Mixing Coffee and Milk: Ph and Buffers
Date: 07/10/2003 at 19:09:51 From: Libby Subject: Ph level Can you tell me if I did this right? The question is: If I mix coffee (pH 5) and milk (pH 6.9) (50%/50%), what will be the pH of the coffee/milk mixture? I used the formula pH = -log [h+] ph = -log [.5(10^-5) + .5(10^-6.9)] -pH = log [.5(10^-5) + 10^-6.9)] -pH = log 5.0629^-6 -pH = -5.295 pH = approx. 5.3
Date: 07/10/2003 at 20:10:46 From: Doctor Achilles Subject: Re: Ph level Hi Libby, Thanks for writing to Dr. Math. Given the information you have available, that is the best approximation. However, this method makes two assumptions: 1) That you are mixing equal parts coffee and milk. If, for example, you were to mix 3 parts coffee to 1 part milk, then you would have to weight your average appropriately. 2) That neither the coffee nor the milk has any buffers in it. A buffer is something that resists changes in pH. Here are the basics of how a buffer works: pH is a measure of the concentration of free H+ ions in solution. An acid is a chemical that releases H+ ions and a base is a chemical that traps H+ ions. The simplest type of acid is a "strong acid." HCl (hydrochloric acid) is a typical example of a strong acid. In a strong acid, every hydrogen is immediately released as an H+ ion when you put it in "aqueous" (mostly water) solution. So if you put HCl in aqueous solution, every HCl molecule will dissociate (separate) into an H+ and a Cl-. So if you add 100 trillion HCl molecules, you will effectively have added 100 trillion H+ ions. There are also "strong bases." NaOH (sodium hydroxide) is a typical strong base. For a strong base, every molecule of base you add will take a proton out of the solution. What happens in the case of NaOH is actually a 2-step process. First, the molecule dissociates into Na+ and OH-. Then the OH- finds an H+ and they get together to make HOH, which is more commonly known as H2O, or water. This effectively removes one H+ from the solution. Now, there are also "weak acids." In a weak acid, only some fraction of the molecules will add an H+ to the solution. A good example of a weak acid is phosphate (H3O4P). The difficult part about weak acids is that what fraction of the molecules actually *do* add an H+ to the solution depends on the pH of that solution. If the pH is low (therefore a high concentration of H+ ions), then a small fraction of weak acid molecules will release an H+ ion. If the pH is high (a low concentration of H+ ions), then a large fraction of weak acid molecules will release an H+ ion. What that means is that weak acids are very weak when you put them in something that is already acidic, and they are pretty strong when you put them in something that is basic. If you turn that logic around, if you have a weak acid that is at some pH, and you try to add a base to increase the pH, the weak acid will just respond by releasing more H+ ions, and thus keep the pH relatively constant. Similarly, if you try to add acid to decrease the pH, the weak acid will just take back some of the extra H+ ions and thus keep the pH relatively constant. So, weak acids can act as bases. In fact, there isn't really a distinction between a weak acid and a weak base; they are both called "buffers." If you add H+ ions to a buffer, then it will respond by taking some of them up, and if you remove H+ ions, it will respond by releasing them. Buffers aren't perfect, of course, and you can "saturate" a buffer by forcing it to give up all its hydrogens or take up all the H+ ions it can hold. And even a not-quite-saturated buffer can exist over a fairly wide range of pH values. Buffers are essential for survival. Your body has to maintain all its fluids at a constant pH; even one or two tenths of a pH unit of change can be *extremely* damaging. So all of your fluids have a mixture of several different types of buffers. So what does this have to do with milk and coffee? The analysis you used works only if all the acids and bases in the milk and coffee are "strong." However, both milk and coffee have buffers. Milk has more. My guess is that this will cause the pH of the mixture to tend toward the pH of the milk. How much depends on what buffers are in each and what the dynamic ranges of those buffers are. That I can't tell you off hand. The way I would answer the question is to measure the pH of the mixture. Your other option is to analyze the milk and coffee to find the concentrations of all the buffers and then look up their dynamic ranges and relative buffering capabilities, which is a very difficult task. Hope this helps. If you have other questions or you'd like to talk about this some more, please write back. - Doctor Achilles, The Math Forum http://mathforum.org/dr.math/
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