By Marc Sedam (Brewing Techniques)
Water: It is by far the major component in beer. So why is it the one ingredient most often ignored by brewers?
Most home and craft brewers use the water most readily available to them, untreated, to brew all styles of beer. They may add gypsum to an IPA or stout recipe, but do little else to alter the profile of their brewing water. This approach can result in good individual beers, but is not the best way to produce consistently great beers brewed to style. It is no coincidence that brewers in Munich make dark, malty lagers; that those in Burton-on-Trent brew hoppy pale ales; or that early immigrants settling in the American Midwest (where the water was soft like that of Bohemia) brewed Pilsener-like lagers. The quality and composition of the local water in each case uniquely accentuates the flavors in these indigenous styles. You will no doubt find that if untreated water is used at your local brewpub or brewery, the same trend applies: The best beers are those most suited to the local water supply.
Fortunately, brewers can brew beyond the limitations of their local water supply to create excellent beers of any style. In most cases it takes only a few simple changes to the mineral content of your available water supply to create a medium that will bring out the flavors you’re aiming for. Water treatment: It’s not just for the big brewers anymore.
Begin at the Source
All rational plans for water treatment require knowledge of the specific composition of your local water. This information can be obtained by calling your local water utility and asking for a copy of their most recent water quality report. (Home brewers may be able to get an up-to-date report from a friendly local microbrewery or brewpub.) My water in Durham, North Carolina, comes from a protected upstate watershed. It is wonderfully soft and has remained very stable through the changing seasons and during the past several years. When I requested a water quality report, not only did I receive an overall analysis of my water, but also the actual measurements for each month of the year, including pH and water temperature!
Tables I and III list many minerals of major and minor importance in brewing. A typical water quality report should list all of these minerals and many other trace elements as well. You can compare your water quality report with the mineral profiles of particular styles of beer and embark on a simple water treatment program to replicate the desired mineral profile of almost any style.
The Underlying Principles: pH, Hardness, and Alkalinity
Any discussion of water treatment must be prefaced with an understanding of the principles of pH, hardness, and alkalinity. pH is a measure of relative acidity or basicity; hardness is a measure of the total calcium and magnesium ions in solution; and alkalinity, in this context, is a measure of the water’s buffering capacity. All three are interconnected, interrelated, and intimately tied to the mineral profile. They should all be considered in conjunction with any treatment program because they will have a significant effect on how the treatment is to be performed.
pH: pH is a topic that could fill many, many books, and my oversimplification will no doubt do it a certain injustice. Those interested in more details on pH and measurement can refer to A.J. deLange’s two-part series in BT.
Working with pH. Different steps in the brewing process require different pH ranges. Brewing water, for example, is best kept at a pH range of 6–7. The mash should be kept within pH 5.2–5.5 (at mash temperature) for optimal enzymatic action (alpha- and beta-amylase are proteins and will denature if the pH veers much outside this range). In wort, proper pH is important for coagulation of proteins; during fermentation, the optimal pH will promote a good environment for yeast, but an unwelcome environment for bacteria. The finished beer pH should fall between 4 and 5.
What is pH? The pH of a liquid is determined by the combination of dissociated salts, undissociated salts, and organic compounds it contains. Pure, distilled water is a mixture of hydrogen, or hydronium (H+) and hydroxide (OH–) ions, each having an identical concentration of 10–7 mol/L.* The relative concentration of these two ions determines the water’s pH; thus, when the concentration of the ions are in equilibrium, the water has a neutral pH. When a strongly acidic or basic substance is introduced, it upsets the equilibrium and changes the characteristics of the water. Specifically, water with an excess of hydrogen ions is acidic, and water with an excess of hydroxide ions is basic. Table II, “Distribution of Carbonates Versus pH,” shows how the composition of the three forms of bicarbonate change with respect to pH.
*A mole, or mol, is 6.02 X 1023 atoms or a particular element — one mole of an element is equal to its gram molecular weight.
In mathematical terms, pH is the negative logarithm of the hydrogen ion concentration in solution (–log [H+]), most commonly expressed as a number between 1 and 14. Though it may seem backwards, the pH scale exists such that the greater the concentration of hydrogen ions present in solution (the more acidic it is), the lower the pH. pH values between 1 and 6.99 are acidic and values between 7.01 and 14 are basic; a pH of 7 is neutral. Because of the log scale, the difference between two pH values is not one, but ten. Therefore, a pH 5 solution has 10 times the hydrogen ion concentration as a pH 6 solution and a pH 5.7 solution has 3.1 times the hydrogen ions as a pH 5.2 solution.
How to measure pH. pH can be measured by an electronic pH meter or by lower-tech pH strips. A typical meter will measure pH in increments of 0.01 and display the reading in an easy-to-read liquid crystal display. pH strips are much more widely available and are in the frugal brewer’s price range. The most commonly found strips are accurate for increments of 0.2 pH units and represent pH as a color on a calibrated color scale. pH strip readings are highly subjective when used with worts greater than 15 °L (the slight color changes can also be difficult for some people to distinguish, and impossible for people who are color-blind). When dealing with dark beers, it might be advisable to fine-tune pH in either the brewing water or in the mash with a more highly accurate pH meter. Because pH is a logarithmic scale, each increment weighs heavily, and the more accurate the measurement, the better your batch-to-batch repeatability. More accurate and easier to read pH strips are available, but for those who really want to be sure, a pH meter can be a wise investment.
Hardness: The term “hardness” describes water with which it is hard to generate a lather from sodium-based soap. Hard water makes lathering difficult; soft water (or the lack of hardness) makes lathering easy. Hardness is defined technically as the total concentration of calcium and magnesium dissolved in solution. Alkali metals that are less electronegative, such as sodium and potassium, are much more stable in water (meaning they will not precipitate), have little effect on mash pH, and thus do not significantly figure into the calculation of total hardness (see Table I).
How to measure hardness. Hardness is (perhaps confusingly) listed in a water analysis report as “ppm hardness as CaCO3.” Though it may not be apparent, this reading also takes into consideration the other minerals that make up hardness; the “as CaCO3” convention simply allows for an easy comparison of hardness (represented by the calcium cation “Ca”) to alkalinity (represented by the carbonate anion “CO3”). Hardness is quantitatively measured by titration to end point with a chelating agent such as EDTA that binds magnesium and calcium ions.
Alkalinity: Alkalinity is a measure of the buffering capacity of the anions in solution, and, with pH, can complete the chemical picture of your water. A buffer prevents changes in pH by maintaining a relatively constant concentration of hydrogen and hydroxide ions within a certain pH range. Bicarbonate is a strong buffer and the major component of the alkalinity of brewing water; the relationship between alkalinity and hardness is apparent.
How alkalinity is measured. Alkalinity is quantitatively measured by titration with a strong mineral acid until the buffering capacity of the anions in solution is neutralized; that is, the buffering power of the solution has been overcome and the pH is able to change. This value is expressed, after multiplying by a conversion factor based on the sample size, as the “ppm alkalinity as CaCO3.”
Permanent versus temporary hardness: Water hardness can be either permanent (noncarbonate) or temporary (carbonate); the designations in parenthesis give you an idea on what each is based. Calcium carbonate precipitates (drops out of solution). It is tenuously soluble in water, and the solubility is entirely pH dependent (see Table II, “Distribution of Carbonation Versus pH”). Water that has a high concentration of calcium or magnesium and roughly similar levels of carbonate ions has “temporary hardness”; vigorous boiling and aeration will result in a precipitation of calcium carbonate and, to a lesser extent, magnesium carbonate (magnesium carbonate is 300 times more soluble than calcium carbonate). The water can be decanted off the precipitate, leaving the mineral salts behind. This robs the water of soluble calcium and magnesium (the components of hardness, by simplified definition), decreasing the overall hardness of the water. Water that has a high concentration of calcium and magnesium ions but a low concentration of carbonate ions has “permanent hardness”; that is, no amount of boiling and aeration will precipitate out calcium beyond the concentration of carbonate present.
Water with high levels of carbonate (temporary) hardness tends toward a pH of 8.3–8.4 because of the equilibrium between carbonates on one hand and atmospheric carbon dioxide on the other. It is not necessary to look at the individual concentrations of calcium, magnesium, and carbonate on your water analysis; checking only the values for hardness and alkalinity will give you a very good idea of the basics needed to treat your water (though it is still important to know about the concentrations of individual ions to accurately brew to style).
Working with hard water. Permanently hard water is ideal for brewing purposes and responds well to acidulation in the mash and kettle. Temporarily hard water (containing more than 50 ppm alkalinity as CaCO3) is more problematic in brewing and may need to be treated to reduce bicarbonate levels. The most common method is to vigorously boil and aerate the water as described above. Other methods of treating temporary water hardness are available. Brewers can add a portion of toasted malt or dark-roasted malt (both are naturally acidic) or lactic acid to the mash, which will help to overcome moderately alkaline waters, as will the addition of calcium and magnesium in the form of sulfate or chloride salts or dilution with distilled water (more on these techniques in later sections).
Residual alkalinity. Temporary hardness can be calculated by determining “residual alkalinity.” Bob Kolbach derived an equation to calculate residual alkalinity in 1953; it takes into account all of the minerals that contribute to changes in the pH of beer. Using this calculation to determine the course of water treatment to be conducted before dough-in can greatly improve starch conversion, lautering, and the overall quality of the beer by preventing large “swings” in pH that inevitably result from adjustment done during the mash.
Mineral Reduction Techniques
Now that the composition of normal, potable water has been explained, we can attempt to adjust its mineral content to create the right brewing environment. The three most common options available are boiling, filtration (including reverse osmosis and deionization techniques), and dilution. Almost any beer profile can be achieved even from very hard water by choosing a combination of these treatments.
Boiling: I have often described the ease of home brewing to others as follows: “If you can boil water, you can make beer.” Preboiling your brewing water is an easy water treatment step that has many beneficial effects.
Boiling reduces carbonate levels by forcing calcium and magnesium to precipitate out of solution, thereby removing most temporary hardness.* (Any pH or mineral change from a reduction in calcium can be adjusted in later stages.) It removes dissolved oxygen that might otherwise interact with mash chemistry. It also drives off chlorine that water utilities add to your water, thus, reducing the potential to create chlorophenols from reactions in the mash. Boiling also kills microbes (except spores) that might reside in the water, thereby reducing the risk of contamination. Note: If you water is treated with chloramines, most sources suggest that boiling alone will not be sufficient to reduce chlorine content, but research is pending. Carbon filtering should be able to solve this problem, but check with your filter manufacturer to be sure.
On the downside, boiling robs brewing water of valuable calcium (raising the pH and, in my experience, negatively affecting the gelatinization of starch granules) and may impose high energy costs. A brewer’s ability to treat water by preboiling is also limited by time and by the size of the boiling vessel.
*Conventional brewing wisdom suggests that aeration is necessary to provide the means for carbon dioxide to be scrubbed out. Some recent discussions in brewing circles suggests that steam from the boil alone can provide the means for CO2 scrubbing. Thus, heating to just below boiling might provide enough heat for the reaction to occur, but would require aeration.
In a home brewing setting, the advantages make a strong case for preboiling all brewing water because the associated energy cost is small and (relatively) infrequent. In fact, boiling is frequently the only treatment necessary for brewing extract-based beers. Once the water cools, it can be decanted off the top of the mineral salt precipitate and is ready for further treatment or brewing. You must make sure not to remove too much calcium carbonate from solution without replacing it in further treatments as calcium chloride (CaCl2) or calcium sulfate (CaSO4).
The disadvantages of preboiling at a commercial scale, however, are significant enough that few, if any, brewpubs or microbreweries use this method. Energy costs alone make this treatment prohibitive.
Filtration: Filtration does not remove minerals and definitely has a higher initial price tag for the hardware, but it does offer valuable benefits and enables you to treat a large volume of water for what turns out over time to be a small cost. Acceptable filtration programs can treat water for about $ 0.02/gal ($ 0.005/L) over the life of the filter!
Carbon filtration. The most common type of filter cartridge contains activated carbon (charcoal) and a tightly-spun lattice of “plastic” with a permeability of <0.5 μm. The design prevents all microbes from passing through, leaving the treated water contaminant-free. Treatment with this type of filter may remove troublesome chloramines, increasingly used to treat city water. The activated carbon absorbs most of the chlorine (which, if left in the water, can lead to the formation of chlorophenols) and organics (nitrates, nitrites) from the water. The two most common filters are made by Brita and Pur and can be found as a water pitcher (about $ 25) or a sink-top attachment ($ 45–60) in almost any home products store. For the purposes of treating large volumes of water, the sink-top filter is more appropriate because it filters the water before it leaves the tap.
Activated carbon/sterile filtration is also appropriate for commercial systems, provided contact time with the filter is long enough. This is done by matching the size of the filtration apparatus with your needed flow rate. A commercial filtration company can size filters based on need.
Reverse osmosis. Reverse osmosis (RO) involves passing water through a series of individual pressurized membrane filters that remove organics, inorganics, microbes, and some minerals. The “bulk water” machines frequently found in grocery stores often use reverse osmosis to treat the local water and usually carbon filter it as well; this water usually sells for $ 0.25–0.35/gallon. It is essentially similar to very soft spring water or distilled water.
Reverse osmosis alone does not affect the chlorine level to an appreciable extent, which means that chlorinated water must also be passed through an activated carbon filter before it will be acceptable for brewing. This method is more expensive on a small-scale setting, but is quite suitable for a large, commercial brewery.
Deionization. This method is also impractical for small-scale brewers but suitable for larger operations. Deionization is a process in which water minerals are removed by ion-exchange resins. The first step of the process removes cations (like calcium, magnesium, sodium, and iron) and exchanges them with hydrogen ions. The second step removes anions by exchanging them with hydroxide ions.
Deionization removes the entire mineral concentration of the water, but does not appreciably reduce the chlorine concentration. Deionized water, like reverse-osmosis water, must be passed through an activated carbon filter to remove chlorine. Of course, a combination of reverse osmosis and deionization techniques, followed by a pass through an activated carbon filter, will yield ultrapure water suitable for any use, especially brewing, and is commonly used in many scientific laboratories.
A word about water “softeners”: Permanently hard water leads to many problems in domestic life, not the least of which is the eventual “caking” of minerals in the water pipes, dishwasher, washing machine, and so forth. To combat these problems, many homes now have water softeners directly attached to the water supply or as part of the filter apparatus that treats the water before it enters the home’s plumbing system. Water softeners come in the form of columns impregnated with cation-exchange resins, or can be added as a handful of minerals and chelating agents (commonly referred to as “water treatment chemicals”) that help remove calcium and magnesium from solution, often replacing these minerals with sodium. The sodium content of water treated with either method is entirely too high for brewing and creates unacceptable brewing water.
Dilution: One of the easiest and most underrated methods of water treatment is a simple dilution with distilled water. The decrease in total minerals is in direct proportion to the amount of distilled water added. For example, to adjust your Dortmund-style tap water to Dublin-style water (see Table V, above), you could dilute the tap water with an equal quantity of distilled water, reducing the overall hardness from 750 ppm to 375 ppm — not a perfect match, but the hardness value will be much closer. Boil the portion of your water to be diluted and add it to the appropriate amount of distilled water. Of course, a Dortmund-to-Plzen dilution might not be worth the cost of the distilled water: It would require a 1:10 dilution, but the mineral profile comes remarkably close.
Salt of the Earth — and Water
If your local water supply is fairly soft, or your brewing water has been treated to remove or reduce undesirable minerals through one of the methods mentioned above, the water is now ready to be further adjusted by the addition of mineral salts.
The calculation and addition of brewing salts is one area in which a practical knowledge of the metric system greatly simplifies the process. Why? Because ppm, the unit of measurement for mineral content, is equal to mg/L. Five gallons of beer is equal to 18.9 L, so you already know the final volume of your wort (give or take some adjustments for make-up and sparge water). From here, it is relatively simple to determine the number of milligrams of salt necessary (if you know the percent composition of each ion in the salt) to reach the desired concentration.
Quantity: The amount of salt to add depends on the molecular weight of each salt and whether it has “water of hydration” associated with it; that is, water that was trapped within the crystalline structure of the mineral during its formation. Hydration essentially dilutes the concentration of ions per given weight of salt. Epsom salt, for example, has seven water molecules of hydration, which provide 33% of the total weight in 1 g of salt. Occasionally you will see a salt listed as anhydrous (abbreviated “anh”), which means that all water of hydration has been driven off, and the resulting 1-g mass consists of minerals only. Anhydrous salts should be kept tightly sealed as they will adsorb water from the air.
For this reason, salts should be measured by weight (grams or ounces) and not by volume (teaspoons or tablespoons) for complete accuracy. Few brewers, however, have access to accurate gram or partial-ounce scales, so I have included the approximate weight of one teaspoon of each common salt in Table IV, “Salt Ion Contribution Scale,” on page 68. For example, 1 g of a freely soluble mineral salt in 1 U.S. gallon of room-temperature water will increase the total dissolved solids by 264.2 ppm at room temperature. To know the increase of each individual component of a particular salt, you must know the relative composition of each ion as a part of the total composition. A summary of the increase (in ppm) of each mineral from the addition of 1 g of salt in a standard 5-gallon batch is also given in Table IV, on page 68.
Method: Mineral salts show different solubilities (carbonates from chalk are especially affected), so adjusting the water before dough-in will better solubilize the salts. A preferred method of adding salts is to dissolve them in 1 gallon of water, adjust the pH, and add the “salt water” to the larger volume of brewing water, also pH-adjusted. Most salts can be added directly to the brewing water this way (though some brewers prefer to add carbonates only as needed during the mash to adjust pH).
It should be noted, however, that chalk (CaCO3) is insoluble in basic or neutral pH. It can be added to the grist at dough-in, where a more acidic pH exists, or to pre-acidified water. After the first temperature rest is reached, check the pH and adjust if necessary.
Another reason to add salt to the brewing water is to remove more carbonates from temporarily hard water. If a considerable amount of carbonate remains after boiling, for example, you can add a calculated amount of another calcium-containing salt (gypsum, calcium chloride, or lime) to precipitate calcium carbonate from solution. Two words of caution: First, the amount of calcium added should not be greater (in ppm) than the water’s total alkalinity, with sufficient calcium remaining for the positive mash reactions listed in Table I on page 64 (generally at least 50 ppm of calcium should remain in water after the precipitation of the carbonate).
Second, the amount of anions added in conjunction with the calcium must be closely monitored so that unsuitable flavors are not added. You may not be able to add enough calcium without throwing off the overall balance of the water (such as too many sulfates or chloride). The best method to remove excess carbonates without affecting flavor is through the use of slaked lime [Ca(OH)2], since the anion of the salt is hydroxide. If using hydrated (or slaked) lime, monitor the pH of the liquor carefully; only a small amount is necessary to affect pH. Consequently, the use of slaked lime to reduce carbonates should be the first step in the treatment, followed by vigorous boiling and aeration, then acidification to a desired pH for the remainder of the mineral treatment schedule. Lime can be found in any garden supply shop (check the label to make sure it contains only calcium hydroxide with a trace of magnesium hydroxide). Food-grade lime can also be found as “pickling lime” where canning supplies are sold. Avoid creating “dust” when adding to water — the powder can burn the eyes, nose, and throat.
Putting It all Together—Two Sample Treatment Schedules
Given all the tools presented here, you can put together a water treatment plan that can create any type of brewing water. I offer two examples using my own water as a starting point in an attempt to match the mineral profiles of Dortmund and Plzen.
I am fortunate to have very soft water, which allows me to create the appropriate mineral profile for any beer style. My main water treatment is to raise it to a brief boil (5–10 minutes), then cool it and add mineral salts appropriate to brew a given beer.
pH, hardness, and alkalinity adjustment: Though the pH of my water is adjusted to 7.3 at the treatment plant, its alkalinity is so small (about 9.8 ppm as CaCO3) that no adjustment is theoretically required to establish a reasonable mash-in pH. Mash pH can be predicted for grists composed of pale base malts only (that is, no colored malts) by using the following simple formula:
pH = pH0 + [0.00168 X Alkalinity (ppm as CaCO3) – 0.0012 X Ca (mg/L) – 0.000982 X Mg (mg/L)].
where the residual alkalinity is calculated within the brackets and pH0 is the mash pH you obtain by mashing about a cupful of grist with cold water. pH0 usually has a value between 5.70 and 5.80. Using the values for alkalinity, calcium, and magnesium for Durham water we see that the mash pH is estimated to be 0.005 pH units less than the distilled water mash pH. Thus the mash pH with my water theoretically should fall very near the distilled water mash pH, that is, between 5.70 and 5.80, which is an acceptable room temperature mash-in pH. In reality, I must adjust the pH slightly with a small amount (usually less than 5 mL) of 88% lactic acid or dilute phosphoric acid* to reach this range. If we look at water like Munich’s, with its alkalinity of 164, for comparison we would find the dough-in pH expected to be about 0.17 pH units higher than pH0. This would be unacceptable and acidification of the water prior to mash-in would be necessary.
Softening the water reduces the alkalinity (but also the calcium), leading to a net lower mash pH. Alkalinity can be neutralized by the addition of small amounts of mineral (hydrochloric, sulfuric, phosphoric) or organic (lactic, citric, tartaric) acids, but keep in mind that colored malts contain a fair amount of acid and will thus reduce often reduce alkalinity naturally in the mash. (It works for brewing Munich Dunkles.) If 10% of the grist consists of specialty malts, the pH decreases by 0.3 units; used as 20% of the grist, specialty malts will reduce the pH by about 0.5 units. Most of my beers need initial acidification of the water by 0.5 units, and the extra pH drop from specialty malts then gets me to the desired range in the mash.
An alternative, and all-natural, way to acidify the mash is to hold a portion of the total grist at 95 °F (35 °C) for two or three days. This temperature creates the perfect environment for the growth of acidulating bacteria. You then add the acidified mash to the remainder of the grist and the brewing process continues as usual. Take care to boil the wort well to ensure total destruction of the acidifying bacteria. I usually do a mini-sparge with the acidified mash, pressure cook the “acid wort” to ensure no bacteria survive, and add the acid wort to the “regular” wort after the sparge until the desired pH is reached.
Mineral salt additions: Dortmund-style water. The water is now ready to be adjusted with the addition of mineral salts. The first step is to compare my water supply with those of the classic brewing centers of the world (Table V). Clearly, my water needs a little bit of everything to match the Dortmund profile. This is one situation in which the brewer’s goal is to add carbonate, not remove it. Since I have only sporadic access to the milligram scale, I’ve added the minerals in teaspoons. Using the values given in Table IV, for my 5-gallon batch I would use the following additions to get me relatively close:
Gypsum..................................................... 1.25 tsp
Epsom salt..................................................... 1 tsp
Calcium chloride.............................................. 1 tsp
Chalk........................................................... 3 tsp
Baking soda................................................. 1.5 tsp
*A word of caution: Brewing pH ranges are safe to work in without much consideration to personal protective equipment. However, certain corrosive mineral acids used to adjust the pH/alkalinity of the brewing water have extreme pH values and are very dangerous. Phosphoric acid, for example, has a pH of 1.52 and should be handled only by an experienced person wearing personal protective equipment such as heavy polypropylene gloves, goggles, and a protective apron. Home brewing shops frequently stock food-grade organic acids such as lactic acid (88% lactic acid has a pH of 1) for adjusting the pH of brewing water. Organic acids are less corrosive than mineral acids of a similar pH and are safer to handle. Nonetheless, thick latex gloves such as dishwashing gloves should still be worn when using any strong organic acids.
This treatment schedule results in a total hardness only 3 ppm greater than the target profile. The only critical difference between the two water profiles after treatment is alkalinity. Additional bicarbonate could not be added without negatively affecting the beer with high levels of sodium. Adding this amount of alkalinity would also require additional pH adjustment after the minerals solublize. Adding these salts to my pH-adjusted (6.0) preboiled water increased the pH to 7.86; I had to add phosphoric acid to bring the now-treated water back to pH 6.0. A difference of only 3 ppm is close enough for me, and I’m ready to brew a delicious Export.
Plzen-style water. Creating the Plzen water profile is even easier. All I have to do is dilute my water 1:1 with distilled water and pH-adjust it with acid to achieve a nearly identical profile.
Treat Your Water Right
The quality and composition of your brewing water has as much influence on the overall quality of the final product as yeast selection and fermentation temperature. As with many advanced brewing methods, the first time around the block may seem complicated. But as you get more comfortable “customizing” your water, the extra five minutes spent on the calculations becomes as routine as preparing your yeast a few days before brewing. Similarly, you will find that the final product is proof enough that the effort was worth it.
Several aspects of brewing chemistry were touched on only lightly in this article, and I invite those interested in more detail to read Brewing Lager Beer by Greg Noonan and A Textbook of Brewing by Jean DeClerck. Both sources go deeper into the topic than I am able to cover here and are invaluable for helping brewers gain a wider understanding of water chemistry. The internet also offers many sources dealing with water chemistry, though the usual “buyer beware” warnings apply — some sites have incomplete or inaccurate information. You should take it all with a grain of salt.