ACADEMIC QUESTION: S.G, soluability, physics OR Why am I stupid?

[woozy]

Obviously I have a misconception somewhere. But where?

This are my conceptions; one (or more) of them must be wrong:

[edit: I thought it was clear I meant which conceptions were *fundamentally* flawed "false hypothesis" that lead to the false conclusion and not which conceptions contain errors or are wrong because they are conclusions drawn from false hypothesis. Conceptions containing errors that are not fundamental to the argument bear correction but don't yield false conclusions.]

1. A specific gravity reading is ratio between the density of liquid compared to the density of water (calibrated for a specific temp. but lets not bog ourselves down). Thus, for example, if a solution has an s.g. of 1.046 that means the solution is 1.046 times as dense as water.

2. Density is mass/volume. Weight is measure of gravity on a mass and in this case can be considered synonamous with mass so density is (on earth at sea level) also a measurement of weight/volume.

[edit: "can be considered synonamous" has received a lot of criticism. Mass and weight, are of course, utterly different concepts. I should have worded this more carefully. My intention was not to imply they were the same thing but that, for the purpose of this argument density, although defined as mass to volume, can be used to also express weight to volume. This doesn't fundamentally affect the argument.]

3. Thus: a gallon of something with an s.g. of 1.046 will be 1.046 times as heavy as a gallon of water.

4. A gallon of water weighs 8 lbs so a gallon of something with an s.g of 1.046 will weigh 8.368 lbs.

[This is incorrect. "A pints a pound the world around" apparently is *never* true. A gallon of water is 8.33 lbs. It doesn't affect the argument but it does lead to incorrect values.]

5. Soluable means disolves in water thus adding it to water will not increase the volume.
[*THIS* is fundamentally incorrect and gives rise directly to the incorrect conclusion.]

6. Sugar is soluable in water thus added a pound of sugar to a gallon of water will result is one gallon of solution.

[Since this is based on a false hypothesis this is, of course, incorrect.]

7. Sugar has a diastatic power of 46 PPG which means adding 1 lb of sugar to one gallon of water will yield a solution with a s.g. of 1.046

[This has two errors, neither fundamental to the argument. i) "diastic power" simply was not the term I wanted. "diastatic power" is a measure of enzyme activity and sugar, of course, has none. I incorrectly used it to mean the degree to which it effects gravity. ii) One doesn't add sugar to a gallon of water; one adds sugar and enough water to make a gallon of solution.]

8. Thus 1 lb of sugar added to a gallon of water will be one gallon in volume and thus weigh 8.368 lbs.
[This is based on the false hypothesis #5 so as a result is false]

9. Adding a lb of sugar to a gallon of water causes no chemical of physical reaction that will result in any loss of mass or weight.

10. 1 lb of sugar weighs a lb. A gallon of water weighs 8 lbs so mixing the two results in a solution weighing 9 lbs.
[Well, 9.33 lbs...]

11. 9 lbs is a different weight than 8.368 lbs

Which of my conceptions is [fundamentally]wrong?
[#5 ]

 

[evrose]

#5 is wrong. Soluble means it dissolves in water, but the total volume DOES increase.

#6 also wrong. Adding a pound of sugar to one gallon of water results in a solution that has more than one gallon total volume. The sugar has volume.

#8 is also wrong. One pound of sugar added to a gallon of water will have greater than one gallon total volume. The weight will = weight of water + weight of sugar. The volume will = volume of water + volume of sugar.

Another way to think of it is this; if you dissolve one pound of sugar in a gallon of water (resulting in a solution with a volume of more than one gallon, I don't have to time to do the math, you need the density of sugar), then evaporate enough water away to make the total volume of the solution exactly one gallon again - the resulting sugar/water solution will contain less than one gallon of water, but a greater total mass (sugar is more dense than water)... hence the increase in SG. Make sense?

With that in mind, you have to recaluclate your assumptions below that... I don't have time to write out all of the equations... sorry...

 

[jfk69]

#5- volume will increase
#6- volume will be more than one gallon
#9- weight will increase (and at this point my head is starting to hurt)

 

[woozy]

Must be 5. Adding sugar must increase the volume somewhat.

So when you do an all-grain that adds honey or a partial mash, when you do the additions is the change in volume taken into account? Or is just considered negligible?
====
6 and 8 are direct results of 5 so they are not "wrong" in the sense of addition errors.

9 is not wrong. The total weight of sugar and water whether separate or together will remain the same.

----
But about 5...

so many beer recipes and/or calculators seem to talk of adding DME/LME/sugar etc. without taking any account of the additional volume. Although it is pretty small.

++++

1 gallon + 1 lb of sugar will weigh 9 lbs, have a gravity of 1.046 and thus will have a volume of 9/8.386 = 1.08 gallons (or 9/V = 8 * 1.046).

Which gives us a way to measure the volume of sugar, I guess. 1 lb of sugar has a volume of 1.2 cups. That is when you discount air.​

Wrong.

1 gallon + 1 lb of sugar will weigh 9 lbs. You boil it down to 1 gallon with s.g. of 1.046 or weight 8.368 so you boiled off .632 lbs of water which is .079 gallons (I was close) so the original volume was 1.079 gallons.

Thus one lb of sugar has a volume of 1.264 cups. Who knew?

====

I wouldn't want to boil it down. Then I'd get a gallon but it's gravity would be higher still and the weight heavier still.​

Wrong. I would want to boil it down because it's one gallon total.

 

[ACbrewer]

The root of yoru problem is #5.
When mixing solutions, chemists refer to the disolved into solovent mixed to Volume. Infact, Brix (a measure of sugar) and Plato(another measure of sugar) are both defined as "this much sugar in water to this volume" I think 1 Brix is 1 gram to 100 grams total solution. So for this volume is totally dispensed with.

I'm not sure how AG brewers handle the adding sugar or honey to the volume. Although for honey, 1 lb is about 1/12 of a gallon, or 10 oz, so that is somewhat negligable for the 35-37 points of sugar.

As to sugar V +water V = total V, in a solution, In a solution, there is some space savings, but not 100%.

Anyhow if you do mixing, remember that 46 ppg of something like sugar or DME is pounds mixed with water to 1 gallon total.

 

[evrose]

Must be 5. Adding sugar must increase the volume somewhat.

So when you do an all-grain that adds honey or a partial mash, when you do the additions is the change in volume taken into account? Or is just considered negligible?

You don't measure the OG until the final volume is reached.

For example, you start with 10 gallons of water (I'm making the math easy here). The SG of water is 1.00.

You then add 20 pounds of grain. The total volume is now water + grain. Doesn't matter much (other than to size your mash tun) what the actual number is.

You then boil down to 10 gallons total. Only water is lost - the sugar from the grains remain.

The resulting wort is more heavier than the starting water because sugar is more dense than water.

 

[woozy]

Anyhow if you do mixing, remember that 46 ppg of something like sugar or DME is pounds mixed with water to 1 gallon total.

Ah. I did *not* know that.

So.. I *would* boil down to a gallon with an s.g. of 1.046.

===
I realized after I posted that this is never an issue with extract (which tells you to top off) nor with all-grain (without additions) because you work the added volume from the grain sugars into the loss of water to grain absorbtion and only measure the pre-boil volume from there.

I guess we would assume the additions add to volume. Not sure that recipes do that much though. With sugar and DME it should be relatively small (about a cup a pound). But with LME I imagine it is quite large.

 

[brewkinger]

Actually, the root of the problem is in #2.

Mass is the amount of matter that an object contains (think atoms)
Volume is the amount of space that a certain mass occupies
Weight is the measure of the gravitational pull on an object (which has a mass)

So... the mass and weight of an object are NEVER synonomous, but because we are only familiar with our planet and it's gravity, the two are commonly thought of as the same.

If you took a pound of sugar to Mars, it would have the same mass but different weight.

Based on that misconception, the others that have been pointed out can be explained and understood better.


If you took an object that has a mass of

 

[woozy]

So I made two mistakes:

5. Soluable means disolves in water thus adding it to water will not increase the volume.

Wrong


7. Sugar has a diastatic power of 46 PPG which means adding 1 lb of sugar to one gallon of water will yield a solution with a s.g. of 1.046

Inaccurate: 46 PPG means mixing 1 lb of sugar with water into one gallon of solution

Which if followed out gives a rather interesting measurement for the volume of sugar.

 

[woozy]

Actually, the root of the problem is in #2.

...
So... the mass and weight of an object are NEVER synonomous, but because we are only familiar with our planet and it's gravity, the two are commonly thought of as the same.
...
Based on that misconception, the others that have been pointed out can be explained and understood better.

I didn't say they were synonomous. I said they could be *considered* synomous. i.e. density as a measure of mass/volume is the essentially the same as weight/volume and measuring of a lb of sugar and lb of water as weight or as mass will not alter anything.

And it doesn't. This in no way can be considered a "root" of the problem. Using mass rather than weight would have yielded the same results.

I only mentions this to get to 3) which *is* correct: a gallon of 1.046 solution is 1.046 times as *heavy* (_because_ it is 1.046 times as massive) as a gallon of water. After that we can toss any usage of mass out the window.

 

[ACbrewer]

Ah. I did *not* know that.

So.. I *would* boil down to a gallon with an s.g. of 1.046.

===
I realized after I posted that this is never an issue with extract (which tells you to top off) nor with all-grain (without additions) because you work the added volume from the grain sugars into the loss of water to grain absorbtion and only measure the pre-boil volume from there.

I guess we would assume the additions add to volume. Not sure that recipes do that much though. With sugar and DME it should be relatively small (about a cup a pound). But with LME I imagine it is quite large.

I forget how volumetricly sugar or DME work out to their mass, the stacking of sugar crystals makes it a little randome maybe 10%? it is enough that it is better to weigh out 5oz of bottling sugar than use 2/3 cup but I digress.

anyhow 1 cup in 1 gallon is 1 part in 16, or about 4%, or 1% on 5 gallons, so if you added 1 cup of volume, your OG readings would move by 1%, or not that much on 5 gallons (ok .8%) say from a 1.050 to a 1.0495ish, which is effectivly 1.050.

LME would be like honey, or about 10 oz of volume for 1 lb of LME/Honey. For Honey this varries a bit, but usually 12lb of honey = 1 gallon and is about 35 to 37 ppg. LME is more consitant at 37ppg, but I've never checked it's volume.

Going with the honey value, this means 6lb of LME at most would add 60oz volume to solution, or about 1/2 a gallon (64)- 10% assuming there is no space saving from disolving. And yes there is some space saving from disolving. the water and sugar can get closer than the sugar or water alone can, something about the molecules having charged edges.

Still, I'd guess that the lines on a typical bucket are good for 2 to 3 oz, assuming you have lines. My point being that just adding up to 1 lb and thus 10oz of volume on 5 gallons (640 oz) is adding about 1.5%... hardly noticble, You'd need a hydrometer sensetive to the .0005 to see it. since most are sensetive to .001 or I'm inclinded to things this is 'fudgable'

 

[ACbrewer]

Inaccurate: 46 PPG means mixing 1 lb of sugar with water into one gallon of solution


Which if followed out gives a rather interesting measurement for the volume of sugar.

EXACTLY.

(we can discuss brix at another time)

 

[brewkinger]

I didn't say they were synonomous. I said they could be *considered* synomous. i.e. density as a measure of mass/volume is the essentially the same as weight/volume and measuring of a lb of sugar and lb of water as weight or as mass will not alter anything.

And it doesn't. This in no way can be considered a "root" of the problem. Using mass rather than weight would have yielded the same results.

I only mentions this to get to 3) which *is* correct: a gallon of 1.046 solution is 1.046 times as *heavy* (_because_ it is 1.046 times as massive) as a gallon of water. After that we can toss any usage of mass out the window.

And I was politely telling you that they cannot be *considered* synonomous.
One is a measure of the actual amount of matter that an object contains, while the other is a measure of the pull that the Earth has on that matter.
They are commonly *considered* to be the same thing, but they are not.

As far as dissolving it in water goes, the overall mass of the water/sugar increases, but the amount of space (volume) that is taken up is pretty is EXACTLY the same as the volume of the water did.
I say pretty much because every single grain of sugar that does not dissolve in the water adds a tiny bit of volume to the overall amount.
With a boiled solution, this would be negligible because all the sugar would be dissolved.

I never said #3 was wrong.

 

[rpkincaid]

Sugar has a diastatic power of 0.

Diastatic power is a measure of enzyme activity.

 

[brewkinger]

I didn't say they were synonomous. I said they could be *considered* synomous. i.e. density as a measure of mass/volume is the essentially the same as weight/volume and measuring of a lb of sugar and lb of water as weight or as mass will not alter anything.

Academically speaking, as the holder of a Masters Degree in Chemistry, the formula is:

Density = Mass / Volume

In not one text book (I have 43 different ones) does the formula ever get rewritten as

Density = Weight (or Mass, whatever you prefer) / Volume

If you can find me one that does, I will eat a pound of sugar.

While you are searching the textbooks, think about this:
Which is heavier: a pound of sugar or a pound of lead?

 

[woozy]

And I was politely telling you that they cannot be *considered* synonomous.

Perhaps "synonomous" was the wrong word. Perhaps equivalent would have be better. What actually meant linearly dependent. My entire point being that "denser means heavier". That's the *only* reason I brought up the relationship of mass to weight at all.

As far as dissolving it in water goes, the overall mass of the water/sugar increases, but the amount of space (volume) that is taken up is pretty is EXACTLY the same as the volume of the water did.
I say pretty much because every single grain of sugar that does not dissolve in the water adds a tiny bit of volume to the overall amount.
With a boiled solution, this would be negligible because all the sugar would be dissolved.

Which has nothing to do with mass or weight.

I never said #3 was wrong.

But to get to #3, that an equal volume of a denser material will be *heavier* in than other material in proportion to their relative density, by means of assuming directly determined by mass (and that density is defined via mas rather than via weight) was the only reason for me making the ill-worded clause in #2. As #3 is correct and the basis of all that followed you can't really claim that #2 is "the root" of all misunderstanding.

The "root" was clearly #5. (#7 was inaccurate but wouldn't, in itself have led to any conceptual errors; just measuring errors).

 

[woozy]

Sugar has a diastatic power of 0.

Diastatic power is a measure of enzyme activity.

I stand corrected. But the point was sugar has PPG of 46.

 

[brewkinger]

Check out this link:
http://winemaking.jackkeller.net/hydrom.asp

The table at the bottom of the page might help us all understand what is happening here.

 

[Bookworm]

From a chemistry standpoint finding the end result from creating a solution can be a bit tricky. Depending on the Solvent (water) and Solute (whatever is dissolved in the water) the two starting volumes (excluding air) will not necessarily equal the ending volume. It is a fun experiment to prove this. Take 50ml of water and 50ml of alcohol and mix them. 50+50=100 correct? Not in this case, you will have less than 100ml solution. Why? Because water molecules are big and have space between them and alcohol molecules are much smaller so some of them fill those spaces and you end up with a smaller volume. The mass of the two combined did not change. There is a very slight exothermic reaction from the rearrangement of a few hydrogen bonds. The reaction is so slight that it can be ignored when evaluating the results.

 

[brewkinger]

Perhaps "synonomous" was the wrong word. Perhaps equivalent would have be better. What actually meant linearly dependent. My entire point being that "denser means heavier". That's the *only* reason I brought up the relationship of mass to weight at all.


Which has nothing to do with mass or weight.

But to get to #3, that an equal volume of a denser material will be *heavier* in than other material in proportion to their relative density, by means of assuming directly determined by mass (and that density is defined via mas rather than via weight) was the only reason for me making the ill-worded clause in #2. As #3 is correct and the basis of all that followed you can't really claim that #2 is "the root" of all misunderstanding.

The "root" was clearly #5. (#7 was inaccurate but wouldn't, in itself have led to any conceptual errors; just measuring errors).

And now I stand corrected.

 

[woozy]

Academically speaking, as the holder of a Masters Degree in Chemistry, the formula is:

Density = Mass / Volume

In not one text book (I have 43 different ones) does the formula ever get rewritten as

Density = Weight (or Mass, whatever you prefer) / Volume

Well, duh! If I thought that was the definition I would have used it and avoided the whole mess.

As very direct and simple corrollary weight = g*mass; so density = weight/volume*g. All I was saying was that weight and mass are directly corelated and therefore the weights of equal volumes of material will be proportional to their densities.

Which is heavier: a pound of sugar or a pound of lead?

Actually the puzzle as I heard it was with feathers and gold and that the kicker was that when shipping feathers poundage actually refers to a volume measurement and when shipping gold it refers to weight and so the pound of feathers actually weighed more than a pound and thus was heavier than the pound of gold which, duh, weighed a pound.

I haven't been able to find a copy of this book since and every reliable source has told me that this is bull**** and it seems to me that if a "pound" did measure volume than a "pound" of feathers being less dense than your average material should weigh *less* than a pound. (Or if the volume referred to the gold a volume-pound, which I haven't find any evidence of ever having existed, ... a volume-pound of gold would have weighed *more* than a lb.)

 

[scutiger]

This thread is taking me back to physical chemistry and thermodynamics, fun times.

 

[Bookworm]

At sea level and normal atmospheric pressure a pound is a pound. Has nothing to do with the density of the material. Once you increase the elevation a pound is no longer a pound but the difference is not worth worrying about for most applications. But it is part of the reason that mass is used for scientific applications. By the way you can not definitively determine mass with most scales. To be absolutely accurate you need a balance.

 

[brewkinger]

Now you have me a little confused.
"As very direct and simple corrollary weight = g*mass; so density = weight/volume*g. All I was saying was that weight and mass are directly corelated and therefore the weights of equal volumes of material will be proportional to their densities."

What does the "g" represent?

 

[woozy]

The really annoying thing is I *never* thought soluability meant volume wouldn't increase.

It's just that when a read these fast and loose recipes and rule of thumb calculations which glossed over any change in volume I figured, well, I never did take a chemistry class so maybe that *is* what it means... after all, I've never *observed* the water level of my tea cup going up when adding huge amounts of sugar... I always assumed that was because the volume of the sugar was mostly air and the actual rise it the water level was small in comparison ... but maybe it just gets somehow more densely packed.

Arrgh. I really should learn not to second guess myself.

 

[brewkinger]

At sea level and normal atmospheric pressure a pound is a pound. Has nothing to do with the density of the material. Once you increase the elevation a pound is no longer a pound but the difference is not worth worrying about for most applications. But it is part of the reason that mass is used for scientific applications. By the way you can not definitively determine mass with most scales. To be absolutely accurate you need a balance.

And I am not sure where to begin with this.

The gravitational pull on an object on this planet (ie the weight of the object) is in NO way, shape or form affected by altitude.
No, no, no.

 

[brewkinger]

The really annoying thing is I *never* thought soluability meant volume wouldn't increase.

It's just that when a read these fast and loose recipes and rule of thumb calculations which glossed over any change in volume I figured, well, I never did take a chemistry class so maybe that *is* what it means... after all, I've never *observed* the water level of my tea cup going up when adding huge amounts of sugar... I always assumed that was because the volume of the sugar was mostly air and the actual rise it the water level was small in comparison ... but maybe it just gets somehow more densely packed.

Arrgh. I really should learn not to second guess myself.

Yeah, I can honestly say that is ALL of the chemistry classes that I have ever taken or taught, not once did I come across an instance where this was ever addressed.
I too have never seen the level of coffee rise in my cup, but truthfully it would be so miniscule as to be inperceptible with the human eye.

Looking at that table that I referenced, a # of sugar IN a gallon of water (as opposed to DISSOLVED in a gallon of water) relates into around 10.5 oz of additional volume, so just over a cup of water (might be noticeable if you looked carefully)

You learn something new every single day.

 

[woozy]

Now you have me a little confused.
"As very direct and simple corrollary weight = g*mass; so density = weight/volume*g. All I was saying was that weight and mass are directly corelated and therefore the weights of equal volumes of material will be proportional to their densities."

What does the "g" represent?

Gravity. Which just makes it more confusing as a conversion formula rather than a definition as a lb-mass is a different object than a lb-weight but a lb-mass weighs a lb-weight (on earth at sea level) so the conversion formula is the very misleading weight = mass.

Basically, for all practical purposes I wish to say is

weight = mass*constant
density = mass/volume
so density = weight/volume*constant

where constant = 1 lb(weight)/1 lb(mass) when once defined can be ignored and assumed to be 1 on earth and sea level (in good weather).

 

[woozy]

And I am not sure where to begin with this.

The gravitational pull on an object on this planet (ie the weight of the object) is in NO way, shape or form affected by altitude.
No, no, no.

Sure it is. Basic physics. The gravitational pull between two objects are determined by their masses and the distance between their centers. Closer we are to the center of the earth we are the heavier we are. The further away we are, the lighter. Thus if we are drifting past mars earths gravitional pull on us is negligible. The difference of a mountain height is minimal, but measurable. (Clocks run slower too. Or is it faster?)

Think about it. There's a point in space were you are weightless. There's a point where you have weight. Is that a sharp line where you go from zero to full-weight via crossing a millimeter thick line? Or is it a gradient and there's a spot an ounce. Another where you weight two ounces and get heavier the closer you get to earth? (Of course, it's hard to *percieve* weight without a floor to stand against.)

 

[woozy]

Yeah, I can honestly say that is ALL of the chemistry classes that I have ever taken or taught, not once did I come across an instance where this was ever addressed.

Well, I'm sure in some basic class where they cover conservation of mass and address that if you have add things together their weight will be the sum.

I never thought about this until I started reading recipes talking about the affect of adding lbs of LME affecting the s.g. but completely glossing over any change of volume and in some cases outright assuming volume would remain the same.

I mean, I should have realised that of course that makes no sense. You pour atoms into other atoms they take up the same amount of space but... well, there's all those "densely packed" counter examples and I never had a chemistry class nor a fluid dynamics class so maybe soluability is all about densely packing and slipping into cracks... Or maybe those recipes are oversimplifying and simply ignoring change in volume... naw, can't be. Must be me cause I don't know as much about beer as they do it follows I don't know enough about chemistry either. Densely packing into slips it is.:smack:[

I too have never seen the level of coffee rise in my cup, but truthfully it would be so miniscule as to be inperceptible with the human eye.

Well, you've never *looked*, have you?

I've never measured the weight of mixing two things together, either. Maybe mixing sugar to water caused mass to change. Well, my intuition on *THAT* at least, was still in the range of common sense. Well, there is conservation of *mass* but, obviously, no such equivalent law of conservation of *volume*. (Oh, wait... You can compress gas but not liquids [as my girlfriend told me once when we were contemplating a used condom])

I've got to start trusting myself over basic physics when reading articles about beer.