Acids and Bases: Brønsted–Lowry Theory (an interactive educational thread)

I’m starting this thread in ‘interactive seminar form’ for the benefit of beginners and burgeoning chemists who haven’t had the benefit of a higher education in science or chemistry and want to develop a better understanding of what makes acids and bases tick.

Being a normal thread anyone is welcome (and it’s FREE! ) to contribute, correct me or ask questions. Of more knowledgeable contributors I ask only to take one thing into account: this thread is not about cutting edge chemical theory, rather because of its stated intent shouldn’t really exceed A-level/1st year Uni levels of sophistication. If interest warrants it, we can always build up.

To improve searchability frequent thread navigation posts will be included.
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Upcoming instalments are:

1. Water as an acid and a base
2. Weak and strong acids and bases: Acid/base equilibrium constants
3. Essential pH calculations

[Edited on 20-1-2016 by blogfast25]

Water as an acid and a base:

An acid can be most simply defined as a proton donor, a base as a proton receptor. For a generic acid HA and base B, the proton (H⁺ exchange can be summarised as:

$$\mathrm{HA} + \mathrm{B} \leftrightarrow \mathrm{BH^+} + \mathrm{A^-}$$

Water, the most used solvent, is itself both an acid (albeit a very weak one) and a base because of the auto-dissociation reaction:

$$2\mathrm{H_2O} \leftrightarrow \mathrm{H_3O^+} +\mathrm{OH^-}$$

The formed cation is called the oxonium ion (in some texts: ‘hydronium ion’) and the anion the hydroxide ion.

As we’ll see later on, the auto-dissociation equilibrium leans far to the left and the concentrations of oxonium and hydroxide ions in pure, neutral water are very, very small. But the fact that water can act as proton receptor or proton donor is the basis of Brønsted–Lowry theory.

When an acid dissolves in water we can now re-write our first reaction equation as follows:

$$\mathrm{HA} + \mathrm{H_2O} \leftrightarrow \mathrm{H_3O^+} + \mathrm{A^-}$$

And when a base dissolves in water we can now re-write our first reaction equation as follows:

$$\mathrm{B} + \mathrm{H_2O} \leftrightarrow \mathrm{BH^+} + \mathrm{OH^-}$$

From here we can understand that in Brønsted–Lowry theory acidity/alkalinity is a concept that is relative to the acidity/alkalinity of water! An acid is a proton donor that is stronger than water and a base is a proton receptor that is stronger than water.
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Notes:

1. Acid base reactions can also take place in other, protonatable solvents and are the subject of other theories. We’ll only concern ourselves with non-aqueous acid base reactions at the end of this seminar.
2. Further reading for the curious: why water forms oxonium ions (scroll to below the fold).

Weak and strong acids and bases: Acid/base equilibrium constants

Quote: Originally posted by Oscilllator

Wonderful use of formatting there Blogfast. A Slightly off-topic question: You mentioned Chemical activities should be used, but I'm not quite sure what they are. The wiki page mostly just says that it's an "effective concentration", but I don't really understand that. What exactly is a chemical activity, and why is it that they are measured using vapor pressures?

Essential pH calculations:

Quote: Originally posted by ELRIC

Sorry. It seems to have been fixed after I made that post

Quote: Originally posted by j_sum1

Nice work Blogfast. Were you going to discuss what happens with a diprotic acid?

Conjugated acids, bases and buffers:

Consider again a generic weak acid and its de-protonation:

$$\mathrm{HA} + \mathrm{H_2O} \leftrightarrow \mathrm{H_3O^+} + \mathrm{A^-}$$

$$K_A=\frac{ C_HC_A}{C_{HA}}$$
And:

$$K_W=C_HC_{OH}=10^{-14}$$

It can be shown and is well known from empirical evidence that the:

$$A^-$$

... ion is itself a weak base. Consider for example how the alkali metal acetates, carbonates, and other alkali metal salts of weak acids form solutions that are slightly alkaline. This is due to the following protonation reaction:

$$A^- + H_2O \leftrightarrow HA + OH^-$$

An equilibrium equation can be defined for this equilibrium:

$$K_B^*=\frac{C_{HA}C_{OH}}{C_A}$$

Now if we multiply both equilibrium constants we get:

$$K_AK_B^*=C_HC_{OH}=K_W$$

And:

$$pK_A+pK_B^*=pK_W=14$$

A^- is called the conjugated base of HA (the asterisk points to the conjugation).

Entirely analogously to the above, for a weak base:

$$B+H_2O \leftrightarrow BH^+ + OH^-$$

... the protonated form BH⁺ is the conjugated acid of B. An example are the ammonium salts (of strong acids) which react slightly acidic in watery solution.

Here we can write:

$$K_BK_A^*=C_HC_{OH}=K_W$$

And:

$$pK_B+pK_A^*=pK_W=14$$

Conclusions: the conjugated base of a weak acid is a weak base. The conjugated acid of a weak base is a weak acid. The de-protonated strong acids and protonated strong bases on the other hand react neutrally.

The sum of the p-values of an acid (or base) and its conjugated base (or acid) always equals 14.

Buffer solutions (principle only):

Consider again the equilibrium constant for a weak acid:
$$K_A=\frac{ C_HC_A}{C_{HA}}$$
We can rework this as follows:

$$C_H=K_A\frac{C_{HA}}{C_A}$$

Assume we now prepare a solution that contains both the free acid HA at concentration C and its conjugated base A^- (e.g. delivered by a Na salt) at concentration C^*, then we can write:
$$C_H=K_A\frac{C}{C^*}$$

And:

$$pH=pK_A-\log\big(\frac{C}{C^*}\big)$$

These are known as the buffer equations.

For:

$$\frac{C}{C^*}=1$$

Then:

$$pH_{buffer}=pK_A$$

Buffers are also frequently prepared from a weak acid and a weak base (not conjugated to the acid).

Buffer solutions have the advantage of having a ‘robust’ pH: pH is not significantly affected by the addition of small amounts of acid or base. The target pH of the buffer can be manipulated by means of the C/C^* acid to conjugated base ratio.
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Exercise:

The pK_B of ammonia (NH₃ is 4.75. Estimate the pH of a 0.025 M solution of ammonium sulphate (assume the sulphate ion to be neutral).

Coming up: Multi-protic acids and mixtures of acids

[Edited on 21-1-2016 by blogfast25]

Multi-protic acids and mixtures of acids

wonderful work up of the topic bf

3 thoughts:
How about some sample problems at various levels from noob to hard core? (I do see a few )
A really basic work up might be less intimidating for the complete novice (eg a simple case study of HCl showing pH change as it is diluted etc)
Someone may be able to contribute a pKa table for some acids?

this will be great for the tutorial subforum discussed in another thread. thx for getting us started

This is a very nice treatment of an important subject. Now maybe we can understand more of what Nicodem is about when he talks pKa's.

Blogfast, you can get paid for this kind of thing you know!

@diddi:

By all means suggest a 'hardcore' problem and I'll cut my teeth on it.
A table of pK value of common acids and bases was linked to higher up.

@Magpie:

'Real life' teaching, moi? It's my crowd-control powers that would let me down! (Kermit gets it in the chops!)

Thanks both of you for the encouragement!

Acidometry and pH indicators

(Cautionary note: this is a fairly basic theoretical treatment of acidometry, not a treatise on the merits of practical titration, down to which mag stirrer bar to use for which titration!)

A strong base like NaOH completely dissociates in water:

$$NaOH(s) \to Na^+(aq) + OH^-(aq)$$

A strong acid completely deprotonates in water:

$$HA + H_2O \to H_3O^+ + A^-$$

By mixing such solutions, we get neutralisation:

$$H_3O^+ + OH^- \to 2H_2O$$

During the addition of the base to the acid the pH of the solution changes strongly.

If we assume the concentrations of acid and base to be:

$$C_a, C_b$$

... and we start from a volume V_a of acid then if we add a volume V_b of acid, the resulting oxonium concentration can be calculated from:

$$C_H \approx 10^{-7}+\frac{C_aV_a-C_bV_b}{V_a+V_b}$$
$$pH=-\log C_H$$

At:

$$C_aV_a=C_bV_b$$

Then:

$$C_H=10^{-7}, pH=7$$

And before any addition of NaOH solution:

$$C_H=C_a, pH=-\log C_a$$

By slow addition of an alkaline solution to an acid solution and monitoring the pH we now have a means of measuring the concentration of the acid from:

$$C_a =C_b\frac{V_b}{ V_a }$$

This is the basis of acidometry, aka acid base titration.

A typical pH curve for the addition of a strong alkali (like NaOH) to a strong acid is shown below.



Note that the pH doesn't change very much until you get close to the equivalence point. Then it surges upwards very steeply. This steep surge is easy to detect.

Titration of a weak acid with a strong alkali

A typical pH curve for the addition of a strong alkali (like NaOH) to a weak acid (e.g. ethanoic acid) is shown below.



The start of the graph shows a relatively rapid rise in pH but this slows down as a buffer solution containing ethanoic acid and sodium ethanoate is produced. Beyond the equivalence point (when the sodium hydroxide is in excess) the curve is just the same as that end of the strong acid - NaOH graph.

pH of equivalence points

A titration is a neutralisation with the formation of a salt solution:

$$Na^+(aq)+OH^-(aq) + HA(aq) \to Na^+(aq)+A^-(aq)+ H_2O(l)$$

In this post it was shown it was shown that the resulting anion A^-, or conjugated base, is a weak base.

This means that unlike the titration of a strong acid with a strong base, the equivalence point for a titration of a weak acid with a strong base is not located at pH=7 but somewhat higher (as the relevant graph also shows).

At the equivalence point the concentration of A^- is:

$$C_A=\frac{C_a}{V_A+V_B}$$

Using the equation for pH the pH at equivalence point can then be estimated.

Analogously, the pH of the equivalence point will be lower than 7 when titrating a weak base with strong acid.

The position (pH) of the equivalence is important for the selection of the correct indicator.
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Titration of sodium carbonate:

The titration of sodium carbonate with a strong acid (usually HCl) is an important one because sodium carbonate can be used as a Primary Standard, allowing to standardise the concentration of acid titrant solutions. It’s also a bivalent base.

Sodium carbonate dissociates completely when dissolved in water:

$$Na_2CO_3(s) \to 2Na^+(aq) + CO_3^{2-}(aq)$$

The carbonate ion is a bivalent base, with equilibrium constants:

$$pK_{B1}=7.7, pK_{B2}=10.4$$

Two neutralisation reactions take place during titration, perfectly separated from each other due to the difference in pK_B:

$$ CO_3^{2-}+H_3O^+ \to HCO_3^- + H_2O$$

$$HCO_3^- + H_3O^+ \to CO_2 + 2H_2O$$
A typical titration curve shows the two distinct equivalence points:


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pH indicators and equivalence point detection:

Although potentiometric end-point determination has been around for decades, colourful pH indicators continue to be widely used in acidometry.

pH indicators are weak acids that show different colours depending on whether to molecule is protonated or not. I'll represent the protonated and deprotonated forms resp. as:

$$\mathrm{HIn},\:\mathrm{In^-}$$

In water, the indicator deprotonates weakly according:

$$\mathrm{HIn}+\:\mathrm{H_2O} \leftrightarrow \mathrm{In^-}+ \:\mathrm{H_3O^+}$$

and:

$$K_{HIn}=\frac{C_{H3O}C_{In}}{C_{HIn}}$$

Bear in mind that K_HIn is really small, typically in the range of 10^-3 to 10^-11 or so.

We can rearrange the last expression slightly as follows:

$$\frac{K_{HIn}}{C_{H3O}}=\frac{C_{In}}{C_{HIn}}$$

Also remember that:

$$pH=-\log{C_{H3O}}$$

And:

$$pK_{HIn}=-\log{K_{HIn}}$$

We can now see that if:
$$pH=pK_{HIn}$$
... the ratio of protonated to deprotonated indicator equals 1! So if both species have different colours, at that pH the colour will be in between the colours of these species.

But if:

$$pH < pK_{HIn}$$

... then the protonated species will dominate and the colour will be that of HIn.

And if:

$$pH>pK_{HIn}$$

... then the deprotonated species will dominate and the colour will be that of In-.

In summary we can say that:

$$pH=pK_{HIn}$$

... is the turning point of the indicator.

If the turning point of the indicator more or less coincides with the pH of the equivalence point:

$$pH_{EP} \approx pK_{HIn}$$

... then the equivalence point will be detected accurately.
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Coming up: Amphoterism

[Edited on 23-1-2016 by blogfast25]

Quote: Originally posted by Etaoin Shrdlu

I always found the latter easier to read.

Amphoterism

Species that can behave as acids or bases, usually metal hydroxides, depending on solution oxonium concentration (pH), are called amphoterics.

Take a generic amphoteric metal hydroxide, usually insoluble in neutral conditions:

$$M(OH)_n(s)$$
In the presence of oxonium ions a series of protonations can take place:
$$M(OH)_n(s)+H_3O^+(aq) \leftrightarrow [M(OH)_{n-1}H_2O]^+(aq)+H_2O(l)$$
$$[M(OH)_{n-1}H_2O]^+(aq)+H_3O^+(aq) \leftrightarrow [M(OH)_{n-2}(H_2O)_2]^{2+}(aq)+H_2O(l)$$
Up to:
$$[M(H_2O)_m]^{n+}(aq)$$
Note that n and m are not necessarily equal.

So this leads to the solvation of the hydrated M cation.

But in the presence of hydroxide ions the amphoteric species can also form anionic hydroxide complexes :
$$M(OH)_n(s)+OH^-(aq) \leftrightarrow [M(OH)_{n+1}]^-(aq)$$

$$[M(OH)_{n+1}]^-(aq)+OH^-(aq) \leftrightarrow [M(OH)_{n+2}]^{2-}(aq)$$
Up to:
$$[M(OH)_{m}]^{(m-n)-}(aq)$$

Note that n and m are not equal.

So this leads to the solvation of M to a hydroxy-complexed anion.

This also explains why the hydrated M cation of an amphoteric reacts slightly acidic:
$$[M(H_2O)_n]^{n+}(aq)+H_2O(aq) \leftrightarrow [M(H_2O)_{n-1}(OH)]^{(n-1)+}(aq)+H_3O^+(aq)$$

Some well known amphoteric metal cations include:
$$Al^{3+},Cr^{3+},Be^{2+},Sn^{2+},Sn^{4+},Pb^{2+},Pb^{4+},Zn^{2+},Cu^{2+},Sb(+3),Sb(+5),As(+3),As(+5)$$

For aluminium, the distribution of the various species in function of pH for a dilute solution is shown in the following graph:



The vertical axis is the relative concentration of the species.
<hr>
Coming up: Enthalpy of neutralisation.
Acids in non-aqueous media and super acids.


[Edited on 24-1-2016 by blogfast25]

Quote: Originally posted by AJKOER

....... ........ In the case of dilute HCl where the addition of a salt is not problematic for a particular application, one may consider the addition of anhydrous calcium chloride (or, a concentrated solution thereof) as a possibility. The reason relates to the apparent significant increase in the so called 'activity level' upon adding MgCl2 or CaCl2 or NaCl (in declining order of preference). Here is a real world reference relating to practical significance in the field of Hydrometallury where leaching out minerals from ores efficiently and cheaply is a major concern. Source: See "Hydrometallurgy in Extraction Processes", Vol I, by C. K. Gupta and T. K. Mukherjee, page 15 at http://books.google.com/books?id=F7p7W1rykpwC&pg=PA15 . Note, the author claims there is data confirming that a 2M HCl in 3M MgCl2 or CaCl2 (and also FeCl3) behaves like 7M HCl! Here is a quote on the matter of discussion in one of the reference sources previously provided by Bfesser on Thermodynamic Activity (see http://en.wikipedia.org/wiki/Thermodynamic_activity ): "When a 0.1 M hydrochloric acid solution containing methyl green indicator is added to a 5 M solution of magnesium chloride, the color of the indicator changes from green to yellow—indicating increasing acidity—when in fact the acid has been diluted. Although at low ionic strength (<0.1 M) the activity coefficient approaches unity, this coefficient can actually increase with ionic strength in a high ionic strength regime. For hydrochloric acid solutions, the minimum is around 0.4 M.[1]" [Edited on 22-10-2014 by AJKOER]

Enthalpy of neutralisation:

Acids in non-aqueous media and super acids:

Quote:

An acid can be most simply defined as a proton donor, a base as a proton receptor. For a generic acid HA and base B, the proton (H<sup>+</sup> exchange can be summarised as:

$$\mathrm{HA} + \mathrm{B} \leftrightarrow \mathrm{BH^+} + \mathrm{A^-}$$

For water:

$$2H_2O(l) \leftrightarrow H_3O^+(aq) + OH^-(aq)$$

Strong acids are acids that completely deprotonate:
$$HA + H_2O \to H_3O^+ + A^-$$

They do so because they are stronger acids than the oxonium ion.

This leads to the so-called levelling effect:

Acids that are stronger than oxonium completely deprotonate and cannot be distinguished from each other in water (on acid strength).

The well known strong mineral acids cannot be ranked in water:

$$HClO_4=HCl=H_2SO_4=HNO_3$$

But in a solvent like glacial acetic acid (anh. ethanoic acid) this is no longer true because of the auto-dissociation:

$$2HOAc \leftrightarrow H_2OAc^+ + OAc^-$$

The structure (with resonance) of protonated ethanoic acid is:



The protonated species of a non-aqueous solvent is referred to as the solvonium ion.

Now the mineral acids are weaker than H₂OAc^- and they are only partly deprotonated, in the order:
$$HClO_4>HCl>H_2SO_4>HNO_3$$

So in glacial acetic acid, the mineral acids behave like weak acids: only partly deprotonated and without levelling effect.

A frequently used application of this type of chemistry is non-aqueous acidometry of very weak bases. Take pyrazole e.g. With a pK_B = 11.5, a 0.1 M solution in water would have an estimated pH of about 7.8, so it can’t be titrated in water.

Below are the (potentiometric) titration curves of pyrazole and other weak bases in GAA with 0.1 M HClO₄ in GAA:



Note how, like in water, larger and steeper potential jumps are obtained for bases with smaller pK_B.

GAA allows the titration of bases with a pK_B up to about 12.

The titration of weak acids, in particular those insoluble in water (like higher fatty acids) in non-aqueous solvent is also practiced for analytical purposes.

An example is the titration of higher fatty acids in methanol/benzene mixtures. The titrant solution is obtained by dissolving a known quantity of Na metal in dry methanol in the absence of CO₂, forming the strong base sodium methoxide. Dry benzene is then added to a volumetric ratio of about 5 (benzene/MeOH) to finalise the titrant solution. A solution of Thymol blue in MeOH is used as indicator to titrate the fatty acid (and other weak acids). Titration is performed under nitrogen to a blue equivalence point.

Super acids

The most interesting of the super acids are the non-HF based, non-corrosive carborane acids, which were introduced here.