OT: Chemistry Question

curvature?

Are you trying to measure the Brix number for making wine, or something else? If so, the operating range is usually customized for the application. For wine, the target value is typically about 24% before fermentation. If you have 45% sugar in your grape juice, you'll end up with a very acidic wine. If you're making wine, don't worry much about what happens over about 35 degrees. Only about half the sugar is converted to alcohol, so a Bx = 24 usually results in

12-15% alcohol content. Most of the better commercial wine Brix meters max out at 50%. The cheap ones for wine max out at about 35%. I wouldn't worry (much) about what happens above 45% with wine.

There are other ranges. For example, if the refractometer is made for honey, the typical range is Bx = 35 to 95.

It's difficult to build a refractometer that's accurate over the entire range of surgar concentrations, so the measurement range is usually broken up into smaller ranges, where non-linearities can be more easily dealt with. For example, 3 ranges: Other types of refractometers:

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I misread Paul's post the first time. But he said he was wanting to use something made for measuring sucrose solutions for other things. I had a neat solution for measuring sugar solutions, but then realized that was not the problem.

But thanks for the post. I learned something.

Dan

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5%.

me

45% by weight is a lot of sugar in solution. It's a lot less by mole fracti on - the proportion of water molecules (molecular weight 18) to sugar molec ules (the molecular weight of sucrose is 342.3) - it's one sugar molecule t o 19 water molecules.

But water will hydrogen bond to the sugar molecules - probably one water mo lecule to each of the eleven oxygen molecules in sucrose, leaving only eigh t free water molecules, which isn't enough to form a complete shell of unbo nded water between adjacent sugar molecules.

So the knee would be the point where the solute molecules start interacting - where roughly half the water molecules in the solution are hydrogen bond ed to sugar molecules, and some of them start being bonded to two sugar mol ecules.

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Bill Sloman, Sydney

I'm looking at re-purposing a refractometer, intended for wine-making, for measuring something else (not sugar).

The meter I have reads from 0 to 32% BRIX (percent sugar). Over this range, the relationship is very linear. So, for this unit, its a non-issue. But if I have to get a meter that goes above 45%, I want to have some idea what causes the knee in the concentration vs index of refraction curve.

If I need to go into this range, the relationship is non-linear. So I'm trying to find out what sorts of problems I'll have by understanding the underlying chemistry/physics.

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tion - the proportion of water molecules (molecular weight 18) to sugar mol ecules (the molecular weight of sucrose is 342.3) - it's one sugar molecule to 19 water molecules.

molecule to each of the eleven oxygen molecules in sucrose, leaving only ei ght free water molecules, which isn't enough to form a complete shell of un bonded water between adjacent sugar molecules.

ng - where roughly half the water molecules in the solution are hydrogen bo nded to sugar molecules, and some of them start being bonded to two sugar m olecules.

I'm not seeing any knee in this data:

And this abstract says there is no knee for sucrose: " However, the refractive index of sucrose shows a linear relationship with concentration. The accuracy of the measurements is estimated to be better than 0.3%."

Refractive index of solutions at high concentrations.

The commodity Brix meter scale is marked either in Bx numbers or percent sugar. A few are also marked with the refractive index. The wine Brix meter relies on the assumption that the solution is water plus sugar, and nothing else. If you try to measure the sugar content of partially fermented wine, which contains some alcohol, the calibration goes awry and you have to do some compensating based on the estimated alcohol percentage. If you can find one that reads out the refractive index directly, you should be ok. However, you still have to build a chart of refractive index and your mystery compound concentration. Don't forget to compensate for changes due to temperature.

Well, if you're using a wine Brix meter that maxes out at 35%, it will probably read off scale at higher concentrations. I think you'll need a different meter, possibly repurposing the one made for honey.

I don't have any experience measuring unspecified compounds. However, my guess(tm) is that a table (spreadsheet) of refractive index to concentration could easily include compensation for any non-linearities.

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Not an answer to your question, but maybe an idea you can use. Just make a measurement and if the result is very high, just dilute the sample with an equal amount of water and remeasure. Then double the new measurement to get the actual concentration. The extra time would be a problem if you ne ed to make lots of measurements.

Dan

Dunno whether this is of any use to you, Paul, however GNU 'units' gives:

You have: brix Definition: interpolated table with points brix(0) = 1 * 0.99717g/cm^3 brix(1) = 1.0039 * 0.99717g/cm^3 brix(2) = 1.0078 * 0.99717g/cm^3 brix(3) = 1.01173 * 0.99717g/cm^3 brix(4) = 1.01569 * 0.99717g/cm^3 brix(5) = 1.01968 * 0.99717g/cm^3 brix(6) = 1.02369 * 0.99717g/cm^3 brix(7) = 1.02773 * 0.99717g/cm^3 brix(8) = 1.0318 * 0.99717g/cm^3 brix(9) = 1.0359 * 0.99717g/cm^3 brix(10) = 1.04003 * 0.99717g/cm^3 brix(11) = 1.04418 * 0.99717g/cm^3 brix(12) = 1.04837 * 0.99717g/cm^3 brix(13) = 1.05259 * 0.99717g/cm^3 brix(14) = 1.05683 * 0.99717g/cm^3 brix(15) = 1.06111 * 0.99717g/cm^3 brix(16) = 1.06542 * 0.99717g/cm^3 brix(17) = 1.06976 * 0.99717g/cm^3 brix(18) = 1.07413 * 0.99717g/cm^3 brix(19) = 1.07853 * 0.99717g/cm^3 brix(20) = 1.08297 * 0.99717g/cm^3 brix(21) = 1.08744 * 0.99717g/cm^3 brix(22) = 1.09194 * 0.99717g/cm^3 brix(23) = 1.09647 * 0.99717g/cm^3 brix(24) = 1.10104 * 0.99717g/cm^3 brix(25) = 1.10564 * 0.99717g/cm^3 brix(26) = 1.11027 * 0.99717g/cm^3 brix(27) = 1.11493 * 0.99717g/cm^3 brix(28) = 1.11963 * 0.99717g/cm^3 brix(29) = 1.12436 * 0.99717g/cm^3 brix(30) = 1.12913 * 0.99717g/cm^3 brix(31) = 1.13394 * 0.99717g/cm^3 brix(32) = 1.13877 * 0.99717g/cm^3 brix(33) = 1.14364 * 0.99717g/cm^3 brix(34) = 1.14855 * 0.99717g/cm^3 brix(35) = 1.1535 * 0.99717g/cm^3 brix(36) = 1.15847 * 0.99717g/cm^3 brix(37) = 1.16349 * 0.99717g/cm^3 brix(38) = 1.16853 * 0.99717g/cm^3 brix(39) = 1.17362 * 0.99717g/cm^3 brix(40) = 1.17874 * 0.99717g/cm^3 brix(41) = 1.1839 * 0.99717g/cm^3 brix(42) = 1.1891 * 0.99717g/cm^3 brix(43) = 1.19434 * 0.99717g/cm^3 brix(44) = 1.19961 * 0.99717g/cm^3 brix(45) = 1.20491 * 0.99717g/cm^3 brix(46) = 1.21026 * 0.99717g/cm^3 brix(47) = 1.21564 * 0.99717g/cm^3 brix(48) = 1.22106 * 0.99717g/cm^3 brix(49) = 1.22652 * 0.99717g/cm^3 brix(50) = 1.23202 * 0.99717g/cm^3 brix(51) = 1.23756 * 0.99717g/cm^3 brix(52) = 1.24313 * 0.99717g/cm^3 brix(53) = 1.24874 * 0.99717g/cm^3 brix(54) = 1.25439 * 0.99717g/cm^3 brix(55) = 1.26007 * 0.99717g/cm^3 brix(56) = 1.2658 * 0.99717g/cm^3 brix(57) = 1.27156 * 0.99717g/cm^3 brix(58) = 1.27736 * 0.99717g/cm^3 brix(59) = 1.2832 * 0.99717g/cm^3 brix(60) = 1.28909 * 0.99717g/cm^3 brix(61) = 1.29498 * 0.99717g/cm^3 brix(62) = 1.30093 * 0.99717g/cm^3 brix(63) = 1.30694 * 0.99717g/cm^3 brix(64) = 1.31297 * 0.99717g/cm^3 brix(65) = 1.31905 * 0.99717g/cm^3 brix(66) = 1.32516 * 0.99717g/cm^3 brix(67) = 1.33129 * 0.99717g/cm^3 brix(68) = 1.33748 * 0.99717g/cm^3 brix(69) = 1.34371 * 0.99717g/cm^3 brix(70) = 1.34997 * 0.99717g/cm^3 brix(71) = 1.35627 * 0.99717g/cm^3 brix(72) = 1.36261 * 0.99717g/cm^3 brix(73) = 1.369 * 0.99717g/cm^3 brix(74) = 1.37541 * 0.99717g/cm^3 brix(75) = 1.38187 * 0.99717g/cm^3 brix(76) = 1.38835 * 0.99717g/cm^3 brix(77) = 1.39489 * 0.99717g/cm^3 brix(78) = 1.40146 * 0.99717g/cm^3 brix(79) = 1.40806 * 0.99717g/cm^3 brix(80) = 1.41471 * 0.99717g/cm^3 brix(81) = 1.42138 * 0.99717g/cm^3 brix(82) = 1.4281 * 0.99717g/cm^3 brix(83) = 1.43486 * 0.99717g/cm^3 brix(84) = 1.44165 * 0.99717g/cm^3 brix(85) = 1.44848 * 0.99717g/cm^3 brix(86) = 1.45535 * 0.99717g/cm^3 brix(87) = 1.46225 * 0.99717g/cm^3 brix(88) = 1.46919 * 0.99717g/cm^3 brix(89) = 1.47616 * 0.99717g/cm^3 brix(90) = 1.48317 * 0.99717g/cm^3 brix(91) = 1.49022 * 0.99717g/cm^3 brix(92) = 1.4973 * 0.99717g/cm^3 brix(93) = 1.50442 * 0.99717g/cm^3 brix(94) = 1.51157 * 0.99717g/cm^3 brix(95) = 1.51876 * 0.99717g/cm^3

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You have two non-linearities to handle:

1. From instrument shadow boundary position to RI, and
2. From RI and temperature to concentration.

The case 1. is an instrument calibration and case 2. is dependent on the chemistry you'll handle.

Please note that the RI to concentration may be strongly (and non-linearly) dependent on temperature.

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-Tauno Voipio

Compact code isn't your thing, is it :)

Jamie

Concentrated solutions are a chemical bete noire; there are probably clusters of sugar molecules forming, instead of individual molecules in a dilute solution of mainly-water. Explaining the density of familiar salt+water solutions is a fairly heavy topic in physical chemistry.

Sugar refractometry for fermentation doesn't need to accurately measure dense syrups...

That's the compiler's job. ;-) It's the programmer's job to make the code readable.

molecule to each of the eleven oxygen molecules in sucrose, leaving only ei ght free water molecules, which isn't enough to form a complete shell of un bonded water between adjacent sugar molecules.

You have the right idea, but the bonding has an element of just giving a go od fit to the water environment. You have an average number of water molecules fi tted to each other of about 15. Molecules like ethanol, ethyl ether, tetrahydrof uran "fit" in well, so they don't lower the entropy much. H2O looks like an O with two H wings on it. Ether has an O with two ethyls on it. But it's n ot a perfect fit in the water structure, so ethyl ether solubility decrease s at high temperatures, due to the entropy effect. (hydrophobic effect.)

Sugar is so soluble in water that water seems to dissolve in it. There seem s to be more sugar structure in the melt than water. At high temperatures o f syrup cooking (240 F), the melting point increases, and it acts like a eu tectic of two solids.

r molecule to each of the eleven oxygen molecules in sucrose, leaving only eight free water molecules, which isn't enough to form a complete shell of unbonded water between adjacent sugar molecules.

good

les > fitted to each other of about 15.

it.

ity > decreases at high temperatures, due to the entropy effect. (hydrophob ic

ems > to be more sugar structure in the melt than water. At high temperatur es of

Thank you for spelling out my "right idea" in more detail.

Sadly, the OP was asking why there was a curve in the refractivity versus s ugar content curve at 45% by weight of sugar, and you've not said anything useful about why 45% by weight should be magic. I did at least address that question.

It does seem to be the point where the solution switches from being sugar d issolved in water to being water dissolved in hydrated sugar.

--
Bill Sloman, Sydney

That's an idea. Or I can pick up a refractometer with a different BRIX range (candy or jam making, for example). Assuming the non-linearity built into the device calibration is easy to compensate for.

Wine making junk is easy to come by in these parts. $20 for a simple optical RI tester when some garage winery either goes out of business or goes big time and springs for a digital unit. RI testers for applications other then winemaking are more expensive.

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. .

Interesting. I'll try messing with these numbers and see what I get. Is that g/cm^3 cm^3 of solvent or the resulting solution?

For low concentrations, the volume of solution remains pretty constant (if I recall my chemistry correctly). But if this relationship breaks down at some concentration, that might result in the knee I'm seeing in the curve.

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I'm not seeing a knee from the data in "Index of Refraction of Aqueous Solutions of Sucrose" from the CRC Handbook, but a second-order polynomial fits the data quite well.

% sugar index of refraction

0 1.333 10 1.3479 20 1.3639 30 1.3811 40 1.3997 50 1.42 60 1.4418 70 1.4651 80 1.4901 85 1.5033

y = 7E-06x^2 + 0.0014x + 1.3333

Michael

AFAIK, grams of solute per cubic centimeter of solution.

That's the usual method of expressing w/v concentration, in cgs units.

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"Design is the reverse of analysis" 
                   (R.D. Middlebrook)