HOMEBREW Digest #4946 Tue 07 February 2006


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	FORUM ON BEER, HOMEBREWING, AND RELATED ISSUES
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Contents:
  Re: when to pitch Lager yeast ("Greg 'groggy' Lehey")
  Preserving a yeast starter (Matthew Frayer)
  How can I buildup the oxygen (lipids) levels of existing yeast cells? ("Steve Seeley")
  Re: when to pitch Lager yeast (Scott Alfter)
  Yikes...more on hydrometers? ("Mike Sharp")
  Re: when to pitch Lager yeast (Bob Tower)
  Pycnometry ("A.J deLange")
  When to pitch lager yeast (Randy Ricchi)
  Re: when to pitch Lager yeast (Jeff Renner)
  Pitching lagers and steeped in bitterness ("Peed, John")
  softened water in brewing ("steve.alexander")
  Thanks for the help; sorry for the delay; I'm planting hops! (Bill Velek)
  Water Questions ("A.J deLange")

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---------------------------------------------------------------------- Date: Tue, 7 Feb 2006 14:30:27 +1030 From: "Greg 'groggy' Lehey" <grog at lemis.com> Subject: Re: when to pitch Lager yeast On Monday, 6 February 2006 at 5:43:33 -0600, lkowens at uiuc.edu wrote: > I made a Dortmunder on Saturday. With my immersion chiller, > I couldn't get the wort to cool below 60F. In this > situation, which is the better strategy: 1)put the chilled > wort in the refrigerator to finish cooling, then pitch the > yeast when the wort cools to 50-55 or 2) pitch the yeast at > 60 and slowly drop the temperature of the refrigerator after > the yeast has been pitched. I've read with option 2 I'll get > more diacetyl, esters, and fusels. For some definition of "more". > But option 1 makes me nervous because I don't want to wait 10-12 > hours to pitch the yeast. I picked option 2 this time, Well, the pitching temperature doesn't depend on the style as much as it does on the yeast, and you haven't said what that was. Many people, myself included, pitch lagers a little warmer (round 13 to 15<insert degree sign here>C, or about 55 to 59<insert degree sign here>F). This is based on the popular Weihenstephan 34/70 "Bohemian Lager" yeast. After a few hours I then drop the temperature to about 10<insert degree sign here>C, or 50 <insert degree sign here>F. > but am afraid I'll end up with a fruity/butterscotchy Dortmunder. Don't worry about diacetyl yet. You address that afterwards with a diacetyl rest at about 18 <insert degree sign here>C/64 <insert degree sign here>F. I'm not so sure about esters, but I'd be surprised if pitching at 15 <insert degree sign here>C would produce discernable quantities of esters. So: I'd say you made the correct decision. Greg - -- Finger grog at lemis.com for PGP public key. See complete headers for address and phone numbers. Return to table of contents
Date: Mon, 6 Feb 2006 23:15:24 -0500 From: Matthew Frayer <mjfrayer at gmail.com> Subject: Preserving a yeast starter Hi all. I am a long time reader and first time poster with question about yeast starters. First of all my situation is that a prepped a 3 quart yeas= t starter with a bavarian lager yeast last week and had a horrendous brew day on sunday which in the end found me with 20 pounds of fresh compost and no wort to pitch the above mentioned yeast into. My question is what would be the best way to preserve this starter so that I can use it in a batch that = I will do in approximately 2 weeks. Thanks to all Matt Return to table of contents
Date: Mon, 6 Feb 2006 20:45:14 -0800 From: "Steve Seeley" <seseeley at hotpop.com> Subject: How can I buildup the oxygen (lipids) levels of existing yeast cells? Hi all, Is it possible to buildup the oxygen (lipids) levels of existing yeast cells? Or can this only be done for daughter cells? I have collected yeast out of a primary that I would like to reuse. However these yeast should have depleted oxygen reserves that need building up. Thanks for any help, Steve Seeley (Shingle Springs, CA between Sacramento and Tahoe) Return to table of contents
Date: Mon, 06 Feb 2006 21:54:27 -0800 From: Scott Alfter <scott at alfter.us> Subject: Re: when to pitch Lager yeast lkowens at uiuc.edu wrote: > I made a Dortmunder on Saturday. With my immersion chiller, > I couldn't get the wort to cool below 60F. In this > situation, which is the better strategy: 1)put the chilled > wort in the refrigerator to finish cooling, then pitch the > yeast when the wort cools to 50-55 or 2) pitch the yeast at > 60 and slowly drop the temperature of the refrigerator after > the yeast has been pitched? You forgot option 3, which is what I use with lagers: Pitch at 70-75, keep it there until the fermentation takes off, then crank the temperature down to the low-to-mid-50s. White Labs recommends this (in its craftbrewer FAQ) to minimize lag time. It's what I've used for Pils, and it works for me. Diacetyl comes later in the fermentation. Regardless of the pitching temperature, once the fermentation slows down, you'll want to bring the temperature back to around 70 for 2-3 days for a diacetyl rest. Once that's done, bring the temperature down into the low-to-mid-30s for lagering. If you still want to chill your wort down into the 50s for pitching, try using a swamp-cooler pump to circulate a sink full of icewater through the chiller. I have to do this in the summertime just to get the wort into the 70s. With enough ice, I could get lower temperatures if I wanted them. Scott Alfter scott at alfter.us Return to table of contents
Date: Mon, 6 Feb 2006 22:41:34 -0800 From: "Mike Sharp" <rdcpro at hotmail.com> Subject: Yikes...more on hydrometers? Michael Eyre is re-opening pandora's box, asking about Weight for O.G. readings. It was HBD #4899, and I think the post you're remembering was from AJ. He described using a pyncnometer for this. I doubt you'll get anywhere near the accuracy you're looking for using a graduated cylinder. A volumetric flask would be closer, but still not that good. http://hbd.org/hbd/archive/4899.html The problem is that you can't accurately measure the volume of liquid in a graduated cylinder--not to the degree you'll need. Think about the cross-section of your cylinder, and the cross-section of the "reading" end of a hydrometer. A volumetric flask has a narrow neck, but even so, I have a hard time getting *exactly* 50ml in mine. And to that error, you add the error in your balance... Regards, Mike Sharp Return to table of contents
Date: Mon, 6 Feb 2006 22:48:02 -0800 From: Bob Tower <bob at constructotower.com> Subject: Re: when to pitch Lager yeast Linda of Champaign, IL cannot chill her lager wort with her immersion chiller to pitching temperature and wonders what the best strategy is for when to pitch: wait to pitch until the wort chills under refrigeration or pitch in the 60s (F.) and gradually lower the temperature. My advice would be that if you are confident in your post boil sanitation techniques then go ahead and wait until you reach pitching temperature. If you've kept contamination out then another 10-12 hours isn't going to hurt the wort. You will get a MUCH cleaner lager if you pitch cold rather than pitch warm and then chill. You may even want to try cold pitching in which you chill the wort to about 5 F. lower than your fermentation temperature and then pitch the yeast allowing the wort to then warm up to the target fermentation temperature. That's what I do on all my beers (ales and lagers) and the results have been spectacular for me. On the other hand, if you've had problems in the past with sanitation then it's probably not worth the risk to wait to pitch thus allowing beer spoiling organisms to have such a large head start. Pitching warm would be the lesser of two evils if post boil sanitation is not excellent. You will get more off flavors than if you had pitched cold but if there's contamination that gets a 12 hour head start that will create infinitely more off flavors by comparison. Bob Tower / Los Angeles, CA Return to table of contents
Date: Tue, 07 Feb 2006 12:33:21 +0000 From: "A.J deLange" <ajdel at cox.net> Subject: Pycnometry I can't get the search engine to work either but here's what I posted around 29 November. If you look in the archives starting a little before that date you should be able to find the whole thread. Steven Parfitt describes the fine art of pycnometry which is carried out pretty much as he describes with a couple of differences. First go to http://www.kimble-kontes.com/html/pg-15123R.html and have a look at the flask used. There are other forms of pycnometers (see Vol II of DeClerck) but this one seems best for brewing applications. It is essentially a small Erlenmeyer flask with a side capilary tube and a ground mouth fitted with a ground glass plug with attached thermometer. To use the thing the first step is to clean it thoroughly and dry it thoroughly (alcohol and ether washes are often used). Then tare it on the balance fully assembled. Now fill with cool distilled water and insert the thermometer/plug. As the plug is inserted water will exit through the side capillary. Wipe the bottle dry and repeat the alcohol wash though you shouldn't really need to do this as the next step is to wait for the cool water to warm to the reference temperature (15C) and while this is taking place any water on the outside should evaporate. As the water warms it expands and some is pushed out the capillary. Soak this up with a bit of paper towel using a quick swipe so you don't draw any water out of the capillary but rather only get that which has pushed up above its tip. When the reference temperature is reached cap the capillary and weigh. Record the weight. Now dump the water and thoroughly dry the flask (alcohol and ether) or rinse it thoroughly with the beer to be measured. Fill with beer cooled to below the reference temperature. Needless to say it must be completely degassed. Wash the outside thoroughly and dry (or allow drying to occur while waiting for the temperature reference to be reached). Proceded as with the water. The ratio (weight_with_beer - tare)/(weight_with_water - tare) is the apparent specific gravity of the beer and can be easily adjusted to give the true specific gravity but it's not worth the trouble to do this as the difference should be beyond the fourth decimal place. A.J. Return to table of contents
Date: Tue, 07 Feb 2006 08:10:10 -0500 From: Randy Ricchi <rricchi at houghton.k12.mi.us> Subject: When to pitch lager yeast Linda is concerned that she pitched her lager yeast at 60F, rather than waiting until the wort cooled to the low 50's. Linda, I routinely pitch my lager yeast at about 58 degrees, which is about as cool as I can get the wort without using a lot more water and time with my immersion chiller. I pitch the yeast, oxygenate, and put the fermenter in my chest-freezer-turned-fermenting-fridge which is usually set at around 52 degrees. I get very clean ferments with this method. White Labs has recommended pitching lager yeast as warm as 70 degrees, and then only lowering the temp after you see signs of activity. I've never done that, and wouldn't want to try it, either, but by pitching at 60 and immediately putting in your fridge, the wort will be down to the low 50's before you actually start to see signs of fermentation. I would rather do this than let that wort sit for 12 hours with no yeast in there to keep the bad guys subdued. Return to table of contents
Date: Tue, 7 Feb 2006 10:03:18 -0500 From: Jeff Renner <jsrenner at umich.edu> Subject: Re: when to pitch Lager yeast Linda <lkowens at uiuc.edu> wrote: > I made a Dortmunder on Saturday. With my immersion chiller, > I couldn't get the wort to cool below 60F. In this > situation, which is the better strategy: 1)put the chilled > wort in the refrigerator to finish cooling, then pitch the > yeast when the wort cools to 50-55 or 2) pitch the yeast at > 60 and slowly drop the temperature of the refrigerator after > the yeast has been pitched. I've read with option 2 I'll get > more diacetyl, esters, and fusels. But option 1 makes me > nervous because I don't want to wait 10-12 hours to pitch > the yeast. I picked option 2 this time, but am afraid I'll > end up with a fruity/butterscotchy Dortmunder. What would > you do? I suggest option 2 without reservations, based both on theory and personal experience. The wort won't spend that much time at 60F, and actually, that's not terribly warm considering that many commercial lagers are fermented as warm as 58F (not that I recommend it). You certainly won't get esters, and diacetyl wouldn't be produced by that regimen anyway. You don't have to be all that slow in dropping the temperature if you are doing it simply in the fridge, and not with chilling coils. Just put it in the fridge set to 50F and it will be fine. My well water runs 48F (9C) this time of year, so chilling to near that point (which is also my preferred lager fermentation temperature) is no problem, but in warmer weather, I just take it down as far as it will go easily. I have stopped as high as the upper 60'sF (~20C) with good results. As a matter of fact, after doing this in warm weather a few times and being pleased with the faster start and quicker fermentation (perhaps because of more yeast growth?), this is now my SOP. So, which did you do? Jeff - --- Jeff Renner in Ann Arbor, Michigan USA, jsrennerATumichDOTedu "One never knows, do one?" Fats Waller, American Musician, 1904-1943 Return to table of contents
Date: Tue, 7 Feb 2006 08:56:47 -0800 From: "Peed, John" <jpeed at elotouch.com> Subject: Pitching lagers and steeped in bitterness Linda asks about pitching yeast in lagers. I just started doing lagers and on the first one, a German Pils, I fermented the starter at 68 F, pitched at about 70F and after it started fermenting I struggled to get it down to 50 (took 12 hours to go from 70 at pitch time to 50 during a raging ferment). The beer was mostly fermented at 55 F and it turned out fine - no diacetyl and reasonably crisp and flavorful. I say pitch at 60, set for 50 and everything will turn out just fine - just get that yeast beefed up. I like to decant and rejuice several times during starter buildup, then decant and juice the night before, then juice the morning of the brew, so it's fermenting full tilt when I pitch it. I'm getting starts in four to six hours in the low 50's. I since have been doing starters closer to 50 F, pitching at around 55 and fermenting at 50. It'll take a while before I can decide how much difference it makes, but I certainly wouldn't worry about pitching at 60 and setting for 50. Isomerization of the hop alpha acids requires mechanical mixing as well as heat - as in, a good roiling boil - so I don't think standard bitterness extraction rules apply to steeping hops. I think you'll get some bitterness from hot steeping (above 200 F), but I also think that, as Dave suggests, you get a good bit of a perception of bitterness just from the pungent flavor of the oils. John Peed Oak Ridge, TN Return to table of contents
Date: Tue, 07 Feb 2006 16:13:00 -0500 From: "steve.alexander" <-s at adelphia.net> Subject: softened water in brewing I have a question ! It's a water question, so I'm copying HBD's Aqua Rex, A.J deLange hoping for his sage comments on the topic. Several events have recently conspired which cause me to question the common HBD wisdom that softened water should never be used for brewing. First I (well my wife) has recently considered getting a softener for my somewhat too hard well water. This is probably rational since we do get a little carbonate precipitate on counters. This past weekend I put together a little presentation on brewing water issues for a local BJCP class, and one of the 20 attendees asked the question outright - "what's the problem with brewing with softened water ?". My immediate answer was that so long as you hit the proper mash pH via acid addition and don't mind exchanging some of the calcium ions for sodium ions (both flavor positive to an extent in beer) that I see no problem. Water hardness is defined by the total concentration of calcium(Ca) and magnesium(Mg) ions in the water, and is further subdivided into temporary hardness due to Ca & Mg carbonates and the remainder is called permanent hardness and is is primarily due to Ca and Mg sulfates, Chlorides and other salts of Ca & Mg. The temporary hardness, that due to carbonates, will precipitate if you do more than sneeze hard. They are less soluble at increased temps, so they precipitate after a boil. If you increase the calcium ion content, for example by adding lime (calcium hydroxide) then the carbonate equilibrium is shifted and you get precipitation. If you add acid to the water and drop the pH much below the carbonate specie cross-over point at pH 6.35, then nearly all of the bicarb ions (HCO3-) are converted to carbonic acid (H2CO3) which readily dissociates into CO2 + H2O and so is lost. This temporary hardness is typically the primary cause of alkalinity and buffering, since it may require a significant amount of acid to drive all the (normally) bicarbonate species to carbonic. The brewing problem with temporary hardness is that it malt doesn't provide enough acidity to overcome the alkalinity and drive the pH to normal mash range. Actually pale malt added to distilled water only reaches a pH of 5.8 at mash temp according to M&BS, to removing carbonate isn't a complete solution to the mash pH issue. Now we often read that Ca ions are very positive for mashing and the meaning seems to be that extra Ca ions in the mash cause the precipitation in the mash of hydrogen (and di-hydrogen) phosphate ions as calcium phosphate (Ca3(PO4)2) which cause the mash to become more acidic, lower pH. This is why some brewers add gypsum (calcium sulfate) to the mash water. The gypsum adds to the permanent hardness. The extra calcium ?may? even shift the calcium carbonate equilibrium and precipitate some chalk and reduce the temp hardness (is this correct AJ - I'm not entirely certain). But the extra calcium is certainly involved in mash acidification by phosphate precipitation. Actually phosphates precipitation doesn't explain the entire effect, and supposedly inositol and other organic ions precipitate and act to lower mash pH. Since phosphates are needed for yeast (or human) metabolism and inositol is a yeast nutrient, part of the b vitamin complex, I think there is a valid question about how advisable it is to precipitate vital minerals and nutrients to acidify the mash. Obviously experience is that this is not usually a problem. So that's the background .... My question is this - I own a bottle of food grade phosphoric acid - so, assuming I accept the flavor impact of increased sodium and decreased calcium in the final beer or am willing to make additions, why should I care whether I use tap water or it's softened twin ? Obviously if we intended to use only traditional mash acidification methods then the carbonate and lack of calcium would be a problem. OTOH if I add 50 cents worth of acid to my brewing water then the carbonates go up in a fizz and the malt phosphates & inositol are intact, or perhaps enhanced if I use phosphoric acid. So what's the problem with softened acidified water for brewing ? Yes there can be special cases where the sodium levels become too high (don't use softened burton water) or you knock 100% of the Ca out of the water and get oxalate haze but this isn't typical. Detailed questions: === 1/ Adding an acid (lets assume phosphoric, H3PO4 for example) to water with temp hardness from CaCO3 seems pretty straightforward at first. The carbonate appear as an bicarb ion (HCO3-) at neutral pH, and the acid dissociates to <H+,H2PO4-> and perhaps a little <H+,H+,HPO4--> depending on pH. Some of the hydrogens attach to the bicarb form carbonic acid (H2CO2). What is left in solution ? The balance seems to be CaCO3 + H2O => Ca++ HCO3- OH- and H3PO4 => H+ H2PO4- resulting in H2CO3 Ca++ OH- H2PO4- ignoring the carbonic which is presumably largely lost, what does the rest add up to ? I read in M&BS that malt phosphates combine with excess calcium ions to form Ca3.(PO4)2 [aka tri(tert) orthophosphate, natural whitlockite] but this is just slightly soluble [ 20ppm or ~0.065mMol] in cold water. Obviously we can't detect any minor precipitate from the mash, but I don't see a precipitate when adding phosphoric to chalky water. Why ? 1a/ The above would balance if it produced brushite: CaHPO4.2H2O and this is probably just soluble enough to avoid precipitation on cold water (solubility of 316ppm or 1.75mMol) unless you have very chalky water. In hot water the solubility drops so I expect that if it's brushite we'd normally see precipitation at hi-temp. 1b/ OTOH I suppose the calcium and phosphates might be available as equal molarity of Ca(HPO4)2.H2O and Ca3(PO4)2 where the former is soluble, but the latter (the same whitlockite as in the mash) is not, so if this is the case I'd expect part of the calcium would precipitate with a phosphoric addition increasing the acidity 3Ca++ 3H2PO4- => Ca3.(PO4)2 (precip) 6H+ What is the result here and why does this (does this ?) differ from the mash phosphate precipitation ? == 2/ Now assume we start with temp-hard water as in 1/ and run it through a water softener. I assume we replace every Ca++ with 2Na+ ions in the softener. (note this means that every 20ppm of Ca ions are replaced with abt 23ppm of Na ions, 15% more mass) CaCO3 + H2O => Ca++ HCO3- OH- then after softening, at neutral pH it's 2Na+ HCO3- OH- 2a/ If we add phosphoric as above and ignore carbonic we get 2Na+ OH- H2PO4- and if we evaporated the water I assume we end up with one of the Na2HPO4.nH2O hydrates of monohydrogen orthophosphates which are highly soluble. Does that sound right ? 2b/ As a generality it looks like the Ca.X water compounds (carbonate, sulfate, chloride) are all considerably less soluble than the corresponding Na2.X counterparts, so I assume that adding non-carbonate calcium (hydroxide, sulfate) to the softened water will reintroduce the possibility or precipitation of chalk or whitlockite or whatever. I'm being lazy here -I should really re-read that college chem textbook chapter on equilibrium but ... -S Return to table of contents
Date: Tue, 07 Feb 2006 16:36:49 -0600 From: Bill Velek <billvelek at alltel.net> Subject: Thanks for the help; sorry for the delay; I'm planting hops! Anyway, from the various replies that I've received, I've determined that hops can, indeed, grow in Arkansas, but that I shouldn't put them in my garden, and I need to keep them away from my tomatoes due to wilt. The majority of people reported that hops are easy to grow and make a BIG difference in the quality of homebrew. I've picked a nice spot in my yard that should work, am getting ready to order my rhizomes, and am planning a trellis of sorts. That is what I am writing about now -- to see what folks think of this idea. Instead of using a pulley which could jam from the bins, my thoughts are of using a removable lock-pin at the base of each pole, to be able to just swivel the pole down to a horizontal position. Until I drop it down to harvest the hops cones, I will also use cable and stakes for guidelines to help support it against the wind. Does anyone think that will work? Thanks for any advice. Beautiful day today, so I'm going to go out and till up the spot I've picked for my hops, and I've just cracked open a bottle of homebrew. :-) HAPPY DAYS ARE HERE AGAIN! Cheers, Bill Velek Join "HomeBrewers" international grid-computing team and help mankind by donating spare computer power for medical research such as cancer; we're in the top 10% and passed the MillerTime team: http://tinyurl.com/b7ofs Return to table of contents
Date: Wed, 08 Feb 2006 02:17:02 +0000 From: "A.J deLange" <ajdel at cox.net> Subject: Water Questions Steve asks a bunch of interesting but not easily answered questions. Before I tackle them let me answer the general question "Why can't you brew with softened water?" and note that his answer "You can." is correct if you do things right. The main objection to softened water is that the typical home softener removes hardness which is generally good without touching alkalinity which is generally bad. In particular the residual alkalinity (alkalinity minus 1/3.5 times the sum of the calcium plus half the magnesium hardness) attains its maximum value when the hardnesses are zeroed (the softener will not quite zero them but come fairly close). Thus if the calcium is replaced by the addition of gypsum or calcium chloride the residual alkalinity can be restored with the only difference being that there is now an amount of sodium equivalent (in the chemical sense) to the original hardness as well as the anion (at the same equivalence) of the calcium salt used to restore the residual alkalinity. The water might be getting a little crunchy. Thus pH control can be handled with softened water just as it can with unsoftened by replacing the lost calcium and magnesium and the other benefits of those ions realized as well. But why do this? Isn't it much easier to just open the bypass valve on the softener when drawing brewing water and then close it again when finished? This is what I do with my neutralizer (I tossed the softener out a couple of years ago). Question 1 summarizes to "I add phosphoric acid to water with bicarbonate. What's left at equilibrium?" The answer is carbonic acid, bicarbonate ion, carbonate ion, phosphoric acid, monobasic phosphate ion, dibasic phosphate ion, tribasic phosphate ion, hydrogen ion, hydroxyl ion and any other anions and cations present in the original water. What changes is the relative amounts of these. Some carbon dioxide gas will have escaped and some hydroxyl apatite, Ca10(PO4)6(OH)2 may have precipitated. If any calcium carbonate was present some of it will have dissolved, some carbonate ions will have converted to bicarbonate, some bicarbonate to carbonic and some carbonic to CO2. The phosphoric acid will have gone through succesive dissociations losing 1, 2 and eventually 3 protons and some of the (PO4)-3 may coalesce with calcium and precipitate (it is extremely insoluble). One can calculate the concentrations but the process involves solving a system of 10 equilibrium equations (ignoring magnesium) by numerical means (vary the pH until the total electronic charge is 0 and then use the pH to calculate the concentrations of carbo and phospho species). This material was the subject of the talks I gave at Louvaine and the AHA convention last year. I'm sending a set of the slides to Steve in a separate e-mail and will do the same for anyone else who wants them. Just drop me an e-mail. What may be of particular interest in them ar the bubble diagrams which show the flow of species in a carbo/phospho system. So my answer to Question 1 is a bit of a copout. What actually happens depends on the chemistry of the water being treated (alkalinity and pH) and how much phosphoric acid is added. Add enough to get the pH to 4.3 and you'll drive out all the carbo (converts to CO2). For lesser amounts of acid a smaller fraction of the carbo will be converted. There will be little carbonate thus the major carbo species will be bicarbonate. Similarly with the phosphates for normal brew pH's they will be mostly the mono and dibasic forms. There will be very very little tribasic phosphate and thus small liklihood of any precipitation. What is different with the normal mash tun reaction is that in this case myoinositolhexaphosphate hydrolyzes to release mostly the monobasic phosphate which reacts by 10Ca+ + 12HCO3- + 6H2PO4- + 2H2O --> Ca10(PO4)6(OH)2 + 2H+ + 12H20 to precipitate apatite and release hydrogen ions thus lowering the mash pH. With respect to Question 2 the chemistry is basically the same except that two of the 10 equilibrium equations, i.e. those involving the solubility products of calcium and carbonate and calcium and phosphate are no longer involved (with a real softener they would be but would be of minor significance in the solution). And yes, adding back calcium from another source would render them significant again. Also yes, equilibrium chemistry is what this is all about and the caveats that go with it apply. Return to table of contents
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