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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/ 
Associated Topics:
College Physics
High School Physics/Chemistry

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