Some Basic Concepts of Chemistry: Class 11 Chemistry · Chapter 1

Leave dosa batter out overnight and by morning it has risen and turned sour. An iron gate left out through the monsoon grows a flaky brown crust. A green mango shut in a paper bag turns soft and sweet. In each case the substances themselves have changed into new ones. Chemistry (रसायन विज्ञान) asks what substances are made of, how their particles are arranged, how they behave and how they turn into other substances.

This unit builds the toolkit for the whole course. We sort matter into types, learn to measure quantities and report them honestly, meet the laws that persuaded scientists that atoms are real, and learn to count atoms by weighing them with the mole. By the end you will be able to predict how much product a reaction can give, a skill you will use in almost every later chapter.

Development of Chemistry

Chemistry as an organised, measuring science is only about three hundred years old, but people practised it long before that. Medieval alchemists chased two prizes that never existed: a philosopher's stone (पारस, paras) to turn iron or copper into gold, and an elixir of life. From about 1300 to 1600 CE many turned to medicines, a phase called iatrochemistry. The quests failed, but they left real skills behind: distilling, crystallising, purifying and weighing. Arab scholars carried this craft into Europe, where chemistry became a quantitative science in the eighteenth century.

China and India had alchemical traditions of their own. Sanskrit texts call the subject Rasayana Shastra; it covered metallurgy, medicine, dyes, glass and cosmetics. The timeline picks out a few Indian achievements for which the evidence is good.

Some of these ideas sound surprisingly modern. Grinding and heating metals into very fine bhasma powders changes how they behave, and studies of some bhasmas report particles only tens of nanometres across, the size range of today's nanotechnology. Kanada's paramanu, proposed many centuries before John Dalton's atomic theory of 1808, is the clearest early Indian statement that matter is made of particles. From the eighteenth century, imported goods and colonial rule pushed many indigenous techniques into decline, and modern laboratory chemistry reached Indian colleges only in the late nineteenth century.

What these traditions lacked was a way to count the particles Kanada imagined. Before this unit ends you will be able to say how many molecules there are in a single paracetamol tablet.

1.1 Importance of Chemistry

Chemistry is often called the central science: it borrows laws from physics and lends explanations to biology, geology, medicine and engineering. The ozone overhead, the signal racing along a nerve and the silicon chip in your phone are all chemistry at work.

• Food. Fertilisers such as urea feed most of India's crops; since 2015 all Indian urea has been neem-coated so that its nitrogen is released more slowly. Pesticides, preservatives and packaging come from chemists too.
• Health. Chemists design, make and purify medicines, from paracetamol to anti-cancer drugs. Oral rehydration solution, a balanced mix of glucose and salts, has saved millions of children with diarrhoea.
• Materials. Polymers, optical fibres, lithium-ion batteries, superconducting ceramics and conducting plastics all came from designing substances with chosen electrical, magnetic or optical properties.
• Environment. Chemists replaced the CFCs that were thinning the ozone layer, which is now slowly recovering. Managing greenhouse gases such as carbon dioxide and methane is a big open problem.
• Economy. Industries making acids, alkalis, fertilisers, dyes, cement, polymers, metals and medicines employ millions of people.

Challenges remain, from the chemistry of living cells to storing solar energy and turning waste into resources. All of that work rests on the basic ideas of this unit, starting with what matter is.

1.2 Nature of Matter

A pebble, the air in a football, the water in a matka and your own body share two things: each has mass, and each takes up space. Anything with both properties is matter (द्रव्य). Light, heat and sound are not matter; they are forms of energy.

1.2.1 States of Matter

Whether a sample is a solid, a liquid or a gas depends on how its particles are spaced and how freely they move. Locked into a regular pattern and able only to jiggle on the spot: that is a solid. Still touching, but free to slide past one another: a liquid. Widely spaced and racing about at random: a gas.

Changing the temperature or the pressure turns one state into another. Heat ice and it melts; heat the water and it boils; cool the steam and the steps run backwards. Pressure matters too: LPG is a gas in the open air but is squeezed into a liquid inside a cylinder, which is why a full cylinder sloshes.

1.2.2 Classification of Matter

Matter in bulk can be sorted with three questions (Fig. 1.2). The first: can a physical method such as sieving, filtering, a magnet, evaporation or distillation separate it into simpler parts? If yes, it is a mixture (मिश्रण); if no, it is a pure substance.

The substances in a mixture are its components, and their proportions are up to you: nimbu-paani can be made sweeter or sourer at will. If the components are spread evenly down to the level of particles, so that a sip from the top tastes like a sip from the bottom, the mixture is homogeneous, like brass, vinegar or well-stirred nimbu-paani. If the make-up changes from one part to another, often with visible bits, it is heterogeneous, like muddy water, fruit salad or iron filings stirred into sulfur powder. Physical methods pull mixtures apart: a magnet lifts out the iron filings, a filter holds back the mud and evaporation leaves salt behind from sea water.

A pure substance has a fixed composition and the same properties in every sample, like distilled water, copper, sucrose or baking soda. Sucrose from sugarcane and from sugar beet holds carbon, hydrogen and oxygen in identical proportions by mass, and no filtering or evaporating will pull those elements apart.

Pure substances are of two kinds. An element (तत्व) contains only one kind of atom. Its atoms may stay single, as in helium or a piece of iron, or join into molecules, as in two-atom chlorine, three-atom ozone or eight-atom sulfur (Fig. 1.3). A compound (यौगिक) is made when different elements join chemically, always in the same proportion by mass; pulling them apart again takes a chemical reaction.

A compound is a genuinely new substance. Sodium is a soft metal that reacts violently with water and chlorine is a poisonous green gas, yet together they form table salt. A compound's properties are not an average of its elements' properties.

1.3 Properties of Matter and their Measurement

Every substance has a set of properties that identify it, much as a fingerprint identifies a person. To use them in science we must observe and, wherever possible, measure them.

1.3.1 Physical and Chemical Properties

Melting ice still leaves you with water, so a melting point is a physical property: you can observe it while the substance keeps its identity. Burning turns paper into ash and gases, so flammability, which shows itself only as the substance changes into new ones, is a chemical property. A silver anklet has both kinds: its shine and density are physical, while its slow blackening in air, as silver reacts with traces of sulfur compounds, is chemical.

Chemists use both kinds to describe, explain and predict how substances behave. The rest of this section is about measuring physical properties.

1.3.2 Measurement of Physical Properties

Saying a door is '2.1 tall' tells nobody anything; '$2.1\mathrm{m}$' tells everyone. A measured quantity is always a number together with a unit, the number saying how many of that unit fit into it.

Your grandparents may remember buying ghee by the seer and gold by the tola; India began switching to metric units in 1958. The metric system, created in France in the 1790s, steps up and down in powers of ten, so conversions are easy, unlike Britain's English system of inches, feet and pounds. Science needed more than that: one system agreed by every country.

1.3.3 The International System of Units (SI)

Seven base quantities, each with one base unit, form the core of the International System of Units, or SI after its French name, Le Système International d'Unités; speed, volume, density and every other quantity are derived from them. SI was adopted in 1960 at the 11th meeting of the General Conference on Weights and Measures (CGPM), the body behind the Metre Convention, a treaty signed in Paris in 1875.

Since 20 May 2019 every base unit is fixed by giving an exact value to a constant of nature, so the unit can be reproduced in any well-equipped laboratory: the second through a frequency of the caesium-133 atom, the metre through the speed of light, the kilogram through the Planck constant, and so on.

Prefixes scale SI units by powers of ten, so we avoid strings of zeros: a carbon–carbon bond is about $154\mathrm{p}\mathrm{m}$ long and a tablet may hold $500\mathrm{m}\mathrm{g}$ of medicine.

The full list runs from yocto (${10}^{-24}$) to yotta (${10}^{24}$), and since 2022 from quecto (${10}^{-30}$) to quetta (${10}^{30}$).

1.3.4 Mass and Weight

Carry a $1.00\mathrm{k}\mathrm{g}$ packet of atta to the Moon and it holds exactly the same flour: its mass, the amount of matter in it, has not changed. Yet it presses on your hand only a sixth as hard, because its weight, the pull of gravity on it, depends on where it is: about $9.8\mathrm{N}$ in Delhi, $1.6\mathrm{N}$ on the Moon. In the lab, mass is found with an analytical balance that reads to $0.0001\mathrm{g}$ inside a glass case that keeps draughts off the pan. The SI unit is the kilogram, but lab amounts are small, so chemists mostly use grams ($1\mathrm{k}\mathrm{g}=1000\mathrm{g}$).

1.3.5 Volume

A school water tank holds about a cubic metre; a beaker, a few hundred cubic centimetres. Both numbers describe volume, the room a substance takes up, measured in length cubed. The SI unit, ${\mathrm{m}}^3$, is far too big for bench work, so chemists use $\mathrm{d}{\mathrm{m}}^3$ and $\mathrm{c}{\mathrm{m}}^3$, and the litre (L), which is not an SI unit but is accepted alongside it.

1.3.6 Density

Why does a steel spoon sink while a wooden one floats? Steel packs far more mass into each cubic centimetre: it has a higher density, the mass per unit volume:

Chemists usually quote $\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$ (the same as $\mathrm{g}\mathrm{m}{\mathrm{L}}^{-1}$) rather than the SI $\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$; $1\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}=1000\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$. Water is $1.00$, iron $7.87$ and gold $19.3\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$: a one-litre carton full of gold would weigh about $19\mathrm{k}\mathrm{g}$. Ice ($0.92\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$) has an open molecular framework, which is why it floats.

1.3.7 Temperature

A fever of 102 °F on a home thermometer, 38.9 °C on a hospital chart and 312 K in a physics lab are the same temperature on three scales. The kelvin (K) is the SI unit. The Celsius scale puts the freezing and boiling points of water at normal pressure at 0 °C and 100 °C; the Fahrenheit scale puts them at 32 °F and 212 °F (Fig. 1.5).

A kelvin and a Celsius degree are the same size; the scales differ only in where zero is. The zero of the kelvin scale, $0\mathrm{K}=-273.15{}^{\circ }\mathrm{C}$, is absolute zero, the lowest temperature possible, so kelvin temperatures are never negative.

1.4 Uncertainty in Measurement

Every number in chemistry came from an instrument or from a calculation built on such numbers. Three habits keep them manageable and honest: a compact way to write huge and tiny numbers, a way to show how certain a measurement is, and a safe way to change units.

1.4.1 Scientific Notation

Atoms and molecules are extremely light and extremely numerous. A single drop of water ($0.05\mathrm{g}$) holds about 1 670 000 000 000 000 000 000 molecules, and a single carbon atom has a mass of about 0.000 000 000 000 000 000 000 019 9 grams. Handling such numbers digit by digit invites mistakes.

Scientific notation writes a number as $N\times {10}^n$, where the digit term $N$ satisfies $1\le N<10$ and the exponent $n$ is a whole number. The two numbers above become $1.67\times {10}^{21}$ and $1.99\times {10}^{-23}\mathrm{g}$. Moving the decimal point $k$ places left adds $k$ to the exponent; moving it right subtracts $k$: $45600=4.56\times {10}^4$ and $0.000093=9.3\times {10}^{-5}$.

• Multiplying or dividing: multiply or divide the digit terms and add or subtract the exponents; then adjust so that $1\le N<10$.
• Adding or subtracting: first rewrite the numbers with the same exponent, then add or subtract the digit terms.

1.4.2 Significant Figures

No measurement is perfect: the instrument has a limited scale and the person reading it limited skill. A kitchen scale might show a bag of dal as $0.50\mathrm{k}\mathrm{g}$, while a laboratory balance gives more digits for the same bag. The digits we write show how much we trust a number.

The significant figures (सार्थक अंक) of a measurement are all the digits known for certain plus one final, estimated digit. Writing $24.36\mathrm{m}\mathrm{L}$ says that $24.3$ is certain and the $6$ is a best estimate. Unless told otherwise, readers take that last digit to be uncertain by one unit either way. Fig. 1.6 shows where the estimated digit comes from.

To count significant figures in a number someone else wrote:

1. Every non-zero digit counts: $4.71$ has three.
2. Zeros before the first non-zero digit only place the decimal point and do not count: $0.0082$ has two.
3. Zeros between non-zero digits count: $30.05$ has four.
4. Zeros at the end count if there is a decimal point: $2.500$ has four, $70.0$ has three. Without one they are not counted: $7000$ has one. Use scientific notation to show more: $7.0\times {10}^3$ has two, $7.00\times {10}^3$ three.
5. Exact numbers, such as counts (11 players in a team) and defined relations ($1\mathrm{m}=100\mathrm{c}\mathrm{m}$), have unlimited significant figures.
6. In scientific notation every digit of $N$ counts: $6.020\times {10}^{23}$ has four.

Careful digits are not enough; results must also be trustworthy. Precision (परिशुद्धता) is how closely repeated measurements agree with each other. Accuracy (यथार्थता) is how close a result is to the true value. A balance that was never zeroed can give beautifully precise readings that are all wrong by the same amount (Fig. 1.8).

A calculated answer can be no more certain than the least certain measurement in it:

• Adding or subtracting: keep as many decimal places as the measurement with the fewest decimal places.
• Multiplying or dividing: keep as many significant figures as the measurement with the fewest.

To round, look at the first digit you drop. More than 5: raise the last kept digit ($3.476\to 3.48$). Less than 5: leave it ($2.843\to 2.84$). Exactly 5 with only zeros after it: make the last kept digit even ($7.45\to 7.4$, $7.55\to 7.6$), so rounding errors do not pile up in one direction. If non-zero digits follow the 5, as in $2.451$, round up ($2.5$).

1.4.3 Dimensional Analysis

The factor-label method (also called the unit factor method or dimensional analysis) changes units safely. Start from a relation such as $1\mathrm{y}\mathrm{d}=0.9144\mathrm{m}$ (exact). Dividing one side by the other gives a unit factor, a fraction equal to one:

Multiplying by 1 never changes a quantity. Pick the factor with the unwanted unit in the denominator, so it cancels, and the wanted unit on top. Units cancel, multiply and can be squared or cubed like algebraic symbols, and several factors can be chained in one line.

1.5 Laws of Chemical Combinations

In the late eighteenth century chemists began to weigh what went into and came out of reactions, and to measure gas volumes. Five regularities emerged, and together they became the evidence for atoms.

1.5.1 Law of Conservation of Mass

The French chemist Antoine Lavoisier (1743–1794) weighed everything. Heating tin in sealed glass vessels, he found that the total mass did not change until the vessel was opened and air rushed in. From many such experiments he concluded that reacting substances never gain or lose matter overall, and set the idea out in his textbook of 1789.

The law can look false at first: a burning candle gets lighter and a rusting nail heavier. In both cases a gas is lost or gained: carbon dioxide and water vapour escape from the flame, and the iron takes up oxygen from the air. Weigh the system with those gases and the total stays the same (Fig. 1.9).

1.5.2 Law of Definite Proportions

The French chemist Joseph Proust (1754–1826), working in Spain around 1799, analysed samples of one compound from very different sources and always found the same proportions of elements by mass. Pure water is a modern example.

Also called the law of definite composition, it lets a chemist identify a substance or check its purity from an analysis. (A few solids, such as iron(II) oxide, closer to $\mathrm{F}\mathrm{e}{\phantom{X}}_{0.95}\mathrm{O}$, have slightly variable compositions; you will meet such exceptions later.)

1.5.3 Law of Multiple Proportions

Some pairs of elements form more than one compound, and in 1803 John Dalton noticed a pattern in such families. Carbon and oxygen form carbon monoxide and carbon dioxide: $12.0\mathrm{g}$ of carbon combines with $16.0\mathrm{g}$ of oxygen in the first and with $32.0\mathrm{g}$ in the second. For the same mass of carbon, the masses of oxygen are in the ratio $16:32=1:2$, a ratio of small whole numbers.

1.5.4 Gay Lussac's Law of Gaseous Volumes

In 1808 the French chemist Joseph Louis Gay-Lussac (1778–1850) measured the volumes of reacting gases. One volume of hydrogen reacts with exactly one volume of chlorine to give two volumes of hydrogen chloride; one volume of nitrogen and three of hydrogen give two of ammonia, all measured at the same temperature and pressure.

In effect it fixes proportions for gas volumes, and it posed a puzzle that took half a century to settle.

1.5.5 Avogadro's Law

In 1811 the Italian scientist Amedeo Avogadro (1776–1856) suggested that a given volume of any gas holds the same number of molecules as the same volume of any other, if temperature and pressure match. His key move was to separate the atom from the molecule: a molecule of an element could contain several atoms.

Fig. 1.10 shows why this mattered. If hydrogen and chlorine were single, indivisible atoms, one volume of each would hold equal numbers of atoms, and pairing them could give only one volume of hydrogen chloride; Gay-Lussac measured two. If each molecule holds two atoms, every $\mathrm{H}{\phantom{X}}_2$ plus $\mathrm{C}\mathrm{l}{\phantom{X}}_2$ yields two HCl molecules, and the volume doubles as observed.

Dalton and most chemists of his day would not accept that identical atoms could pair up, so Avogadro's idea was largely ignored. In 1860 chemists met in Karlsruhe, Germany, at the first international chemistry conference, to settle the confusion over atomic masses. There the Italian chemist Stanislao Cannizzaro handed out a pamphlet showing that Avogadro's hypothesis gave consistent atomic masses, and the idea was finally accepted.

1.6 Dalton's Atomic Theory

The Greek philosopher Democritus (about 460–370 BCE) called the smallest particles of matter atomos, 'uncuttable', and Kanada's paramanu were a similar idea, but both were philosophical guesses. The English schoolteacher John Dalton (1766–1844) made atoms scientific by linking them to the masses in the laws above. His A New System of Chemical Philosophy (1808) claimed, in modern words:

1. All matter is made of extremely small particles called atoms, which cannot be divided or destroyed in chemical changes.
2. All atoms of a given element are identical, including in mass; atoms of different elements have different masses.
3. Compounds form when atoms of different elements join in fixed, small whole-number ratios.
4. A chemical reaction only rearranges atoms. No atom is created or destroyed.

These claims explain the mass laws. If atoms are only rearranged (claim 4), total mass cannot change (Fig. 1.11). A fixed whole-number ratio of atoms of fixed mass (claims 2 and 3) gives a fixed mass composition. And since atoms combine as whole units, a second compound of the same elements has whole extra atoms, hence the small whole-number ratios of multiple proportions.

The theory had gaps. It could not explain Gay-Lussac's volume ratios, since Dalton rejected molecules of two identical atoms, and it said nothing about why atoms combine. Later work showed that atoms can be split into electrons, protons and neutrons (Unit 2) and that atoms of one element may differ in mass (isotopes, Section 1.7.2). Still, atoms rearranging in fixed ratios is the basis of every chemical equation.

1.7 Atomic and Molecular Masses

If reactions rearrange atoms in fixed ratios, knowing how heavy each kind of atom is turns ratios of atoms into ratios of grams.

1.7.1 Atomic Mass

Atomic masses are relative masses. Since 1961 the reference has been the carbon-12 atom (${}^{12}\mathrm{C}$), assigned exactly 12 units. Why relative? A carbon atom, about $2\times {10}^{-23}\mathrm{g}$, is far too light for any balance, so nineteenth-century chemists could only compare atoms through the masses of elements that combine, starting by calling hydrogen 1. A modern mass spectrometer measures atomic masses directly and precisely, but still reports them in these units.

To express an atom's mass in u, divide its mass in grams by $1.6605\times {10}^{-24}\mathrm{g}$: a chlorine-35 atom of $5.8067\times {10}^{-23}\mathrm{g}$ has an atomic mass of $34.969\mathrm{u}$. The old 'amu' is now written u, the unified atomic mass unit.

1.7.2 Average Atomic Mass

Most natural elements are mixtures of isotopes, atoms of one element with different masses. The atomic mass in the periodic table is the average over a natural sample, each isotope weighted by how common it is:

1.7.3 Molecular Mass

The molecular mass is the sum of the atomic masses of all the atoms in one molecule. For ammonia, $\mathrm{N}\mathrm{H}{\phantom{X}}_3$: $14.007+3(1.008)=17.031\mathrm{u}$. For carbon dioxide, $\mathrm{C}\mathrm{O}{\phantom{X}}_2$: $12.011+2(15.999)=44.009\mathrm{u}$.

1.7.4 Formula Mass

Ionic compounds have no separate molecules. Solid sodium chloride is a vast lattice of $\mathrm{N}\mathrm{a}{\phantom{X}}^{+}$ and $\mathrm{C}\mathrm{l}{\phantom{X}}^{-}$ ions, each surrounded by six of the other kind, with no 'NaCl molecule' to weigh. We add up the atomic masses of the simplest formula, the formula unit, to get the formula mass. For calcium chloride, $\mathrm{C}\mathrm{a}\mathrm{C}\mathrm{l}{\phantom{X}}_2$: $40.078+2(35.45)=110.98\mathrm{u}$.

1.8 Mole Concept and Molar Masses

A bank weighs a bag of coins instead of counting it, and a paper shop sells sheets by the ream of 500. Chemists face the same problem on a gigantic scale: a pinch of salt holds about ${10}^{22}$ ions. Their counting unit is the mole (मोल); the amount of substance $n$, in moles, is an SI base quantity.

The number of entities per mole is the Avogadro constant, $N_{\mathrm{A}}=6.02214076\times {10}^{23}\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}$ (the bare number is the Avogadro number), exact by definition since 2019. Its value makes the mole and the u fit together exactly: $N_{\mathrm{A}}$ atomic mass units add up to one gram.

Counting one particle per second, day and night, one mole would take about $1.9\times {10}^{16}$ years, over a million times the age of the universe. A mole of hydrogen atoms, of water molecules or of NaCl formula units all contain the same $6.022\times {10}^{23}$ entities.

A substance's molar mass (मोलर द्रव्यमान) $M$ is how many grams one mole of it weighs, in $\mathrm{g}\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}$. Because of Eq. (1.8), $M$ has the same number as the atomic, molecular or formula mass in u: $\mathrm{C}\mathrm{O}{\phantom{X}}_2$ $44.01$, $\mathrm{N}\mathrm{H}{\phantom{X}}_3$ $17.03$ and $\mathrm{C}\mathrm{a}\mathrm{C}\mathrm{l}{\phantom{X}}_2$ $110.98\mathrm{g}\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}$. (Since 2019 the molar mass of carbon-12 is not exactly $12\mathrm{g}\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}$, but it is off by less than a part per billion.)

Three relations link moles to measurable things; together they form the 'mole map' of Fig. 1.13.