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From MyMCAT

Contents 1 Introduction 2 Kw 3 The pH Scale 4 pOH 5 pKa and pKb 6 pH and Temperature

Introduction

While recognizing acids and bases is a trivial process, identifying which of a group of acids is strongest, or the effects of dilution with water or even neutralization with a base, is not as simple. To solve these problems one must know a bit more about acids and bases.

K_w

If we return to the idea of equilibriums and how acids dissociate to form an equilibrium of hydroniu ions and bases dissociate to form hydroxide ions, what happens when we look at water on its own? Pure water undergoes significant hydrogen bonding, and often these polar molecules are strong enough to pull their neighbours apart into ions, that is to say,

or,

While there is only a very small fraction of dissociated ions, it is still an equilibrium nonetheless, and we can determine the K_eq for it, which we call the dissociation constant of water, or K_w. We can also measure this value analytically to determine it.

(Remember that there the dissociation expression should include the reactants on the bottom of the fraction, but since the only reactant is H₂O, we do not include it!)

Thus, in pure water, the [H⁺] is 1x10^-7 and [OH^-] is 1x10^-7 (since there is a one to one correspondence and the product is 1x10^-14. That being said, to avoid working with awkward powers and concentrations, the pH scale was created.

The pH Scale

In keeping consistent with the dissociation of pure water, a log of concentration scale is used where 7 (ie -log(10^-7) ) is neutral. Thus the pH of any solution is -log( [H⁺] ). The log represents getting the power and the negative is used to make the values positive since the values are in fact all very small.

Thus on this scale, 0 - 7 represent acidic conditions, 7 neutral, and 7 - 14 basic conditions, and all correlate to a specific concentration of hydronium ions. Acids have more hydronium than pure water and bases have less.

pOH

The exact same scale can be used to represent the hydroxide ion concentrations. In this case however the reciprocal effect is measured. A pOH of 1 would mean that it is very rich in OH^- ions and thus very basic (NOT acidic!).

The two scales can be easily converted between each other as,

1. If 0.003 moles of HBr is dissolved in 2 liters of water, what is the resulting pH?

	2.8
	4.8
	8.8
	10.8
→	To get the pH we must first find the hydronium concentration. HBr is a strong acid, this 0.003 moles of HBr will directly dissociate into 0.003 moles H+ and 0.003 moles Br-. 0.003moles H+ in 2 liters H2O implies a concentration of 0.003/2 or 0.0015. Thus the pH is -log( [0.0015] ) = 2.8. If we were unsure as to how to do this, we could at least tell that it could not be basic, thus we can narrow it down to 50%.

2. What is the pOH of a solution who's hydronium ion concentration is 2.3x10^-4?

	2.64
	3.64
	10.36
	11.36
→	We are given [H+], thus we can solve for the pH easily. pH = -log([H+]), while not entirely that straight forward, we will atleast know it is between 3 and 4. More specifically, we can tell it is closer to 4 than it is 3, because 2.3 is on the smaller side of the possible coefficients from 1-10. Thus if we assumed the pH were 3.5, we could get the pOH by subtracting that from 14. 14 - 3.5 = 10.5.

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pKa and pKb

the same idea of -log() can be used not only on concentrations, but also on dissociation constants. The pKa of an acid dissociation, is -log( K_a ) and the pKb of a base dissociation is -log( K_b ). The values that are obtained are not however represented on any scale from 1-14, they are purely used for comparing acid/base strengths.

Because a negative log was taken, smaller values of pKa actually represent a larger Ka, or more dissociation of hydronium ions and a more acidic/ low pH solution. The same idea goes for bases, lower pKb values represent more basic solutions.

1. Given their pK_a values below, which is the strongest acid?

	4.35
	2.36
	1.35
	1.1
→	The smaller the pKa, the stronger the acid. This is because a small pKa reflects a large Ka, which in turn represents a high dissociation constant and thus a large concentration of hydronium ions. Therefore, 1.1 is really 10-1.1, which will be the largest of the possible answers, and thus represent the strongest acid in the set.

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pH and Temperature

Acid/Base dissociation, like solubitlity, is dependent on temperature. Higher temperatures imply higher dissociation constants, thus K_a and K_b values are temperature dependent. Values given are typically stated at 25C, however one should know the theory behind acidity and its relation to temperature.

If one looks back at the equilibrium,

then it is clear that the dissociation constant obtained, K_w = 1x10^-14 is entirely dependent on temperature, as are the concentrations of H⁺ and OH^- at this temperature. So, when temperature increases above 25C dissociation increases and we can no longer use a pH scale based on 14. If dissociation increases, K_w will become larger (as well as the concentrations) and so it may change to something like 6 being neutral and going from 1 to 12, if K_w just so happened to become 1x10^-12.

Do not be confused by this however, just because the pH says 6, it does not mean it has turned acidic, 6 is simply the new neutral position as the scale has become smaller.

1. If at 45 degrees Celsius, the K_w of water is 1x10^-18, which of the following pH's would represent a basic solution?

	4
	6
	8
	10
→	If the dissociation of pure water is 1x1018, then the pH scale would go from 1 - 18, and 9 would be neutral because [H+] = [OH-] = 1x10-9. Thus anything below 9 would be acidic, 9 would be neutral, and everything larger would be basic. The MCAT will not test anything beyond this basic understanding of the relationship between changing pH scale and temperature as it is out of scope.

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