LearnChem · Part IV — What makes a reaction go further, or faster?
Vinegar dissolves an eggshell. This module says what acid means, what weak means, and why those are two different things. It also builds the number pH from nothing, as a count of tens.
"Why does an eggshell vanish in vinegar?"
The answer is a handover, one proton at a time. By the end you can put a number on how far it goes.
Module 18 showed how a balance answers a push. Add product and the balance gives some of it back. Heat a balance and it shifts towards the side that takes heat in. Module 17 gave every balance a number, K, for where it settles. Module 6 priced a bond. All three come back here. An acid in water is a balance. Warm water is a balance under a push. A buffer is a balance answering a push.
Drop a raw egg into a glass of vinegar. Bubbles form on the shell. Leave it a day or two and the shell goes soft. Leave it longer and the shell is gone. The egg sits inside its thin inner skin. The shell was calcium carbonate. Vinegar is ethanoic acid in water. Something in the vinegar took the shell apart. That something is the subject of this module.
Drop a tooth into a glass of cola and leave it there for a week. Cola is mild enough to drink, and it holds far less acid than any laboratory bottle. What happens to the tooth?
Answer from your gut. The reveal follows.
The shell is calcium carbonate, CaCO3. Vinegar is ethanoic acid, CH3COOH, dissolved in water. Ethanoic acid hands over a proton. A proton is a hydrogen atom stripped of its one electron. It is written H+. The carbonate ion takes two of them. That makes carbonic acid. Carbonic acid falls apart into water and carbon dioxide. The carbon dioxide is the bubbles. The calcium stays in the liquid as a dissolved ion. Written out, the whole thing is one line.
CaCO3(s) + 2 CH3COOH(aq) → Ca2+(aq) + 2 CH3COO-(aq) + H2O(l) + CO2(g)
Read the arrow left to right. Two ethanoic acid molecules each gave up a proton. The carbonate took both. That is the whole story of an acid. An acid is anything that hands a proton over. A base is anything that takes one. Chemists call this the Brønsted definition. Here the carbonate was the base. The shell went because it was made of a base. Water can take a proton too. It can also hand one over, to a readier taker.
Water can be the base too. Put ethanoic acid in plain water and this happens.
CH3COOH(aq) + H2O(l) ⇌ CH3COO-(aq) + H3O+(aq)
A water molecule took the proton. It became H3O+. H3O+ is a water molecule carrying one extra proton. Chemists call it the hydronium ion. The ethanoic acid became CH3COO−, the ethanoate ion. The double arrow says this is a balance. Module 17 defined one. A balance is a reaction that runs both ways and settles. Most of the ethanoic acid keeps its proton. Only a small share hands it over. That share is the subject of §2. Lemon juice curdles milk by the same kind of handover. Its acid hands protons to the protein in the milk. The protein then loses the charge that kept its pieces apart, and they clump.
Think of a market where the only goods are protons. Acids are the sellers. Bases are the buyers. Strength is how readily a seller parts with a proton. A strong acid sells to almost any buyer. A weak acid sells only to a buyer that takes readily. Water is a small trader that both buys and sells. pH is the price of a proton. Where protons are plentiful they are cheap, and the pH is low. §3 builds that number. The picture holds in one way. No proton is ever made or lost in a trade. It only changes hands, as money does. It breaks in one way. A trader can refuse to sell at any price. A molecule cannot choose. What looks like willingness is only the energy cost of letting go, and module 6 priced that cost. So the market picture allows some trades that chemistry forbids.
Ammonia, NH3, is dissolved in pure ethanoic acid, with no water present. One proton changes hands. Which partner is the acid, and which is the base?
— An acid hands a proton over. A base takes one.
Two bottles stand on a bench. Both labels say 0.1 mol/L. One holds hydrochloric acid, HCl. The other holds ethanoic acid. The label counts the acid molecules put into each litre. It says nothing about how many have handed a proton over. Concentration is how much acid is in a litre. Strength is a different thing. This section keeps the two apart.
Same label, 0.1 mol/L, on both bottles. Which sentence is true about the H3O+ inside them?
Commit first. The numbers follow.
The two bottles are nothing alike inside. In the hydrochloric bottle, every HCl molecule has handed its proton to water. So that litre holds 0.1 mol of H3O+. In the ethanoic bottle, most molecules still hold their proton. The balance from §1 sits far over to the left. The H3O+ count is far smaller. §3 puts a number on the gap. The point here is simpler. The concentration is the same, and the amount handed over is not. Strength is the share handed over, not the amount put in.
Hydrochloric acid goes one way only. Its arrow has one head.
HCl(aq) + H2O(l) → Cl-(aq) + H3O+(aq)
Ethanoic acid's arrow has two heads. It is a balance, and module 17 gave every balance a number. K is the product amounts multiplied together, over the reactant amounts, once the balance has settled. For an acid handing a proton to water, that number is written Ka. Ka is the strength dial. For ethanoic acid it is 1.75 × 10−5. That is a small number. Small means the balance sits far to the left. Hydrochloric acid has no honest Ka in water. Every molecule hands over, so nothing is left to measure. What you would measure is water's limit as a taker, not the acid. Chemists call this the levelling effect. Water levels every strong acid to the same thing, H3O+. So strong is a yes or a no. Weak comes in degrees, and Ka is the degree.
Weak does not mean safe. Hydrofluoric acid, HF, is a weak acid. Its Ka is between 6.3 and 6.8 × 10−4, depending on which edition of the reference table you read. It is also one of the most dangerous acids a laboratory keeps. It soaks through skin and attacks what is underneath. And strong does not mean dangerous by itself. Your stomach makes hydrochloric acid every day. The danger of an acid depends on what it is and on how concentrated it is. It depends on how much of it there is, too. Weak and strong say only how willingly it hands over.
Concentrated acids and bases cause severe burns. Concentrated sulfuric acid adds a second hazard. Mixing it with water gives out a great deal of heat. Chemists call this the heat of dilution. Dilution means adding water. If a little water meets a lot of acid, all that heat goes into a small volume. The water can boil where the two touch. Boiling throws acid out as spray and as acid steam. That is why the order of mixing matters in a laboratory. Laboratory practice puts the acid into the water, so the heat spreads through the large volume. The source below states the working rule.
Flinn Scientific, Acid Safety: Safety Tips for Using Acids in School Laboratories, Publication No. 10344, 2 January 2020 · flinnsci.com · all rights reserved, cited as a source of fact
You add water to the hydrochloric acid until its label would read 0.001 mol/L. The ethanoic acid stays at 0.1 mol/L. Which is the strong acid now?
— Strength is how willingly. Concentration is how much.
§2 left a gap without a number. Both bottles were 0.1 mol/L. One held 0.1 mol/L of H3O+. The other held far less. Lemon juice on a cut apple slows the browning. The browning is the work of an enzyme. An enzyme is a catalyst that a living thing makes. Enzymes work only inside a narrow band of acidity, and lemon juice pushes the cut surface out of that band. That band is a number, and this section builds it. The amounts chemists meet run from about a mole per litre down to a ten-millionth and beyond. Writing all those zeros is slow. Counting them is quick. That count is pH.
You have seen pH charts that run from 1 to 14. The 0.1 mol/L hydrochloric acid in §2 sits at pH 1. Make it ten times more concentrated, to 1 mol/L. Where does its pH land?
Guess before you are shown.
From here on, H+ written on its own means H3O+. A bare proton never sits alone in water, and chemists write the short form out of habit.
Write the H3O+ amount as a power of ten. Module 3 wrote the size of a mole as a power of ten. Here the powers are negative. 0.1 mol/L is 10−1, one ten below one. 0.001 mol/L is 10−3, three tens below one. The pH is that count. That is the whole definition. The table does the whole-number cases.
| how much H3O+, in mol/L | written as a power of ten | tens below one | pH |
|---|---|---|---|
| 0.1 | 10−1 | 1 | 1 |
| 0.001 | 10−3 | 3 | 3 |
| 0.000 01 | 10−5 | 5 | 5 |
| 0.000 000 1 | 10−7 | 7 | 7 |
A meter reads pH 9 for a liquid. The table stops at 7. What is the liquid's H3O+ amount?
Now take 1 mol/L. It is 100, no tens below one, so the pH is 0. Go above 1 mol/L and the count goes negative, so the pH does too. Most amounts are not a neat power of ten, and the table cannot count those. The 0.1 mol/L ethanoic acid from §2 holds 1.32 × 10−3 mol/L of H3O+. That amount lies between 10−3 and 10−2, so its pH lies between 2 and 3. Its count is three tens down, less the fraction of a ten that the leading 1.32 supplies. A calculator's log button counts that fraction. Type 1.32, press log, and the button returns 0.12. So the count is 3 minus 0.12, which is 2.88, and the pH is 2.88. The button does the same partial count for any amount you type in. For 0.001 it returns −3, and the sign is minus because the count runs downwards. pH is that count with the minus sign dropped, so pH equals minus the log of the H3O+ amount, written pH = −log[H3O+]. The square brackets mean amount in mol/L. Log is short for logarithm, and a logarithm is a count of tens and nothing more. The button counts the fractions of a ten that you cannot count by eye. It never does anything you could not do yourself for a whole number.
Pure water makes its own H3O+. One water molecule hands a proton to another.
2 H2O(l) ⇌ H3O+(aq) + OH-(aq)
This balance has a constant too. Kw is the H3O+ amount multiplied by the OH− amount. OH− is the hydroxide ion, a water molecule that has lost a proton. At 25 °C, Kw is 1.0 × 10−14. Pure water makes the two in equal amounts. Two equal amounts multiplying to 10−14 are each 10−7. Seven tens below one is pH 7. That is why 7 is called neutral. Neutral means the two amounts are equal. It does not mean the H3O+ is gone. Every litre of pure water holds 10−7 mol of it. Add a base and the OH− rises. The product must stay at 10−14. So the H3O+ falls and the pH climbs past 7. That is the basic side. The scale does not stop at 14 either. 14 is simply where 1 mol/L of OH− sits.
A meter reads pH 3 for a liquid at 25 °C. What does Kw let you say about its OH− amount?
Nobody counts H3O+ ions. A pH meter measures a voltage. An electrode is the probe dipped into the liquid. The meter's glass electrode gives a voltage that shifts with the H3O+ around it. The meter is first dipped into reference solutions of agreed pH. Those set the scale. Then the sample is read against them. Every pH value is a comparison with those standards. IUPAC, the body that sets chemistry's definitions, defines pH this way. Its definition is written in terms of the ion's activity. Activity is the effective amount. In dilute solutions it is very close to the plain amount. This module treats the two as equal, and says so here.
R. P. Buck et al., "Measurement of pH. Definition, standards, and procedures (IUPAC Recommendations 2002)", Pure and Applied Chemistry 74(11), 2169–2200 · doi.org/10.1351/pac200274112169 · cited, not quoted
Body temperature is 37 °C. Pure water there is not at pH 7. Splitting a water molecule into H3O+ and OH− takes in heat. Module 18 said what heat does to such a balance. It pushes it towards the side that takes heat in. So warmer water splits a little more. At 37 °C, Kw is about 2.4 × 10−14, more than double the 25 °C value. The two amounts are still equal. Each is a little above 10−7. The count of tens is about 6.8. So pure water at body temperature sits at about pH 6.8. It is still exactly neutral. Neutral means equal amounts, and they are equal. The pH moves down rather than up because heat makes more of both ions. More H3O+ is a lower count. Read 6.8 as two figures only. The source supports no third digit.
A. V. Bandura and S. N. Lvov, "The ionization constant of water over wide ranges of temperature and density", Journal of Physical and Chemical Reference Data 35, 15 (2006) · doi.org/10.1063/1.1928231 · the 37 °C figure is good to two figures only
A meter reads pH 5.5 for a liquid. You have no calculator. What can you say about its H3O+ amount?
One more count before leaving logarithms. Ka is a number too, so the same counting applies to it. pKa is how many tens below one the Ka sits. Ethanoic acid's Ka is 1.75 × 10−5, between four and five tens below one. Type 1.75, press log, and the button returns 0.24, so the count is 5 minus 0.24, which is 4.76. A low pKa means a large Ka. So a low pKa means a readier acid.
— pH just counts how many tens below one the H3O+ sits.
Take the ethanoic acid at 0.1 mol/L. Add water. The label falls. Does anything else fall with it?
You add water to the 0.1 mol/L ethanoic acid until it is ten times more dilute. Which sentence is true?
Predict, then drive the bench.
§2 named two dials. Water reaches one of them. The bench leaves the top slider alone. Water does not touch it. The strength dial is the acid's own balance constant. A constant does not move when you add water. Only the bottom slider moves, and the pH climbs as it goes left. Now count the climb. From 0.1 mol/L to 0.01 mol/L the pH goes from 2.881 to 3.387. That is a rise of 0.506. Ten times less acid gives half a unit up, not a whole unit. A whole unit would mean ten times fewer H3O+. The acid does not give ten times fewer. The next paragraph shows why.
Call the acid HA, and call the amount of it put into each litre C. Each molecule that hands over makes one H3O+ and one A−, so call that amount x. Now write module 17's balance expression for this acid. It reads Ka = x × x divided by the amount of acid still holding its proton. That number underneath is C minus x, because x of the C has handed over. Now make the one approximation that the whole shortcut rests on. For a weak acid almost every molecule still holds its proton, so x is tiny beside C. Then the number underneath is close to C. The expression becomes Ka = x × x divided by C. Multiply both sides by C, and x × x = Ka × C. So x, the H3O+ amount, is the square root of Ka × C. Now divide C by ten. That is what one step to the left on the bench does. The product Ka × C is divided by ten as well, because Ka has not changed. Its square root is therefore divided by the square root of ten. The square root of ten, multiplied by itself, is ten, so it is half a ten. Taking half a ten off the amount puts half a unit onto the count of tens. That is where the half a unit comes from. The dashed grey line on the bench is this shortcut, drawn at every concentration.
Formic acid has pKa 3.75. Set the bench to it and slide the concentration all the way left, to 10−7 mol/L. Where does the pH sit?
The shortcut has two weak spots. The first is the approximation, which assumed almost all the acid still holds its proton. It bites once the concentration is no longer far above the Ka. At pKa 3 the dashed line errs by more than 0.05 from 1.58 × 10−2 mol/L. For ethanoic acid that happens at 3.16 × 10−4 mol/L. A decade is one tenfold step. The half-unit rule holds for two decades, 0.506 then 0.520. After that the rises grow, to 0.562, 0.680 and 0.871, and then shrink again as the curve flattens under pH 7. They grow because an acid that has handed over nearly everything climbs a whole unit per decade. The second weak spot is water's own H3O+. It bites in the last decade, where the rise shrinks to 0.774.
— Water it down and the pH climbs, but it never gets past seven.
Now use the acid up. Pour sodium hydroxide into ethanoic acid a little at a time. Sodium hydroxide is a strong base. It supplies OH−, and each OH− takes a proton from an acid molecule. Keep pouring until as much base has gone in as there was acid. Chemists call that pouring a titration. This section is enrichment. The CBSE syllabus names the technique but not the curve you are about to draw.
Exactly enough sodium hydroxide has gone in to use up all the ethanoic acid. Where is the pH now?
Commit, then pour it in yourself.
The red dot sits at 8.73 for the default acid, ethanoic acid at 0.100 mol/L. It is not 7. Press the strong-acid button. The dashed line ends at exactly 7.00. Why the gap? The base used up the ethanoic acid. It left ethanoate ions, CH3COO−. Ethanoate is a base. §1 said so, because it takes protons. Alone in water, it takes a few from water molecules. That leaves OH− behind. So the finished mixture is slightly basic. Now sweep the sliders. Over every setting this bench can reach, the end point runs from 7.39 to 10.0. It is never 7. There is no single typical value. Where it lands depends on the pKa and the concentration. Chloride, hydrochloric acid's partner, takes no protons from water at all. That is why the strong acid lands on 7.00.
Chemists call ethanoate the conjugate base of ethanoic acid. Conjugate means paired. This module says partner base. How feeble a base is it? The partner has a balance of its own, in which ethanoate takes a proton from water and leaves OH− behind. Call its constant Kb, the product amounts over the reactant amount, as module 17 defined a constant. Now multiply the acid's Ka by the partner's Kb and watch what cancels. Ka has H3O+ times ethanoate on top, over ethanoic acid underneath. Kb has ethanoic acid times OH− on top, over ethanoate underneath. The ethanoic acid on top of Kb cancels the ethanoic acid underneath Ka. The ethanoate on top of Ka cancels the ethanoate underneath Kb. What is left is H3O+ multiplied by OH−, and §3 named that product Kw. So Ka × Kb = Kw, and the partner's constant is Kw divided by Ka. A readier acid has a larger Ka, so Kw divided by it comes out smaller. A readier acid therefore leaves a feebler partner base, and that is why the end point moves with the pKa.
The blue dot halfway along is worth a look too. Halfway, half the acid has been used up, so acid and partner base are present in equal amounts. Put equal amounts into the balance expression and they cancel, leaving the H3O+ amount equal to Ka. So the halfway pH equals the pKa, and that is how a pKa is measured in practice. It is an approximation. For a pKa of 4.0 or above the gap is under 0.03 anywhere on this bench. At pKa 3.0 and 0.010 mol/L it reaches 0.176. Such an acid has handed over so much that the two halves are no longer equal. A practical question remains. Nobody sees a pH. An indicator is a dye that changes colour with pH. It is itself a weak acid, and its two forms, with and without the proton, have different colours. Bench 4 holds nine of them in ten rows, because one dye changes colour twice.
Slide the pH across. No dye flips at 7. Litmus straddles 7, but its range is three units wide. Litmus has no single pKa at all. It is a mixture of ten to fifteen dyes from lichens, so it has no single balance. That is a fact about litmus, not a missing number. Thymol blue has two rows because the same molecule lets go of two different protons. One goes at a far lower pH than the other. Turmeric is an indicator too, yellow in acid and red in base. Soap is basic. That is why a turmeric stain on a shirt goes red where the soap touches it. Now go back to bench 1. The end point for the default acid is 8.73. Read down the table for a dye whose range contains 8.73. Phenolphthalein does, and so does thymol blue's second change. Methyl orange does not. It would change colour long before the end. The rule is simple. Match the dye's range to the end point, not to 7.
Textbooks give a rule. A dye's range is its pKa plus or minus one. The sixth column in bench 4 applies that rule. Fits means both ends of the measured range land within a quarter of a pH unit of the rule's ends. By that test the rule fits none of the eight dyes that have a measured pKa. That is zero of eight. Swapping in the two disputed pKa values does not change the result. The measured ranges average 1.51 units wide. The rule predicts 2.00. The centre of a range sits up to 0.70 units off the pKa, for phenol red. The arithmetic behind the rule is sound. One unit below the pKa, 9.1 per cent of the dye is in its base form. One unit above, 90.9 per cent is. That span really is 2.00 units. What fails is the eye. A mixed colour reads as changed before the ratio reaches ten to one. So the rule describes what the ratio does, not what you will see. The source line under the table says which two values are disputed.
Phenolphthalein is colourless in acid and pink in base. Bench 1 ends at pH 8.73 for ethanoic acid. Why does the phenolphthalein turn pink there?
— Neutralising a weak acid lands above seven, not on it.
Your blood keeps its pH inside a narrow band. Idli batter does not, and it sours overnight. What holds a pH still? The answer is a mixture. Take a weak acid and its partner base together, in comparable amounts. Chemists call that a buffer. A buffer is a mixture built to hold a pH steady. Guess what it does before you tip anything in.
A buffer holds ethanoic acid and ethanoate in equal amounts. You tip strong acid into it. What happens to the pH?
Predict it, then try to break it.
Read the readout at the default settings. The buffer is 0.100 mol/L of the pair. Tip in acid and watch two numbers. The buffer moves a little. The comparison, unbuffered water, moves a lot. Unbuffered water is water with a little strong acid in it. The acid is just enough to hold the same starting pH, and there is no partner base at all. Set exactly at ethanoic acid's pKa of 4.76, this buffer takes 0.0411 mol/L of strong acid. That much is needed before its pH drops one full unit. The slider's nearest setting is 4.8, so the readout sits a hair off that. Put the same dose into the unbuffered water at pH 4.76. It lands at pH 1.39. That is more than three units, from the same spoonful.
Where did the protons go? They went into the partner base.
CH3COO-(aq) + H3O+(aq) → CH3COOH(aq) + H2O(l)
Each incoming H3O+ meets an ethanoate ion and hands over. The ethanoate becomes ethanoic acid. The H3O+ count barely moves. What moves is the ratio of ethanoate to ethanoic acid. Module 18 said a balance answers a push by giving some of it back. This is that answer at work. The buffer has limits. Slide the set pH. The buffer is strongest when it is set at 4.76, which is ethanoic acid's pKa. There the two halves are equal, and either half can take a hit. Now slide the total amount down to 0.010 mol/L. Push the acid slider all the way, to 0.100 mol/L. The pH lands at 1.02. The partner base ran out long before the dose did. A buffer is a pair that gets used up, not a wall. It trades one big move for a small one, until the trade is exhausted.
Take the same buffer, ethanoic acid and ethanoate in equal amounts. This time you tip in strong base, not acid. What soaks it up?
— A buffer is a pair that trades a big pH move for a small one, until one half runs out.
Tier 1 deals fresh numbers each time, and the benches can check you. Tier 2 needs every step written down. Tier 3 has no answer key.
1.
2.
3. From module 17.
4. From module 6.
5.
The amount of acid is 0.100 mol/L multiplied by 0.02500 L, which is 0.00250 mol. The base must supply the same 0.00250 mol of OH− to use it all up. The volume of base is 0.00250 mol divided by 0.100 mol/L. That is 0.0250 L, or 25.00 mL. The total volume at the end point is 25.00 mL plus 25.00 mL. That is 50.00 mL, or 0.05000 L. One ethanoate ion is made for each acid molecule used up. So 0.00250 mol of ethanoate is present. Its concentration is 0.00250 mol divided by 0.05000 L, which is 0.0500 mol/L. Ka for a pKa of 4.756 is ten to the power minus 4.756, which is 1.75 × 10−5. The partner base's constant is Kw divided by Ka. That is 1.0 × 10−14 divided by 1.75 × 10−5, which is 5.71 × 10−10. Ethanoate takes protons from water and leaves one OH− behind for each proton taken. So the OH− amount is the square root of that constant multiplied by the ethanoate concentration. The product is 5.71 × 10−10 multiplied by 0.0500 mol/L, which is 2.86 × 10−11. Its square root is 5.35 × 10−6 mol/L of OH−. The H3O+ amount is Kw divided by that OH− amount. That is 1.0 × 10−14 divided by 5.35 × 10−6, which is 1.87 × 10−9 mol/L. That amount lies between 10−9 and 10−8, so the pH lies between 8 and 9. The log button counts the fraction, and the count is 8.73. Bench 1 agrees, and the strong-acid line would have stopped at exactly 7.00.
An acid hands a proton over. How willingly is everything else.