PPG, wort gravity, and DME volume

[EscapeArtistBrewing]

How should the typical formula for DME addition to starter wort deal with the volume contribution of the DME itself?

Assume a PPG for the DME is 42 points/lb/gal.
To make 1 gallon of wort with SG=1.042, I would (per common practice) mix 1 gallon water with 1 lb of DME. Please ignore the high SG; I know it should be 1.030-1.040.
According to Pierce, 1 lb of DME adds 9.42oz of volume.

So, making the above mixture creates 1gal+9.42oz = 1.07359375 gal.
If I use the volume of the DME as a "dilution", the SG changes (ever so slightly; see screenshot below):

Should I be thinking about the total points in the contents of the solution that I have? If that's the case, then this 1.074 gallons of solution has contained within it 42 points worth of sugar.
Would this imply that 1.000 gallon of this solution would contain (1.000 / 1.074) * 42 = 39 points worth of sugar?

If so, then the SG for the starter wort is 1.039, not 1.042. (I won't even try to add the complication of adding the volume of the yeast slurry )

Your thoughts will be very much appreciated.

References:
https://byo.com/article/extract-for-all-grainers-advanced-brewing/
https://www.homebrewtalk.com/threads/question-about-ppg-definition.729503/

 

[EscapeArtistBrewing]

A follow-on question: should starter wort be considered, and prepared as, a standard solution?
A standard solution is made by weighing the calculated solute, dissolving in a small amount of solvent, and topping up.

Seems a more accurate way to create 1 gallon of 1.042 wort from 42.0 PPG DME:
1. Completely dissolve 1.0 lb of DME in 1/2 gal of water
2. Top up to 1 gal.

Agree?

 

[mac_1103]

Agree?

It certainly saves the trouble of doing any calculations. OTOH, are we really worried about 3 gravity points one way or the other for a starter?

 

[doug293cz]

Assume a PPG for the DME is 42 points/lb/gal.

According to your Pierce reference, DME is typically about 45 ppg, almost the same as sucrose. But, other than that, you appear to have a good understanding of what is going on.

Brew on

 

[EscapeArtistBrewing]

It certainly saves the trouble of doing any calculations. OTOH, are we really worried about 3 gravity points one way or the other for a starter?

I hear you, @mac_1103, and and the worry goes away after a fine IPA. My interest was mainly in understanding the relationship between PPG and SG, and the notion of number of (points/moles/molecules) of sugar in a volume (concentration) vs gravity.

I love my theory--yes, but there's some practical as well:

Seems better/easier (to me anyway) that making canned starter wort (with my trusty pressure cooker) is best be done by creating a standard solution of wort in bulk in my dutch oven, pouring 0.5 or 1L into Masons, and cook 'em up. No need to boil the solution only to have it's volume reduced/SG changed, no need to measure for each jar, the ability to add the final, correct-SG solution to each jar with the appropriate head space and not have to worry about diluting before use. (I wonder if there is a quality/safety reason that Propper creates a dillutable wort instead of a simple 1.035 solution).

 

[EscapeArtistBrewing]

According to your Pierce reference, DME is typically about 45 ppg, almost the same as sucrose. But, other than that, you appear to have a good understanding of what is going on.

Brew on

I picked 42 PPG because that's the value morebeer's DME calculator assumes. So many sources to play with out there (I love it....)

 

[mac_1103]

I wonder if there is a quality/safety reason that Propper creates a dillutable wort instead of a simple 1.035 solution

I wonder if it isn't just to save on packaging and shipping.

 

[EscapeArtistBrewing]

I wonder if it isn't just to save on packaging and shipping.

I would like to know, definitively, if concentration of wort affects the stability and safety of a "sweet liquid" processed via pressure canning. Does a higher osmotic concentration affect the anti-spore quality of the medium? Wish I knew. C'mon graduate assistants, get cracking!

I wrote the U of Georgia some time ago about USDA standards for pressure-canning wort; I was told that no such studies had been undertaken, and was advised to not process wort. My response was to increase the processing time to 20 minutes at 15 PSI, and not use my cannings beyond two or four weeks.

Given the lack of hot-break I see in Propper, I'm sure their process is not my process (LOTS of hot break in those Masons). But we spin off to an entirely different topic...

 

[hungupdown]

Midwest supplies says: the PPG unit describes the change in specific gravity (points) per pound of malt, when dissolved in a known volume of water (gallons).
So it sounds (like metric grams/litre), that it would mean per litre of water, not per litre of resulting fluid.

 

[mac_1103]

So it sounds (like metric grams/litre), that it would mean per litre of water, not per litre of resulting fluid.

It does sound like that. But I think they're wrong.

 

[doug293cz]

Midwest supplies says: the PPG unit describes the change in specific gravity (points) per pound of malt, when dissolved in a known volume of water (gallons).
So it sounds (like metric grams/litre), that it would mean per litre of water, not per litre of resulting fluid.

As @mac_1103 said, they are wrong, or at least misleading. It is a very misunderstood definition, and many people are confused by it. The definition is based on the volume of the resulting liquid, not the volume of water you started with.

If you would like, I can do a detailed calculation for this that will make it more clear.

Brew on

 

[EscapeArtistBrewing]

As @mac_1103 said, they are wrong, or at least misleading. It is a very misunderstood definition, and many people are confused by it. The definition is based on the volume of the resulting liquid, not the volume of water you started with.

If you would like, I can do a detailed calculation for this that will make it more clear.

Brew on

I would like to see that, Doug, if only to know the parameters that would go into the calculation. Offhand, I would think such items as percent moisture in DME and a quantification of the molecular interaction between solute (DME) and solvent (water) would be of interest. It's been 50 years since P-chem, so I could use a refresher on dissolution chemistry.

 

[doug293cz]

I would like to see that, Doug, if only to know the parameters that would go into the calculation. Offhand, I would think such items as percent moisture in DME and a quantification of the molecular interaction between solute (DME) and solvent (water) would be of interest. It's been 50 years since P-chem, so I could use a refresher on dissolution chemistry.

Yes moisture content plays a part in the PPG, but it can be confusing. Many (most) grains have their potential given on a dry basis, so need to reduce weight by the moisture content for accurate calculations. But, things like DME, LME, honey, etc. usually have PPG given on an "as-is" basis, so that moisture content is already accounted for in the PPG value.

Molecular interactions on dissolution appear to be rather minor, as the deviation of solution density from a simple weighted average of water density and the solute density are quite small. The correlation between solute concentration and SG is very close to linear across a fairly wide range. For more precise calculations, we normally just resort to using a curve fit equation to convert back and forth between SG and mass fraction of solute (as given by °Plato or °Brix.) There is a bit of a fiction involved in that both °P and °Bx are based on pure sucrose solutions, not typical wort extract composition profiles.

The accepted value for the PPG of sucrose is 46.2. If we dissolve 1 lb of sucrose in 1 gal (8.3304 lb @ 20°C) the °P calculation looks like this:

°P = 100 °P * 1 lb / (1 lb + 8.3304 lb) = 10.72 °P​

​

Interpolating in the Bureau of Standards 1918 tables of °Bx vs. SG (20°/20° C) gives the SG as 1.0430, which is below what we should get (1.0462) if the definition was based on 1 gal of solvent rather than 1 gal of solution.

And the volume of solution is:

Volume = 9.3304 lb / (1.043 * 8.3304 lb/gal) =1.074 gal​

​

If we dissolve 1 lb of sucrose in 0.9261 gal of water we get:

0.9261 gal * 8.3304 lb/gal = 7.715 lb​

°P = 100°P * 1 lb / (1 lb + 7.715 lb) = 11.47 °P​

​

And, again interpolating in the °Bx tables gives an SG of 1.0461

And the volume of solution is:

Volume = 8.715 lb / (1.0461 * 8.3304 lb/gal) =1.000 gal​

​

A few rounding errors account for the difference between the expected 1.0462 vs. the calculated 1.0461.

Brew on