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Old 09-29-2012, 07:06 PM   #1
AnthonyCB
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Default 1 kg water + 8 g sugar = 1.003 gravity?

Could someone explain to me why adding 8 grams of sugar to a liter of water only gets you to a gravity of 1.003. I understand that the sugar takes up some volume, but common sense would suggest that you'd get to somewhere closer to 1.008. Presumably this suggests that table sugar has a dissolved density that is only 1/3rd more than the water itself--it adds 5ml of volume and 8 grams to the mass. Is this surprising to anyone else?

Thanks,

Anthony

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Old 09-29-2012, 08:29 PM   #2
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You are confusing specific gravity and density. The density of pure water at 20 °C is 998.203 g/L. Thus a kg of water has volume 1001.8 cc. Adding 8 grams of sucrose to this gives a total mass of 1008 grams. But the volume changes slightly. The density of a solution of 8 grams of sugar in 1000 grams of pure water is 1.00127 g/cc. Thus the volume of 1008 grams of this solution is 1008/ 1.00127 = 1006.72 cc. The volume changed by 0.49% as a consequence of adding the 8 grams of sucrose. Normalizing the density by 0.998203 gives a true specific gravity of 1.00307 which, for a solution this dilute, is indistinguishable from the apparent specific gravity (to 5 decimal places).

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Old 09-29-2012, 09:39 PM   #3
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Quote:
Originally Posted by ajdelange View Post
You are confusing specific gravity and density. The density of pure water at 20 °C is 998.203 g/L. Thus a kg of water has volume 1001.8 cc. Adding 8 grams of sucrose to this gives a total mass of 1008 grams. But the volume changes slightly. The density of a solution of 8 grams of sugar in 1000 grams of pure water is 1.00127 g/cc. Thus the volume of 1008 grams of this solution is 1008/ 1.00127 = 1006.72 cc. The volume changed by 0.49% as a consequence of adding the 8 grams of sucrose. Normalizing the density by 0.998203 gives a true specific gravity of 1.00307 which, for a solution this dilute, is indistinguishable from the apparent specific gravity (to 5 decimal places).
Thanks for the response. Out of curiosity, how would these numbers change for other sugars/starches. Would the change in density be more or less identical for glucose, dextrose or amylose? Is there a rule of thumb or do you just have to know? What about various salts? NaCl, CaSO4 or CaCl? I imagine that NaCl dissociating into sodium and chlorine ions would have a substantially different impact on density than sucrose. But now we're probably venturing out of the realm of brewing.

And don't think your distinction of sg vs density was lost on me. I've clearly used them interchangeably here when I shouldn't have. Thanks for making me think about that (and re-read the wiki page on Specific Gravity).
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Old 09-29-2012, 10:20 PM   #4
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The numbers change very little over the sugars. A 10% by weight solution of sucrose has density 1.03811, for glucose it is 1.03770, and for fructose
1.03852. This is why we can use density/specific gravity to good effect in brewing. Even dextrines and soluble starches are in pretty good agreement with sucrose.

Each soluble substance has its own 'partial molar volume' and you need to know what that is. Brewers usually get their partial molar volume data (though they don't know it as such) from the Plato or Brix tables. The numbers I have been quoting here come from two dimensional polynomials published by ICUMSA (International Committee for Uniform Methods in Sugar Analysis). IOW each industry concerned with measuring concentration by means of density/specific gravity has its own standard formula or table. Data can also be obtained from handbooks, texts etc. Each of NaCl, CaSO4 etc would have its own characteristics.

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Old 09-29-2012, 10:22 PM   #5
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Quote:
Originally Posted by ajdelange
You are confusing specific gravity and density. The density of pure water at 20 °C is 998.203 g/L. Thus a kg of water has volume 1001.8 cc. Adding 8 grams of sucrose to this gives a total mass of 1008 grams. But the volume changes slightly. The density of a solution of 8 grams of sugar in 1000 grams of pure water is 1.00127 g/cc. Thus the volume of 1008 grams of this solution is 1008/ 1.00127 = 1006.72 cc. The volume changed by 0.49% as a consequence of adding the 8 grams of sucrose. Normalizing the density by 0.998203 gives a true specific gravity of 1.00307 which, for a solution this dilute, is indistinguishable from the apparent specific gravity (to 5 decimal places).
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Old 09-29-2012, 10:25 PM   #6
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Quote:
Originally Posted by ajdelange View Post
The numbers change very little over the sugars. A 10% by weight solution of sucrose has density 1.03811, for glucose it is 1.03770, and for fructose
1.03852. This is why we can use density/specific gravity to good effect in brewing. Even dextrines and soluble starches are in pretty good agreement with sucrose.

Each soluble substance has its own 'partial molar volume' and you need to know what that is. Brewers usually get their partial molar volume data (though they don't know it as such) from the Plato or Brix tables. The numbers I have been quoting here come from two dimensional polynomials published by ICUMSA (International Committee for Uniform Methods in Sugar Analysis). IOW each industry concerned with measuring concentration by means of density/specific gravity has its own standard formula or table. Data can also be obtained from handbooks, texts etc. Each of NaCl, CaSO4 etc would have its own characteristics.
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Old 09-30-2012, 07:31 AM   #7
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Quote:
Originally Posted by ajdelange View Post
The numbers change very little over the sugars. A 10% by weight solution of sucrose has density 1.03811, for glucose it is 1.03770, and for fructose
1.03852. This is why we can use density/specific gravity to good effect in brewing. Even dextrines and soluble starches are in pretty good agreement with sucrose.

Each soluble substance has its own 'partial molar volume' and you need to know what that is. Brewers usually get their partial molar volume data (though they don't know it as such) from the Plato or Brix tables. The numbers I have been quoting here come from two dimensional polynomials published by ICUMSA (International Committee for Uniform Methods in Sugar Analysis). IOW each industry concerned with measuring concentration by means of density/specific gravity has its own standard formula or table. Data can also be obtained from handbooks, texts etc. Each of NaCl, CaSO4 etc would have its own characteristics.
Thanks again for the useful info.
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Old 09-30-2012, 03:18 PM   #8
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This actually has implications for brewing beyond predicting SG. A kg of dissolved sugar takes up about 0.63 l. This changes a little depending on the final gravity.

But what this means is that the wort volume produced in the mash is noticeably larger than the amount of water that is added. This is something you need to consider if you want toThe predict the no-sparge lauter efficiency. that efficiency is the volume collected in the kettle over the total wort volume and not over the total water volume.

There is also a true and an apparent grain absorption. We commonly use only the apparent grain absorption.

The true grain absorption is around .19 gal/lb when the apparent one is .12 gal/lb

Kai

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