Which laws of chemical combination follow from Dalton's atomic theory?

Conservation of mass, definite proportions, multiple proportions, and reciprocal proportions all follow from Dalton's postulates. Gay-Lussac's law was better explained later by Avogadro's hypothesis.

Introduction

Q: What is the difference between a compound and a mixture?

A compound has a fixed composition by mass, its components lose their individual properties, and it can only be separated by chemical means. A mixture has a variable composition, its components retain their properties, and can be separated by physical methods.

Q: Why is the law of conservation of mass not exactly true in nuclear reactions?

In nuclear reactions, mass is converted into energy via E = mc squared. In ordinary chemical reactions the energy changes are so small that mass changes are undetectable, so the law holds. In nuclear reactions, mass-energy (not mass alone) is conserved.

Q: How does Avogadro's hypothesis explain Gay-Lussac's law?

Avogadro proposed that equal volumes of gases at the same T and P contain equal numbers of molecules. So the whole-number volume ratios observed by Gay-Lussac are actually whole-number molecule ratios, matching balanced equations.

Q: What is the difference between an atom and a molecule?

An atom is the smallest particle of an element showing its chemical properties. A molecule is the smallest particle of a substance with independent existence. For noble gases, atom and molecule are the same.

Q: Why can percentage yield never exceed 100 percent?

Theoretical yield is the maximum predicted by stoichiometry. Actual yield is less due to side reactions, losses, and reversibility. Values above 100 percent indicate impurities or calculation errors.

Q: How many elements are in the modern periodic table?

As of the latest IUPAC updates, 118 elements are officially recognised, ending at Oganesson (Og, atomic number 118). About 94 occur naturally on Earth.

Q: How many significant figures does 0.005080 have?

Four. Leading zeros do not count, the middle zero does, and the trailing zero after the decimal is significant. In scientific notation: 5.080 x 10 to the minus 3.

ChemistrySome Basic Concepts of ChemistryFor JEE aspirants

Chemistry is the science of matter, its properties, structure, and transformations. In Some Basic Concepts of Chemistry for JEE and NEET, you build the toolkit for every later chapter: SI units and measurement, the classification of matter into elements, compounds and mixtures, the five laws of chemical combination (conservation of mass, definite proportions, multiple proportions, reciprocal proportions and Gay-Lussac's law of combining volumes), Dalton's atomic theory, percentage yield, and the atom vs molecule distinction. This concept lays the groundwork.

Key Formulas - Quick Reference

Dimensional analysis: (original quantity) $\times$ (conversion factor) = (equivalent quantity in new units)
Density: $ρ = \frac{m}{V}$ so mass $= V \times ρ$
Law of conservation of mass: $\sum m_{reactants} = \sum m_{products}$
Percentage yield: $% yield = \frac{actual yield}{theoretical yield} \times 100$
Einstein mass-energy: $E = m c^{2}$
Unit conversions worth memorising: $1 L atm = 101.325 J$ , $1 J = 1 0^{7} erg$ , $1 amu = 1.66 \times 1 0^{- 24} g$

1. Physical vs Chemical Properties

Physical property: a property that can be measured without changing the chemical composition of the substance. Examples: mass, volume, density, refractive index, melting point, colour, hardness.

Chemical property: a property that can only be observed at the cost of the substance itself, i.e. by carrying out a chemical change. Examples: combustibility of hydrogen (verified by burning it), the sweet taste of sugar (verified by consuming and digesting it), rusting of iron.

2. Units of Measurement

Every physical quantity is written as a numerical value multiplied by a unit. Get the unit wrong and the number is meaningless.

Fundamental (Base) SI Units

Fundamental units cannot be derived from one another. The seven base units of the SI system are:

Quantity	Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Thermodynamic temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd

Derived Units

Derived units are combinations of the base units. Some common examples:

Quantity	SI Unit	In base units
Volume	cubic metre ( $m^{3}$ )	$m^{3}$
Density	$kg m^{- 3}$	$kg m^{- 3}$
Velocity	$m s^{- 1}$	$m s^{- 1}$
Acceleration	$m s^{- 2}$	$m s^{- 2}$
Force	newton (N)	$kg m s^{- 2}$
Pressure	pascal (Pa)	$kg m^{- 1} s^{- 2}$
Energy / Work	joule (J)	$kg m^{2} s^{- 2}$

3. Scientific Notation and Significant Figures

Measurements come with a built-in uncertainty. Two conventions let you keep that uncertainty honest.

Scientific notation

Any number is written as $N \times 1 0^{n}$ where $1 \leq N < 10$ and $n$ is an integer. This is compact and unambiguous:

Speed of light $= 3.0 \times 1 0^{8} m s^{- 1}$
Avogadro's number $= 6.022 \times 1 0^{23} mol^{- 1}$
Mass of an electron $= 9.11 \times 1 0^{- 31} kg$

Significant figures

Significant figures are the digits in a measurement that carry meaning. The rules:

All non-zero digits are significant. $285.6$ has 4 significant figures.
Zeros between non-zero digits are significant. $2005$ has 4.
Leading zeros are not significant. $0.0025$ has 2 (only $2$ and $5$ ).
Trailing zeros to the right of the decimal are significant. $2.500$ has 4.
Trailing zeros in a whole number are ambiguous. $100$ can have 1, 2, or 3, so use scientific notation to be clear: $1.00 \times 1 0^{2}$ has 3.
Exact numbers (counted objects, defined constants like $1 km = 1000 m$ ) have infinite significant figures.

Addition/subtraction: the result carries as many decimal places as the input with the fewest decimal places.
Multiplication/division: the result carries as many significant figures as the input with the fewest significant figures.

4. Dimensional Analysis: Converting Units

The safe way to convert between units is the factor-label method. Multiply by a ratio equal to $1$ that cancels the unwanted unit and introduces the wanted one.

For mass: $\frac{1 kilogram}{1000 gram} = 1 = \frac{2.205 pound}{1 kilogram}$ , so $1 kg = 1000 g = 2.205 lb$ .

For a derived unit, first write it in dimensional form, then convert each base quantity. Example: how many erg (CGS) are in $1 J$ (SI)?

Dimensions of work: force $\times$ displacement $= [M L T^{- 2}] \times [L] = [M L^{2} T^{- 2}]$ .

$1 J = 1 kg \times (1 m)^{2} \times (1 s)^{- 2}$

Substituting $1 kg = 1 0^{3} g$ and $1 m = 1 0^{2} cm$ :

$1 J = 1 0^{3} g \times (1 0^{2} cm)^{2} \times (1 s)^{- 2} = 1 0^{3} \times 1 0^{4} g cm^{2} s^{- 2} = 1 0^{7} erg$

Solved Example 1

What is the mass of

1 L

of mercury in grams and kilograms, given density of liquid mercury

= 13.6 g cm^{- 3}

Solution:

Use mass $= volume \times density$ with the conversion $1 L = 1000 cm^{3}$ :

$m = (1 L) \times (\frac{1000 cm ^{3}}{1 L}) \times (13.6 g cm^{- 3}) = 1.36 \times 1 0^{4} g$

Convert to kilograms: $1.36 \times 1 0^{4} g \times \frac{1 kg}{1000 g} = 13.6 kg$ .

Solved Example 2

Convert

1 L atm

to joule (the SI unit of energy).

Solution:

Two conversion factors do it: $1 L = 1 0^{- 3} m^{3}$ and $1 atm = 101, 325 Pa$ .

$1 L atm \times \frac{1 0 ^{- 3} m ^{3}}{1 L} \times \frac{101 , 325 Pa}{1 atm} = 101.325 Pa m^{3}$

Since $Pa = N m^{- 2}$ , we get $Pa m^{3} = N m = J$ , so $1 L atm = 101.325 J$ .

5. Matter and Its Classification

Matter: anything that has mass and occupies space (i.e. anything that exhibits inertia). Chalk, water, air, and a book are all matter.

Matter can be classified based on its chemical composition into pure substances and mixtures, as shown below.

Figure 1: Classification of matter based on chemical composition.

Elements

An element is a pure substance made of only one type of atom. There are $118$ confirmed elements in the modern periodic table (Oganesson, $Og$ , is element $118$ ). About $94$ occur naturally on Earth; the rest are made artificially in nuclear reactions. Roughly $17$ are non-metals, $7$ are commonly classed as metalloids, and the remaining $\sim 94$ are metals.

Compounds

A compound is a pure substance formed when atoms of two or more elements combine chemically in a fixed ratio. The resulting molecule is electrically neutral and has properties different from its constituent elements. Water, for instance, is a liquid at room temperature even though both hydrogen and oxygen are gases.

Mixtures

A mixture is an aggregate of two or more pure substances whose components retain their chemical identity and can be present in any ratio.

Homogeneous mixture: composition is uniform throughout. Every part looks and behaves the same. Examples: air, sugar dissolved in water, brass.
Heterogeneous mixture: composition varies from part to part; components can often be seen separately. Examples: soil, concrete, oil and water, sand mixed with iron filings.

6. Laws of Chemical Combination

Five experimental laws summarise how elements combine to form compounds. Together they were the launchpad for atomic theory.

6.1 Law of Conservation of Mass (Lavoisier, 1774)

In any chemical reaction, the total mass of the reactants equals the total mass of the products. Atoms are neither created nor destroyed in an ordinary chemical change.

Total mass of reactants $=$ total mass of products $+$ mass of unreacted reactants.

Solved Example 3

5.20 g

CaCO_{3}

on heating produces

1.99 g

CO_{2}

and a residue (CaO) weighing

3.20 g

. Show that these results illustrate the law of conservation of mass.

Solution:

Mass of reactant taken $= 5.20 g$ .

Total mass of products $= 3.20 + 1.99 = 5.19 g$ .

Difference $= 5.20 - 5.19 = 0.01 g$ , a tiny experimental error. Within measurement uncertainty, mass is conserved.

6.2 Law of Definite (Constant) Proportions (Proust, 1799)

A given chemical compound always contains the same elements combined in the same fixed proportion by mass, regardless of the source or method of preparation.

Carbon dioxide made by burning coal, by decomposing $CaCO_{3}$ , or by burning methane always has a carbon-to-oxygen mass ratio of $12 : 32 = 0.375$ .

$C + O_{2} \to CO_{2}$

$CaCO_{3} Δ CaO + CO_{2}$

$CH_{4} + 2 O_{2} \to CO_{2} + 2 H_{2} O$

6.3 Law of Multiple Proportions (Dalton, 1803)

When two elements combine to form more than one compound, the different masses of one element that combine with a fixed mass of the other bear a simple whole-number ratio to each other.

Carbon forms two oxides with oxygen:

Carbon monoxide: $12 g C + 16 g O \to CO$
Carbon dioxide: $12 g C + 32 g O \to CO_{2}$

For the same mass of carbon ( $12 g$ ), the masses of oxygen are $16 g$ and $32 g$ , in the ratio $1 : 2$ - a simple whole number ratio.

Solved Example 4

Which pair of compounds illustrates the law of multiple proportions?
(A) sodium chloride and sodium bromide
(B) water and heavy water
(C) sulphur dioxide and sulphur trioxide
(D) magnesium hydroxide and magnesium oxide

Solution:

Multiple proportions needs two compounds of the same two elements. Only option (C) fits: both $SO_{2}$ and $SO_{3}$ are made from S and O alone.

In $SO_{2}$ : $32 g$ of S combines with $32 g$ of O. In $SO_{3}$ : $32 g$ of S combines with $48 g$ of O. Ratio of oxygen masses (for fixed S) $= 32 : 48 = 2 : 3$ . Simple whole numbers, so the law is illustrated.

Answer: (C)

6.4 Law of Reciprocal Proportions (Richter, 1792)

If two elements B and C separately combine with a fixed mass of a third element A, then the ratio of masses of B and C that combine with each other (when they do) is the same as, or a simple multiple of, the ratio in which they combined with A.

Take C, S, and O. In $CO_{2}$ , $12 g$ of C combines with $32 g$ of O. In $SO_{2}$ , $32 g$ of S combines with $32 g$ of O. So the C : S ratio (for the same mass of O) is $12 : 32 = 3 : 8$ .

In carbon disulphide $CS_{2}$ : $12 g$ of C combines with $64 g$ of S, giving C : S $= 12 : 64 = 3 : 16$ .

The two ratios are $\frac{3}{8}$ and $\frac{3}{16}$ , so their ratio is $2 : 1$ - a simple multiple. This law is the basis of the concept of equivalent mass.

Solved Example 5

One part of element A combines with two parts of B. Six parts of element C combine with four parts of B. When A combines with C, which law governs the ratio of their masses?
(A) Definite proportions (B) Multiple proportions (C) Reciprocal proportions (D) Conservation of mass

Solution:

Element B plays the role of the third common element. Since A and C both combine with B, the A : C ratio follows from reciprocal proportions.

From A + B: $\frac{A}{B} = \frac{1}{2}$ . From C + B: $\frac{C}{B} = \frac{6}{4} = \frac{3}{2}$ . So $\frac{A}{C} = \frac{A}{B} \times \frac{B}{C} = \frac{1}{2} \times \frac{2}{3} = \frac{1}{3}$ .

Answer: (C)

6.5 Gay-Lussac's Law of Combining Volumes (1808)

When gases react, they do so in volumes that bear a simple whole-number ratio to each other and to the volumes of gaseous products, provided all volumes are measured at the same temperature and pressure.

Examples (volumes at same T and P):

$1 vol H_{2 (g)} + 1 vol Cl_{2 (g)} \to 2 vol 2 HCl_{(g)} [1 : 1 : 2]$

$2 vol 2 SO_{2} + 1 vol O_{2} \to 2 vol 2 SO_{3} [2 : 1 : 2]$

$2 vol 2 NH_{3} ⇌ 1 vol N_{2} + 3 vol 3 H_{2} [2 : 1 : 3]$

This law directly inspired Avogadro's hypothesis: equal volumes of all gases, at the same T and P, contain equal numbers of molecules.

7. Percentage Yield

Real reactions almost never give the amount of product predicted by a balanced equation. Reasons include:

Some reactant is left unreacted at the end.
Reactants follow a side pathway, giving unwanted by-products.
The product partially reverts to reactants (backward reaction).
Some product is lost during isolation or purification.

Percentage yield is the ratio of the actual (isolated) yield to the theoretical yield, expressed as a percent:

$% yield = \frac{actual yield}{theoretical yield} \times 100$

8. Dalton's Atomic Theory

By analysing the laws of chemical combination, John Dalton (1808) put forward an atomic theory of matter. Its main postulates:

Matter is made of extremely small, indivisible particles called atoms.
Atoms of the same element are identical in mass, size, and chemical behaviour.
Atoms of different elements have different masses, sizes, and properties.
Atoms are the smallest particles that participate in chemical reactions.
Atoms of different elements combine in fixed, simple, whole-number ratios to form compounds.
Atoms are neither created nor destroyed in a chemical reaction.

Limitations of Dalton's Theory

Atoms are no longer regarded as indivisible; they are made of subatomic particles (electrons, protons, neutrons).
It could not explain how atoms of different elements actually differ from one another (structural detail).
It did not explain the nature of the forces that hold atoms together in a molecule.
It did not explain Gay-Lussac's law of combining volumes.
It failed to distinguish between an atom (smallest particle taking part in reactions) and a molecule (smallest particle with independent existence).
It did not account for the existence of isotopes (same element, different mass) or isobars (different elements, same mass).

Modern Atomic Theory

An atom is no longer indivisible; it is made up of electrons, protons, and neutrons.
Atoms of the same element may not be identical in all respects (isotopes have different masses).
Atoms of different elements may share some property (isobars have the same mass number).
Atoms combine in ratios that are fixed and integral but not necessarily simple. In sucrose $C_{12} H_{22} O_{11}$ , the C : H : O ratio is $12 : 22 : 11$ .
Atoms of one element can be transmuted into atoms of another (radioactive decay, nuclear reactions).
Matter and energy are interconvertible via $E = m c^{2}$ , so atoms are not strictly indestructible.

Solved Example 6

Which of the following is an important postulate of Dalton's atomic theory?
(A) An atom contains electrons, protons, and neutrons.
(B) Atoms can neither be created nor destroyed and are indivisible.
(C) All atoms of an element are not identical.
(D) All elements exist in nature as free atoms.

Solution:

Statement (A) is from modern atomic theory (Dalton did not know about subatomic particles). Statements (C) and (D) contradict Dalton. Only (B) matches Dalton's original postulate.

Answer: (B)

9. Atom, Molecule, and Some Related Terms

Atom: the smallest electrically neutral particle of an element that shows its chemical properties. Made up of protons, neutrons, and electrons.

Molecule: the smallest particle of a substance (element or compound) that has an independent, stable existence. Examples:

H_{2}

O_{2}

N_{2}

HCl

CaCO_{3}

He

(monoatomic).

Noble gases like

He

Ne

Ar

exist as single atoms; each atom is also a molecule. Most other elemental gases (H, O, N, halogens) exist as diatomic molecules.

Common Mistakes to Avoid

Watch out

Confusing law of definite proportions with law of multiple proportions. Definite proportions is about one compound (same ratio every time). Multiple proportions is about two or more compounds of the same elements (simple whole-number ratios).
Writing $12 g C : 16 g O$ for $CO$ and then confusing it with $CO_{2}$ 's $12 : 32$ . Always fix mass of one element (usually the common one) before comparing.
Assuming Gay-Lussac's law applies to solids and liquids. It applies only to gases at the same T and P.
Forgetting that percentage yield uses actual yield in the numerator, not the other way around. Actual is always less than or equal to theoretical.
Counting a trailing zero in a whole number like $200$ as significant when it isn't marked. Use scientific notation ( $2.00 \times 1 0^{2}$ ) if you need to state 3 sig figs.
Treating $1 L atm$ as $1 J$ . It is actually $101.325 J$ ; always convert.

Frequently Asked Questions

What is the difference between a compound and a mixture?

A compound has a fixed composition by mass, its components lose their individual properties, and it can only be separated by chemical means. A mixture has a variable composition, its components retain their properties, and can be separated by physical methods like filtration or distillation.

Why is the law of conservation of mass not exactly true in nuclear reactions?

In nuclear reactions, a small amount of mass is converted into a large amount of energy according to $E = m c^{2}$ . In ordinary chemical reactions, the energy changes are so tiny that the mass change is undetectable, so the law holds. In nuclear fission or fusion, the mass loss is measurable, so strictly speaking mass-energy (not mass alone) is conserved.

How does Avogadro's hypothesis explain Gay-Lussac's law?

Avogadro proposed that equal volumes of gases at the same T and P contain equal numbers of molecules. So if $1$ volume of hydrogen reacts with $1$ volume of chlorine to give $2$ volumes of HCl, the number of molecules must also be in the ratio $1 : 1 : 2$ , which fits the balanced equation $H_{2} + Cl_{2} \to 2 HCl$ .

What is the difference between an atom and a molecule?

An atom is the smallest particle of an element that shows its chemical properties. A molecule is the smallest particle of a substance that can exist independently. Atoms of most elements do not exist freely; they combine to form molecules. For noble gases the atom and molecule are the same thing.

Why can percentage yield never exceed 100 percent?

Theoretical yield is the maximum possible product predicted by stoichiometry, assuming complete conversion. Actual yield can only be equal to or less than theoretical because of side reactions, losses, and reversibility. If a calculation gives more than 100 percent, either the actual mass includes impurities or the theoretical yield was mis-calculated.

Which laws of chemical combination are direct consequences of Dalton's atomic theory?

All of them. Conservation of mass follows because atoms are indestructible. Definite proportions and multiple proportions follow because atoms combine in fixed whole-number ratios. Reciprocal proportions is a consequence of atoms having a definite combining capacity. Gay-Lussac's law, however, was better explained later by Avogadro's hypothesis.

How many elements are in the modern periodic table?

As of the latest IUPAC updates, $118$ elements are officially recognised, ending at Oganesson ( $Og$ , atomic number $118$ ). Roughly $94$ occur naturally on Earth; elements beyond uranium (atomic number $92$ ) that are found in nature exist in trace amounts, and the transactinides are made in particle accelerators.

How many significant figures does $0.005080$ have?

Four. Leading zeros do not count, but the zero between $5$ and $8$ does, and the trailing zero to the right of the decimal is significant. Written in scientific notation as $5.080 \times 1 0^{- 3}$ , all four figures are visible.

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