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Acids and Bases
Written by Tim Sheppard MBBS BSc. Last updated 9/11/10

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What is an acid?

One of the most commonly accepted definitions of an acid, the Brønsted-Lowry definition, is that of a proton donor or a hydrogen ion donor. This could be in a number of situations, but it is commonly considered that an acid will dissociate in water, splitting up into two parts and thereby releasing hydrogen ions into solution. This could be represented by the picture shown, where the red blob represents the acid, and the grey bubble represents the hydrogen atom.

In solution, then, an acid will split up into a hydrogen ion and its conjugate base. The reaction is reversible (i.e. the hydrogen ion and conjugate can combine to reform the acid), and it is from the conjugate base's ability to accept the hydrogen ion and reform the original acid that it obtains its name. The acid and conjugate base are in equilibrium; a strong acid will completely dissociate, with none of the original left in solution, but a weak acid will have some of the original acid, and some hydrogen ions.


What is a base?

One of the most commonly accepted definitions of a base, the Bronsted-Lowry definition, is that of a proton acceptor or a hydrogen ion acceptor. This could be in a number of situations, but it is commonly considered that in water, a base will accept the hydrogen ions produced by the dissociation of water molecules themselves. This can be shown clearly in the image shown, where the blue blob represents the base and the grey bubble is a hydrogen atom from the water.

In solution, then, a base will accept a hydrogen ion to become its conjugate acid. The reaction is reversible (i.e. the hydrogen ion and conjugate acid can dissociate to reform the base), and it is from the conjugate acid's ability to donate the hydrogen ion and reform the original base that it obtains its name. The base and conjugate acid are in equilibrium; the molecules of a strong base will almost all accept protons, with virtually none of the original substance left in solution, but a weak base will have some of the original base, and some of its conjugate acid.


What is pH?

pH is defined simply as the negative logarithm, to the base 10, of the concentration of hydrogen ions in solution. This gives an indication of how acidic the solution is by expressing in simple terms how many hydrogen ions exist in solution.

A pH value will usually be given on a scale of 1 to 14, although it is clearly possible for other values to be taken. Since the value is obtained from the negative logarithm of the hydrogen ion concentration, a value of 1 (or even 0) expresses a very large concentration of hydrogen ions, yet is able to do so in only a couple of digits. It has been calculated that water will spontaneously dissociate a small amount to produce a concentration of hydrogen ions equivalent to a pH of 7, giving rise to this value adopting the property of neutral - neither acidic, nor basic. Since a base will take hydrogen ions from a solution, the concentration of hydrogen ions will decrease further, depending upon the strength of the base. It is commonly considered that a strong base (for instance, sodium hydroxide) will have a pH of 14.


What is a conjugate acid-base pair?

Put most simply, a conjugate acid-base pair is made up of two almost identifcal molecules, the only difference being that one of them has an extra hydrogen ion (or ions). The one with the hydrogen ion is called the acid because it can donate the hydrogen, and the one without is called its conjugate base.

When an acid comes apart or dissociates, it forms a hydrogen ion and its conjugate base. The conjugate acid-base pair for this acid is this acid and its conjugate base. The two are in equilibrium, and through acceptance or donation of a hydrogen ion, one species will become the other. Similarly, when a base is in solution, it forms its conjugate acid with a hydrogen from the water molecules. The conjugate acid-base pair for this base is the base and its conjugate acid. The two are in equilibrium, and through acceptance or donation of a hydrogen ion, one species will become the other. This gives the pair an amazing buffering capacity; if hydrogen ions are added to the solution, the base or conjugate base can react with them to produce the conjugate acid or acid respectively, maintaining a constant pH. The opposite is true of removal of hydrogen ions.

In this way, a buffer can be produced that utilises the equilibria of conjugate acid-base pairs to maintain the pH of a particular system. It might be helpful to consider the conjugate acid-base pair passing hydrogen ions between each other. If a molecule of the acid passes its hydrogen ion to a molecule of its conjugate base in the same system, the conjugate base, by definition, will become the acid. The acid, having lost its hydrogen ion, will become its conjugate base. A similar set up could be considered in relation to a base and its conjugate acid. Although in practice it is not simply a case of passing ions between each other, this gives a good idea of the definitions of the conjugate acid-base pairs, and how each species can become its opposite in the pair.


What is Ka?

Ka is an equilibrium constant which applies to acids specifically - the equilibrium constant is Kc, and therefore Ka is just a constant that applies specifically to the dissociation of the acid. Let's take an example:

HA(aq) ↔ H+(aq) + A-(aq)

HA is the general formula for an acid - it shows the hydrogen ion (represented by H) and the conjugate base (i.e. the rest of the molecule, A). HA might be hydrochloric acid, where H is still the hydrogen ion, and A is the chloride.

Because this is an equilibrium, we can apply the equilibrium constant to it - so the product of the concentrations of H+ and A-, divided by the concentration of HA. Notice that because only one molecule is reacting/produced, each concentration is 'to the power of 1', which is negligible. This gives us an idea of how much of the original acid has dissociated - so if there is lots of the original acid left (not much has dissociated) then Ka will be small. Ka can give us an idea of how strong an acid is, because if it is small, it means the acid will not dissociate very well. If an acid is strong, then it will completely dissociated, and the value of Ka will be high (we don't usually refer to Ka if an acid is strong, because we assume it just completely dissociates).

Put simply, Ka is just the equilibrium constant for the dissociation of an acid. However, it provides a very useful measure of the strength of an acid, and is therefore commonly used.


What is pKa?

pKa is defined simply as the negative logarithm, to the base 10, of the acid dissociation constant, Ka. This gives an indication of how strong an acid is by expressing in simple terms how easily it dissociates.

The reason that the concentration of hydrogen ions is expressed as pH is that you often get really small numbers, which would be frustrating to write; taking the negative logarithm simplifies this - in the case of pH, normally to a number between 1 and 14. Similarly with pKa, giving the constant as a negative logarithm will make it simpler, because sometimes the Ka value can be very small too. Where a relatively small Ka meant a weaker acid because less was dissociating, a relatively small pKa value indicates a stronger acid, because taking the negative logarithm of a smaller number will make it larger than the negative logarithm of a larger number.


What is the Henderson-Hasselbalch equation?

Sometimes we may know certain details, but not others. Often we might want to know the pH of a solution, but we can't measure the concentration of hydrogen ions. In these circumstances, we make use of what we do know, and by rearranging the equation for Ka, we can put these values into an equation and find out the pH. This equation is called the Henderson-Hasselbalch equation, after the people that came up with it.

Take the original Ka equation. If we multiply both sides by the concentration of acid (HA) then this cancels out on the right hand side (because the right hand side both multiplies and divides by the same thing, HA). Then divide both sides by the concentration of conjugate base (A-), and this cancels out on the right as well.

Now take the negative logarithm (to the base 10) of both sides. If you don't understand logarithms, ignore this bit - just accept it has to be done! On the left hand side, this can be expanded out because multiplying the contents of a logarithm is the same as adding the individual logs (i.e. log10(AxB) is the same as log10(A) plus log10(B))

Because 'p' of something invariably means 'negative logarithm to the base 10' of something (e.g. pH is -log10[H+]), we can make things even simpler. The right hand side is simply pH, and -log10Ka on the left hand side is simply pKa which leaves us with negative logarithm (to the base 10) of [HA] over [A-]. Using the laws of logarithms again, log(A/B) = log(A) - log(B). So:

-log(A/B) = -(log(A) - log(B))
-(log(A) - log(B)) = -log(A) + log(B)
-log(A) + log(B) = log(B) - log(A)
log(B) - log(A) = log(B/A)
-log(A/B) = log(B/A)

So we can say that -log10([HA]/[A-]) = +log10([A-]/[H+]). Remember that HA is the weak acid, and A- is the conjugate base. We therefore have a general equation to work out the pH depending on certain other factors - and since the pKa will be the same for a particular acid (for a given temperature), we can work out the pH with just a couple of simple measurements.

Ultimately knowing how to calculate the Henderson-Hasselbalch equation is not the most important thing in the world, but knowing the final equation can be very helpful. The animation shows how it is derived from the acid dissociation constant (Ka), but that's just to show that it isn't just some random equation plucked out of no-where - it makes logical sense!


What is Kw?

There's not a huge amount that can be said about this. Once again it's an equilibrium constant derived from Kc, and this time it's using the following equilibrium:

H20(l) ↔ H+(aq) + OH-(aq)

Because the concentration of water (H2O) is almost unchanged (i.e. very little of it dissociates), we multiply both sides by the concentration of water to cancel it out. This gives us simply the product of the two dissociated species - i.e. the H+ and the OH-.

More commonly known as the ionic product of water (because it involves the product of the concentrations of the ions in water: H and OH-), Kw is constant at room temperature, and provides a value of great importance: 1x1014.

The reason this value is so important is that we can work out the pH of water from it. We know that [H ] and [OH-] have to be the same, because they are obtained from the same thing - you get one molecule of each for every molecule of water that dissociates. If [H ] x [OH-] = 1x10-14, then [H ] and [OH-] are both equal to 1x107. If we know the concentration of hydrogen ions, we can work out the pH, and indeed this is what we do - giving the resulting pH of 7, neutral.


What is a buffer?

A buffer is a substance that will oppose small changes in pH. An acidic buffer is a weak acid, and its salt formed with a strong base. A basic buffer is a weak base, and its salt formed with a strong acid. In either case, the buffer will form a large resevoir of conjugate acid-base pairs (the weak acid and its strong conjugate base, or the weak base and its strong conjugate acid) which are in equilibrium - i.e. the production of one species is as rapid as its degradation. If conditions become a little more acidic, the equilibrium will shift to oppose that change, by producing a little more of the basic species and accepting the hydrogen atoms. If conditions become a little more basic, the equilibrium will shift to oppose that change, by producing a little more of the acidic species and donating hydrogen atoms.


Further Reading