amount carried is honestly, the spoon is filled to the brim and no drop of liquid falls while transporting - on the original glass or table. The whole amount exactly 'Y' is efficiently transferred from Glass 1 to Glass 2.

Assumption 3: The two participants are honest, and don't try to take advantage of blurry vision of the other.

(and may be a few more, I will think of them later, while experimenting).

When the first spoon is transfererred from Glass A to B, the quantities are,

A0 = X, B0 = X

A1= X-Y and B1= X+Y- f(X,Y,C, C’, H)

Where f(x,y,c, c', t) is the reduction in the volume due to dissolution and would be depending upon the concentration/ characteristics of the media in which it is transferred (c), the concentration/ characteristics of the media being transferred(c') and the heat of dissolution (H)

Glass B has Y quantity of the material of Glass A so it has concentration of Y/B1

Now an amount Y is transferred from B to A

A1 = X-Y + [ Y^2/(X+Y-f(X,Y,,C,C’,H)] - f(X-Y, Y^2/ Y^2/(X+Y-f(X,Y,,C,C’,H), C1, C1’, H1)

As the concentrations of the constituent change C will change to C1, C’ to C1’, H to H1,

Or will it? It seems to be too complicated… let me have the glass before mixing that will dissolve/resolve the complications and then I will look at this problem again. Don’t wait till then.