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pKas and Acidity.pdf

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CHEM 213
David Perrin

pKas and Acidity Part 1: Acidity is the measure of the probability or propensity of a compound to give up a proton (usually in water and extrapolated to non-aqueous solvents such as DMSO, THF, DMF. Acidity is therefore a dissociation event between an “acid”, generally defined as any proton donor, and a free proton, H + that leaves behind the “conjugate base” This is written as: AH A - + H + - Note that to balance charge, we a dd a charge to A (the conjugate base) because we started with a neutral compound AH. Historically, acids gave anions and protons. T he resulting charge on A has nothing to do with acidity – it is merely an accounting convention that must obey the rule of charge conservation: if HA is a neutral compound and the proton liberated is positive, then A must be an anion written as A -. In other words, strong acids give anions and a proton (think of HCl), but so can very weak acids (think of methanol going to methoxide and a proton) . Nevertheless, d eprotonated A could also be neutral in which case AH would have to be positive for conservation of charge. What if we had started with an amine? + N H N + H th "acid" th base he proton (posi iey cha g d) (neut l) (os i ilycha g d) An ammonium ion (which should not be confused with an amine) goes from a positively charged protonated “ acid” to a neutral amine and the free proton. We normally think qualitatively of amines as bases which in quantitative terms means that the equilibrium as shown above lies to the lef t. That also means that the “acid” in this case is not a strong acid, i.e. it is not likely to give a proton up to solution. That’s a restatement of basicity: i.e. the amine acts a base. However again, the nature of the charged species has nothing to do with the strength of the acid i.e. the extent to which the proton is liberated. Think about a protonated ether – the dialkyloxonium ion is a rather strong acid. We’d like a quantitative measure of this so that we can rank various acids (and bases), and thus we refer to pK as. pKas are values that are related to the acid dissociation equilibrium constant: specifically pKa is the negative log of the Kacid-dissoc A H A- + H + [H+][A ] 𝐾 acid-dissociation [AH] Part 2: What do Ka values mean? A high Ka value is the Equilibrium constant for the dissociation of a given AH. High Ka values mean that the ratio of H + and A is very high compared to the non- dissociated state: AH. The higher the Ka, the more likely AH will give up a proton . When the Ka is high, HA is a strong acid because it has a high propensity to give up a proton. When the Ka is low, AH is a poor acid, i.e. it has a high propensity not to give up a proton. This says nothing about the basicity of AH. AH is not being evaluated as a base, it is being considered as an acid (it could be a base in other contexts but not in this one). On the contrary, A is a base. The higher the Ka of AH is, the weaker an acid AH is , BUT - that also means that A is a stronger base. Part 3 Definition of pKa = –log(Ka) Remember your math: the log function takes big numbers and makes them smaller and are spaced closer: log(10) = 1, log(100) = 2, log(1,000,000) = 6, log(6,543,210) = 6.815 Negative logs (p values) are just a negative sign of the log. So the pKa is an inverted (negative) log-scale function: the lower the pKa number the higher the Ka value and the more the acid will dissociate. Quick exercise: pKa = -5, what is the Ka? 5 Answer: 10 (100,000) Quick exercise: Does a pKa of 16 mean we have a strong acid or a weak one? Answer: very weak. Quick exercise: Does a pKa of 16 mean we have a strong base or a weak one? Answer: irrelevant – the pKa reflects the ability of the molecule to act as an acid , it has nothing to do with basicity. This is subtle but often confuses students. If you answered “a strong base”, w hat you’re probably thinking is: the anion of an acid whose - pKa is 16 is a strong base, which is correct. Said another way- A produced from AH, in a dissociation rea-tion where the pKa is 16, means: A really wants to be protonated and therefore A really is a strong base. So sometimes we abbreviate our thoughts (sloppily) and say A has a pKa of 16 but really it’s AH that has a pKa of 16. This leads to a lot of confusion. Basicity vs. Nucleophilicity Nucleophilicity is a difficult function to predict but there are some clear pointers: 1) First rule of thumb: nucleophiles have lone pairs of electrons – if no lone pair is possible or conceivably available, then the compound cannot act as a nucleophile. 2) For the same atom: an anion of a given element is al ways more nucleophilic than its protonated state – consider an alkoxide vs. an alcohol – which is more nucleophilic? (Answer the alkoxide). This trend is usually the case even when comparing two oxygen nucleophiles but the interpretation is more subtle. For example take a carboxylate vs. an alcohol. They’re both very different but under certain conditions e.g. at pH7, the carboxylate is an anion while the alcohol is protonated and neutral , therefore the carboxylate is the better nucleophile. Carbon anions are far more nucleophilic than neutral carbon atoms (which usually have 4 bonds to different atoms of which at least one is a proton – such a carbon is not going to be a nucleophile based on rule #1). 3) Comparing two anions: the conjugate acid wit h the higher pKa is more likely to be more nucleophilic. For example, compare carboxylate anion vs. an alkoxide anion – it turns out that the alkoxide is more nucleophilic. Another argument is that the negative charge on the carboxylate is resonance stabilized and more delocalized hence less nucleophilic. But another way to look at this is that the lower the pKa of the AH in question, the more stable the anion is and therefore the less reactive it will be. But this becomes more nuanced by steric considerations. For example, the pKa of tert -butanol has a pKa of 19- 20 so tert -butoxide is a very strong base but it is also very sterically hindered. Phenol has a pKa of 10 but phenoxide is a more potent nucleophile than tert - butoxide. Hence Sterics can often dominate in predicting nucleophilicity. 3) Comparing different anions across the periodic stable: the atom on the l eft is usually more nucleophilic: a carbon anion is usually more reactive than an amine anion which is more reactive than an oxyanion which is more reactive than a halide. But again this can be inverted depending on solvent conditions or because of steric arguments. 4) A neutral atom is always more nucleophilic than a protonated cationic state: example an amine is a good nucleophile but an ammonium is not. An alcohol is a poor nucleophile but an alkoxonium ion is an impossibly poor nucleophile. pKas to be memorized. charge pKa (water) Strong acids + - HCl H+ + Cl- neg. -8 HBr H + Br neg. -9 Protonated carbonyls and alcohols R2C=OH +
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