Laws Of Chemical Combination

Two important laws of chemical combination were crucial in understanding how substances react and form compounds. These laws were formulated based on numerous experiments conducted by scientists like Antoine L. Lavoisier and Joseph L. Proust.

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Law Of Conservation Of Mass

This law deals with the relationship between the masses of reactants and products in a chemical reaction.

Statement: The Law of Conservation of Mass states that mass can neither be created nor destroyed in a chemical reaction.

In simpler terms, the total mass of the substances undergoing a chemical change (reactants) is equal to the total mass of the new substances formed (products). There is no net change in mass during a chemical reaction.

Experimental Illustration: Reacting solutions of substances, say X and Y (like copper sulphate and sodium carbonate), in a closed container (e.g., a conical flask with a cork). Weighing the flask and its contents *before* mixing the solutions gives the initial mass. After mixing and allowing the chemical reaction to occur, weighing the flask and contents *again* shows that the total mass remains the same. The cork is essential to ensure no substances or gases produced or consumed can escape or enter, thus maintaining a closed system.

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Law Of Constant Proportions

This law, also known as the Law of Definite Proportions, addresses the composition of chemical compounds.

Statement: Joseph L. Proust stated this law as: In a pure chemical substance, the elements are always present in definite proportions by mass, irrespective of the source or method of preparation of the compound.

This means that a specific chemical compound always contains the same elements combined in the same fixed ratio by mass. For example:

• Water (H₂O): The ratio of the mass of hydrogen to the mass of oxygen is always 1:8, regardless of whether the water is from a river, well, or prepared in a laboratory. If 9 grams of water are decomposed, it will always yield 1 gram of hydrogen and 8 grams of oxygen.
• Ammonia (NH₃): Nitrogen and hydrogen are always present in a fixed ratio of 14:3 by mass.

These laws formed the basis for the development of atomic theory, as scientists sought explanations for these consistent observations in chemical reactions.

What Is An Atom?

Just as buildings are constructed from bricks, or anthills from grains of sand, all matter is composed of fundamental building blocks called atoms.

The concept of atoms as the smallest particles of matter was revived and formalized by British chemist John Dalton in his atomic theory, which built upon the ideas of earlier philosophers and provided explanations for the laws of chemical combination.

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How Big Are Atoms?

Atoms are incredibly tiny particles, far smaller than anything we can observe with our naked eyes or even compare easily to everyday objects. Stacking millions of atoms would only create a layer as thin as a sheet of paper.

The size of an atom is typically measured by its atomic radius, expressed in nanometres (nm). One nanometre is one billionth of a metre: $1 \text{ nm} = 10^{-9} \text{ m}$, or $1 \text{ m} = 10^9 \text{ nm}$.

To put atomic sizes into perspective:

Radii (in m)	Example
$10^{-10}$	Atom of hydrogen
$10^{-9}$	Molecule of water
$10^{-8}$	Molecule of haemoglobin
$10^{-4}$	Grain of sand
$10^{-3}$	Ant
$10^{-1}$	Apple

Even though individual atoms are invisible to the naked eye, their presence constantly affects the world around us. Modern scientific techniques, like scanning tunnelling microscopy (STM), can produce magnified images of material surfaces, allowing us to visualize the arrangement of atoms.

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What Are The Modern Day Symbols Of Atoms Of Different Elements?

Early attempts to represent elements used symbols proposed by John Dalton, which also implied a specific quantity (one atom) of the element.

Later, Jöns Jacob Berzelius suggested using one or two letters from the element's name as its symbol, which is the basis for the modern system.

The International Union of Pure and Applied Chemistry (IUPAC) is the global authority responsible for approving the names, symbols, and units for elements. Current chemical symbols are standardized according to IUPAC guidelines.

Rules for Writing Chemical Symbols:

1. Symbols are typically derived from the English name of the element.
2. If the symbol has one letter, it is always written in uppercase (e.g., H for Hydrogen, O for Oxygen, N for Nitrogen).
3. If the symbol has two letters, the first letter is always uppercase, and the second letter is always lowercase (e.g., Al for Aluminium, Co for Cobalt, Zn for Zinc). It is important to use the correct case (e.g., Co is Cobalt, CO is Carbon Monoxide, a compound).

Some symbols are derived from the element's name in Latin, German, or Greek to avoid confusion or historical reasons (e.g., Fe for Iron from 'ferrum', Na for Sodium from 'natrium', K for Potassium from 'kalium').

Each element is assigned a unique name and a unique chemical symbol.

Element	Symbol	Element	Symbol	Element	Symbol
Aluminium	Al	Copper	Cu	Nitrogen	N
Argon	Ar	Fluorine	F	Oxygen	O
Barium	Ba	Gold	Au	Potassium	K
Boron	B	Hydrogen	H	Silicon	Si
Bromine	Br	Iodine	I	Silver	Ag
Calcium	Ca	Iron	Fe	Sodium	Na
Carbon	C	Lead	Pb	Sulphur	S
Chlorine	Cl	Magnesium	Mg	Uranium	U
Cobalt	Co	Neon	Ne	Zinc	Zn

(This table serves as a reference; memorizing all symbols immediately is not necessary and will happen with practice.)

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Atomic Mass

Dalton's atomic theory introduced the crucial concept that each element has a characteristic atomic mass. This concept was vital for explaining the laws of chemical combination.

Measuring the mass of a single atom is extremely difficult. Therefore, scientists developed the concept of relative atomic mass, comparing the mass of an atom of an element to the mass of a standard reference atom.

Initially, 1/16th of the mass of an oxygen atom was used as the reference unit because oxygen forms compounds with many elements, and this choice often resulted in whole number or near-whole number relative masses for other elements.

Since 1961, the universally accepted standard for measuring atomic masses is the Carbon-12 isotope. One atomic mass unit (u), also known as unified mass, is defined as exactly one-twelfth (1/12th) the mass of one atom of carbon-12.

The relative atomic mass of an atom of an element is the average mass of the atom compared to 1/12th the mass of a carbon-12 atom.

Analogy: Imagine a fruit seller uses a watermelon as a standard. He assigns the watermelon a mass of 12 units (watermelon units). He cuts it into 12 equal pieces and uses one piece as his relative mass unit (1/12th of a watermelon unit). He can then weigh other fruits relative to this small piece.

Similarly, atomic masses of elements are expressed as relative masses compared to the 1/12th mass of a carbon-12 atom.

Element	Atomic Mass (u)
Hydrogen	1
Carbon	12
Nitrogen	14
Oxygen	16
Sodium	23
Magnesium	24
Sulphur	32
Chlorine	35.5
Calcium	40

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How Do Atoms Exist?

Atoms of most elements are not stable enough to exist freely and independently under normal conditions. Instead, they usually combine with other atoms to form molecules or ions.

These molecules and ions then aggregate in large numbers to form the matter that constitutes everything we can see, feel, or touch.

What Is A Molecule?

A molecule is generally defined as a group of two or more atoms that are held together by strong attractive forces called chemical bonds. These atoms can be of the same element or different elements.

A molecule is considered the smallest particle of an element or a compound that is capable of existing independently under ordinary conditions. It retains all the characteristic properties of that substance.

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Molecules Of Elements

Molecules of elements are made up of atoms of the same type.

Some elements exist as individual atoms (e.g., noble gases like Argon (Ar), Helium (He)). Their molecules consist of just one atom; they are called monoatomic.

Most non-metals and some other elements exist as molecules containing multiple atoms.

The number of atoms present in one molecule of an element is called its atomicity.

• Diatomic: Molecules containing two atoms (e.g., O₂, H₂, N₂, Cl₂).
• Tetra-atomic: Molecules containing four atoms (e.g., P₄).
• Poly-atomic: Molecules containing more than four atoms (e.g., S₈).

Metals (like Iron, Copper) and some other elements (like Carbon) generally do not exist as simple molecules in their solid state. They form large structures where a vast, indefinite number of atoms are bonded together.

Type of Element	Name	Atomicity
Non-Metal	Argon	Monoatomic
	Helium	Monoatomic
	Oxygen	Diatomic
	Hydrogen	Diatomic
	Nitrogen	Diatomic
	Chlorine	Diatomic
	Phosphorus	Tetra-atomic
	Sulphur	Poly-atomic

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Molecules Of Compounds

Molecules of compounds are formed when atoms of different elements combine chemically in definite proportions based on mass. These fixed mass ratios result in a fixed ratio of the number of atoms of each element in the compound molecule.

Compound	Combining Elements	Ratio by Mass
Water (H₂O)	Hydrogen, Oxygen	1:8
Ammonia (NH₃)	Nitrogen, Hydrogen	14:3
Carbon dioxide (CO₂)	Carbon, Oxygen	3:8

We can determine the ratio by the number of atoms in a molecule from the ratio by mass and the atomic masses of the elements.

Example: Finding the ratio of atoms in Water (H₂O):

The ratio by mass of Hydrogen to Oxygen in water is 1:8.

Atomic mass of Hydrogen = 1 u

Atomic mass of Oxygen = 16 u

To find the ratio by number of atoms, we divide the mass ratio of each element by its atomic mass:

• For Hydrogen: $\frac{\text{Mass ratio of H}}{\text{Atomic mass of H}} = \frac{1}{1} = 1$
• For Oxygen: $\frac{\text{Mass ratio of O}}{\text{Atomic mass of O}} = \frac{8}{16} = \frac{1}{2}$

The ratio by number of atoms H:O is $1 : \frac{1}{2}$. To get a simple whole number ratio, multiply by 2: $1 \times 2 : \frac{1}{2} \times 2 = 2 : 1$.

Thus, the ratio by number of atoms for water is H:O = 2:1, meaning a water molecule contains 2 hydrogen atoms and 1 oxygen atom, hence the formula H₂O.

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What Is An Ion?

Compounds formed between metals and non-metals typically do not consist of molecules but of charged particles called ions.

An ion is an atom or a group of atoms that has gained or lost electrons, resulting in a net electrical charge.

• A positively charged ion is called a cation (formed by losing electrons).
• A negatively charged ion is called an anion (formed by gaining electrons).

For example, Sodium Chloride (NaCl) is made up of positively charged sodium ions (Na⁺) and negatively charged chloride ions (Cl⁻).

A group of atoms carrying a net charge is known as a polyatomic ion (e.g., Sulphate ion, SO₄²⁻; Ammonium ion, NH₄⁺). Polyatomic ions behave as single units with a fixed charge.

Valency	Name of ion	Symbol	Non-metallic element	Symbol	Polyatomic ions	Symbol
1	Sodium	Na⁺	Hydrogen	H⁻ (Hydride)	Ammonium	NH₄⁺
	Potassium	K⁺	Chloride	Cl⁻	Hydroxide	OH⁻
	Silver	Ag⁺	Bromide	Br⁻	Nitrate	NO₃⁻
	Copper (I)*	Cu⁺	Iodide	I⁻	Hydrogen carbonate	HCO₃⁻
2	Magnesium	Mg²⁺	Oxide	O²⁻	Carbonate	CO₃²⁻
	Calcium	Ca²⁺	Sulphide	S²⁻	Sulphite	SO₃²⁻
	Zinc	Zn²⁺			Sulphate	SO₄²⁻
	Iron (II)*	Fe²⁺
	Copper (II)*	Cu²⁺
3	Aluminium	Al³⁺	Nitride	N³⁻	Phosphate	PO₄³⁻
	Iron (III)*	Fe³⁺
* Some elements exhibit multiple valencies, indicated by a Roman numeral in parentheses (e.g., Copper(I) has valency 1, Copper(II) has valency 2).

Writing Chemical Formulae

A chemical formula is a concise, symbolic representation of the composition of a chemical compound. It shows the elements present in the compound and the relative number of atoms (or ions) of each element.

Writing chemical formulae requires knowing the symbols of the elements and their valencies.

Valency: The combining power or capacity of an element or ion. It represents the number of bonds an atom can form or the charge on an ion.

Analogy: If Hydrogen atoms (H) have 1 arm and Oxygen atoms (O) have 2 arms, then one Oxygen atom needs 2 Hydrogen atoms to satisfy all its arms, forming H₂O. Similarly, if an octopus (O) has 8 arms and humans (H) have 2 arms, one octopus can hold 4 humans ($8 \div 2 = 4$), leading to a hypothetical formula like OH₄ (where the subscript indicates the number of entities attached).

The valency of an element helps predict how its atoms will combine with atoms of other elements to form a compound.

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Formulae Of Simple Compounds

The simplest compounds, made up of only two different elements, are called binary compounds.

To write the chemical formula of a binary compound:

1. Write the symbols of the constituent elements (or ions). For compounds of metals and non-metals, the metal symbol is written first.
2. Write the valency (or charge magnitude) of each element/ion just below its symbol.
3. Criss-cross the valencies (swap them) and write them as subscripts to the symbol of the other element/ion. Ignore the positive or negative signs of charges during the criss-crossing.
4. Simplify the subscripts to the smallest whole number ratio if possible.
5. If a polyatomic ion is involved and needs a subscript greater than 1, enclose the formula of the polyatomic ion in brackets before writing the subscript.

General Criss-Cross Method for Binary Compounds:

Let A and B be two elements, with valencies a and b respectively.

The formula becomes A$_{b}$B$_{a}$.

Examples of Writing Chemical Formulae:

1. Hydrogen chloride:

Formula: HCl (Since subscripts are 1, they are omitted).

2. Hydrogen sulphide:

Formula: H₂S

3. Carbon tetrachloride:

Formula: CCl₄

4. Magnesium chloride (Ionic Compound):

Magnesium ion is Mg²⁺ (charge +2, valency 2), Chloride ion is Cl⁻ (charge -1, valency 1).

Formula: MgCl₂ (Need two Cl⁻ ions to balance one Mg²⁺ ion; total charge $1 \times (+2) + 2 \times (-1) = 0$). Note that charges are not shown in the final formula.

5. Aluminium oxide (Ionic Compound):

Aluminium ion is Al³⁺ (valency 3), Oxide ion is O²⁻ (valency 2).

Formula: Al₂O₃ (Need two Al³⁺ ions and three O²⁻ ions; total charge $2 \times (+3) + 3 \times (-2) = 6 - 6 = 0$).

6. Calcium oxide (Ionic Compound):

Calcium ion is Ca²⁺ (valency 2), Oxide ion is O²⁻ (valency 2).

Applying criss-cross gives Ca₂O₂. Since the subscripts are in a 2:2 ratio, they are simplified to the smallest whole number ratio, 1:1.

Formula: CaO

7. Sodium nitrate (Compound with Polyatomic Ion):

Sodium ion is Na⁺ (valency 1), Nitrate ion is NO₃⁻ (charge -1, valency 1).

Formula: NaNO₃ (Since only one polyatomic ion is needed, brackets are not used).

8. Calcium hydroxide (Compound with Polyatomic Ion):

Calcium ion is Ca²⁺ (valency 2), Hydroxide ion is OH⁻ (charge -1, valency 1).

Formula: Ca(OH)₂ (Since more than one OH⁻ ion is needed (two), the polyatomic ion OH is enclosed in brackets before writing the subscript 2).

9. Sodium carbonate (Compound with Polyatomic Ion):

Sodium ion is Na⁺ (valency 1), Carbonate ion is CO₃²⁻ (charge -2, valency 2).

Formula: Na₂CO₃ (Since only one CO₃²⁻ ion is needed, brackets are not used).

10. Ammonium sulphate (Compound with Polyatomic Ions):

Ammonium ion is NH₄⁺ (charge +1, valency 1), Sulphate ion is SO₄²⁻ (charge -2, valency 2).

Formula: (NH₄)₂SO₄ (Since more than one NH₄⁺ ion is needed (two), the polyatomic ion NH₄ is enclosed in brackets before writing the subscript 2. Only one SO₄²⁻ is needed, so brackets are not required for SO₄).

Key Rules for Writing Chemical Formulae:

• The total positive and negative charges must balance, resulting in a neutral compound.
• The symbol/name of the metal (cation) is written first, followed by the non-metal (anion) in compounds containing both.
• For compounds with polyatomic ions, use brackets around the polyatomic ion's formula if more than one ion unit is required in the chemical formula.

Molecular Mass And Mole Concept

While atomic mass provides the mass of individual atoms, we often work with aggregates of atoms, like molecules or ionic compounds. Concepts like molecular mass, formula unit mass, and the mole help us quantify amounts of substances.

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Molecular Mass

The molecular mass of a substance is the sum of the atomic masses of all the atoms present in one molecule of that substance. It is expressed in atomic mass units (u).

To calculate molecular mass, you add up the atomic masses of all the atoms shown in the molecule's chemical formula.

Answer:

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Formula Unit Mass

For substances whose constituent particles are ions (like ionic compounds such as NaCl, CaCl₂), the term formula unit mass is used instead of molecular mass. It is the sum of the atomic masses of all atoms in a formula unit of the compound.

The calculation of formula unit mass is done exactly the same way as molecular mass, by summing the atomic masses according to the compound's formula.

For example, the formula unit of Sodium Chloride is NaCl. Its formula unit mass is:

(1 $\times$ Atomic mass of Na) + (1 $\times$ Atomic mass of Cl) = (1 $\times$ 23 u) + (1 $\times$ 35.5 u) = 23 u + 35.5 u = 58.5 u.

Answer:

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Mole Concept

Chemical reactions involve the combination of atoms and molecules. Since individual atoms and molecules are exceedingly small and numerous, chemists use a convenient unit for counting them: the mole.

The mole (symbol: mol) is the SI unit for the amount of substance.

One mole of any substance contains a fixed number of elementary entities (atoms, molecules, ions, electrons, etc.). This number is called the Avogadro number or Avogadro constant (N_A).

1 mole = 6.022 $\times 10^{23}$ elementary entities.

This number is analogous to common counting units like a dozen (12 items) or a gross (144 items), but for the incredibly large quantities of particles in chemistry.

A key advantage of the mole is that it links the number of particles to a measurable mass.

The molar mass of a substance is the mass of 1 mole of that substance. It is numerically equal to the atomic mass, molecular mass, or formula unit mass, but the unit is grams (g) instead of atomic mass units (u).

• For atoms, molar mass is the gram atomic mass. Example: Atomic mass of Hydrogen is 1 u, so molar mass of Hydrogen atoms is 1 g/mol. 1 u Hydrogen contains 1 atom; 1 g Hydrogen contains 1 mole ($6.022 \times 10^{23}$) atoms.
• For molecules, molar mass is the gram molecular mass. Example: Molecular mass of water (H₂O) is 18 u, so molar mass of water is 18 g/mol. 18 u water contains 1 molecule; 18 g water contains 1 mole ($6.022 \times 10^{23}$) molecules.

The mole concept allows chemists to work with measurable masses in grams while understanding the number of atoms or molecules involved in chemical processes.

Converting between Mass, Moles, and Number of Particles:

• Number of moles ($n$) = $\frac{\text{Given mass } (m)}{\text{Molar mass } (M)}$
• Number of moles ($n$) = $\frac{\text{Given number of particles } (N)}{\text{Avogadro number } (N_A)}$
• Given mass ($m$) = Number of moles ($n$) $\times$ Molar mass ($M$)
• Given number of particles ($N$) = Number of moles ($n$) $\times$ Avogadro number ($N_A$)

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