Buffer Me: In Depth

NOTE: This post is really science-y.  I wrote it to appease myself and any chemistry students that just don't get buffers.  If it's too much for you, check out my newest post on Dr. Amedeo called Lesula!  Why?  It describes a new monkey discovered in Africa.  It even has lots of pictures of the cute animal!                 

Okay, I’ve decided that I dislike my buffers post.  It’s too simplistic and doesn’t really explain the chemistry involved.  I’m short-changing the topic and have decided to offer a more detailed explanation.  You’ll see that my previous post is not incorrect, just incomplete.  

                Before we begin, we have to learn a few things. 

 

Set-up: In real life, acids and bases are found mixed with water.  So, if you had amazing eyes that could see molecules, you’d see that the liquid mixture called an acid in front of you is a combination of acid molecules and water molecules; a liquid mixture called a base is a combination of base molecules and water molecules.

Acids: Acids can be defined as molecules that release H⁺.  This has been stated as such in previous posts, but I wanted to reiterate it here.  

Bases: Bases can be defined as molecules that accept H⁺.  Once an acid has released an H⁺, the rest of the molecule is – by definition – a base.  It is capable of re-accepting an H⁺ to create a whole acid molecule again.  Figure 75.1 demonstrates this.  For this reason, the rest of the molecule after losing its H⁺ is referred to as a conjugate base.

Weak Acids: I showed you in Figure 75.1 that H⁺ can leave the rest of its molecule and come back together.  This only happens with weak acids.

Strong Acids: Once the H⁺ leaves the rest of the molecule, it will NEVER come back.

Water: Water is both an acid AND a base.  It’s confused like that. (Remember - its pH is neutral!)  It can release an H⁺ (H₂O minus an H⁺ equals OH^-) making it an acid.  It can also accept an H⁺ (H₂O plus an H⁺ equals H₃O⁺), thus making it a base.

The thing about H⁺: It doesn’t like to be alone.  As soon as an acid releases H⁺, it is going to be picked up by a base.  That base may be the conjugate base of your acid or it may be water.  Who picks it up is dependent upon the conditions. 

pH: This is a measure of the H⁺ concentration (how many H+s are floating around).  However, since you now know that H⁺ doesn’t stay as such, the more technical way to describe pH is the measure of the H₃O⁺ concentration.  Chemists tend to not write H₃O⁺ because it’s more tedious than H⁺.  You, dear novice, are supposed to just know what H⁺ truly means.  (There’s a lot of stuff you’re just supposed to know in science, actually).

                Please feel free to take a minute and let that information settle.  

                Ready?

The Anatomy of a Buffer

                Let’s now revisit Figure 75.3.  I said a weak acid placed in water makes a buffer.  This is true!  Pretend we dropped 50 molecules of weak acid in water.  A certain percentage of those 50 molecules are going to release their H⁺.  For the sake of this example, let’s say that 25 molecules will lose their H⁺ and 25 molecules will remain intact.  So, be a scientist for a moment.  Visualize what just happened in your mind.

                50 molecules of acid were poured into water.  25 of them remained as full molecules.  25 of them gave up their H⁺.  Water picked up those 25 H⁺ and made 25 H₃O⁺ (Figure 76.1).  Agreed?

Once the 25 molecules that are going to give up their H⁺ have done so, the mixture is said to be at equilibrium.  The right side of Figure 76.1 shows how the system has changed from when we first put the acid in solution and once it has reached equilibrium.

                Equilibrium is a cool thing.  In my Batman Likes Equilibrium post, I talked about equilibrium in terms of Batmans and Bruce Waynes.  Equilibrium is a state that all systems would like to be at.  All day long, systems are adjusting so they can achieve equilibrium.  This powerful force is what governs almost all biological processes.

                Is equilibrium always achieved when half the molecules give up their H⁺?  No.  Each acid is different.  For one acid (let’s say acetic acid), the number might be 5 out of 50.  For another acid (maybe phosphoric acid), the number might be 40 out of 50.  Chemists know these numbers: they are called equilibrium constants.  We know very well how each acid is going to behave when placed in water.  In fact, we know it so well that we can use math to predict the number of H⁺ released and can accurately tell you the pH of that mixture.

                A weak acid in water that is at equilibrium is a buffer.  The right side of Figure 76.1 is the same as the left side of Figure 75.3.  (Check it out for yourself!)  

                Excellent.  Same information that I gave you in the original buffer post, but with a bit more background to understand what will happen next.

               

                Good.  Great.  So, what happens when we add a lot of H⁺ to the buffer?  What happens when we add a lot of base to the buffer?

                Let’s do H⁺ first.

Adding Acid to a Buffer

                I told you earlier that H⁺ does not exist on its own.  When in water, the H₂O molecule will pick up the H⁺ to make H₃O⁺.  Is that the same things happens when a weak acid is also present in a buffer?

                The answer is no!  

                Acids and bases like to get together.  We all know that.  When H⁺ is around, it’s looking for a base to pick it up.  If all else fails, water will pick it up.  But, water is a last resort.  If any other base is around, it will go there first (picky, huh?).  

                So, our buffer in Figure 76.1, we have a mixture of acids and conjugate bases.  If we add in a bunch of H+, it will be picked up by the conjugate bases.  

                What matters in buffers it the ratio of acid molecules to conjugate base molecules.  As long as that ratio doesn’t change drastically, then you will maintain the same pH.  In other words, the H⁺ molecules are going to other species (conjugate bases) other than water.  When they start being picked up by water and changing the H₃O⁺ concentration, that is when a pH change will occur.

Let’s say we add in 3 H⁺ (Figure 76.2).

 

Before the addition, we have 25 acids and 25 conjugate bases.  

25 acids / 25 conjugate bases = 1.

Upon addition, 3 conjugate bases will step up to accept the newly added H⁺.

After addition, we have 28 acids and 22 conjugate bases.

28 acids / 22 conjugate bases = 1.2

The ratio hasn’t changed that much, therefore the pH hasn’t changed that much.

Adding Base to a Buffer

                When we say we are adding a base to a buffer, typically we mean we are adding OH^-.  What can OH^- do?

                The definition of a base is a species capable of accepting an H⁺.  It’s looking for one.  Where can it get one?  One choice is water (water is so versatile!), but again, water is only a last resort.  If an acid is around, it will take it from there first.

                In our buffer, if we add in some OH^-, the acid molecules will pass off their H⁺ to it to create water.

           Let’s say we add in 3 OH^- (Figure 76.3).

Before the addition, we have 25 acids and 25 conjugate bases.  

25 acids / 25 conjugate bases = 1.

Upon addition, 3 acids will step up to offer their H⁺ to the OH^-.

After addition, we have 22 acids and 28 conjugate bases.

22 acids / 28 conjugate bases = 0.78

The ratio hasn’t changed that much, therefore the pH hasn’t changed that much.

A thought on buffer capacity

                We could have just as easily added 50 molecules of H⁺ or 50 molecules of OH^- to our buffer.  You can go back and look at what that would do to the ratios.  They would change tremendously and, in turn, the H₃O⁺ concentration would change tremendously.  In order for the ratio not to change too much from initial conditions, then you need two things.  One: a large number of acids and conjugate bases in water.  Two: Addition of a much smaller number of H⁺ or OH^-.

 

                These concepts are the very heart of buffers.  I will do one more post on this topic that will be very chemistry-oriented, but will explain why a small change in ratio will not result in a pH change, but large ratio changes will.  The post will be happily short.

REFERENCES

Zumdahl, Steven S. “Chemical Principles, 4^th Edition” (2002) Houghton Mifflin Company, Boston, MA.