Importance Of Chemistry

Science is a human endeavor to understand and describe nature by systematizing knowledge. Chemistry is a specific branch of science focused on the study of the preparation, properties, structure, and reactions of material substances.

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Development Of Chemistry

Modern chemistry is a relatively recent discipline. Historically, its development was driven by quests for the Philosopher's stone (to turn base metals into gold) and the Elixir of life (to grant immortality). Ancient civilizations, including India and China, had sophisticated alchemical traditions encompassing knowledge of various chemical processes and techniques.

In ancient India, chemistry was known by names like Rasayan Shastra and Rasvidya. It included practical applications such as metallurgy, medicine, manufacturing of cosmetics, glass, and dyes. Archaeological evidence from sites like Mohenjodaro and Harappa indicates advanced chemical processes were in use, such as making baked bricks, pottery, glazed pottery, and gypsum cement.

Indians in ancient times also mastered metalworking with lead, silver, gold, and copper, improving copper's hardness with tin and arsenic. Glass manufacturing and coloring using metal oxides were also known.

Texts like Rigveda mention leather tanning and cotton dyeing (1000–400 BCE). The Sushruta Samhita discusses alkalies, while the Charaka Samhita describes the preparation of sulfuric acid, nitric acid, metal oxides (copper, tin, zinc), sulfates (copper, zinc, iron), and carbonates (lead, iron).

The Rasopanishada details gunpowder preparation, and Tamil texts describe fireworks using sulfur, charcoal, saltpetre (potassium nitrate), mercury, camphor, etc.

Notable Indian figures include:

• Nagarjuna: A chemist, alchemist, and metallurgist whose work Rasratnakar focused on mercury compounds and metal extraction methods.
• Rsarnavam (around 800 CE): Described furnaces, ovens, crucibles, and metal identification by flame color.
• Chakrapani: Credited with discovering mercury sulfide and inventing soap using mustard oil and alkalies.

Ancient Indian knowledge extended to materials for building (Brihat Samhita), dyes (Atharvaveda mentioning turmeric, madder, etc.), perfumes and cosmetics (Brihat Samhita, Gandhayukli), paper (17th century), ink (4th century), and fermentation (Vedas, Arthashastra, Charaka Samhita).

The concept of matter being made of indivisible particles also originated in ancient India with Acharya Kanda (600 BCE), known as Kashyap. He proposed the 'atomic theory,' calling the indivisible particles 'Paramanu' – eternal, indestructible, spherical, suprasensible, and in motion. He suggested varieties of atoms exist and combine in pairs or triplets due to unseen forces, theorizing this about 2500 years before John Dalton.

The Charaka Samhita also discussed reducing metal particle size, a concept related to modern nanotechnology, describing the use of metal bhasmas (ashes) for treatments, which are now known to contain metal nanoparticles.

Modern chemistry gained traction in India in the late 19th century with the arrival of European scientists, leading to a decline in traditional practices due to foreign imports.

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Role Of Chemistry

Chemistry is fundamental to science, connecting various disciplines. Its principles are applied widely in:

• Understanding natural phenomena like weather, brain function, and computer operation.
• Industrial production of fertilizers, acids, bases, salts, dyes, polymers, drugs, soaps, detergents, metals, alloys, and new materials.

Chemistry significantly contributes to the economy and human well-being by:

• Improving food production through better fertilizers, pesticides, and insecticides.
• Providing healthcare solutions by isolating and synthesizing life-saving drugs (e.g., Cisplatin and Taxol for cancer, AZT for AIDS).
• Enabling the design of materials with specific properties, leading to superconducting ceramics, conducting polymers, and optical fibers.
• Helping establish industries that produce essential utility goods, creating jobs and boosting the economy.

Chemistry also addresses environmental issues. For instance, chemists synthesized safer alternatives to CFCs, which depleted the ozone layer. However, challenges like managing greenhouse gases (methane, carbon dioxide) remain. Future chemists face intellectual challenges in biochemical processes, enzyme use for chemical production, and synthesizing exotic materials.

To tackle these challenges, a strong understanding of basic chemical concepts is essential, starting with the concept of matter.

Nature Of Matter

Matter is defined as anything that has mass and occupies space. Everything visible around us, from a book to the air we breathe, is composed of matter.

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States Of Matter

Matter exists in three common physical states: solid, liquid, and gas. These states differ based on how the constituent particles are arranged and their freedom of movement.

Particle Arrangement:

• Solids: Particles are packed very closely in an ordered, rigid arrangement, with limited movement (vibrations about fixed positions).
• Liquids: Particles are still close but can move past each other, allowing the substance to flow.
• Gases: Particles are far apart and move randomly and rapidly, occupying the entire available volume.

Characteristic Properties:

• Solids: Have a definite volume and a definite shape.
• Liquids: Have a definite volume but no definite shape; they take the shape of their container.
• Gases: Have neither definite volume nor definite shape; they fill the entire container they occupy.

These states are interconvertible by changing temperature and pressure. Heating a solid turns it into a liquid (melting), and further heating turns the liquid into a gas (boiling/vaporization). Cooling a gas turns it into a liquid (condensation), and further cooling turns the liquid into a solid (freezing).

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Classification Of Matter

At a macroscopic level, matter can be broadly classified into mixtures and pure substances.

Pure Substances:

• Consist of particles that are all the same in chemical nature.
• Have a fixed composition.
• Their constituents cannot be separated by simple physical methods.
• Examples: Copper, silver, gold, water, glucose.

Pure substances are further divided into:

• Elements: Particles consist of only one type of atom. Atoms of different elements are distinct.
  • May exist as individual atoms (e.g., Sodium, Copper).
  • May exist as molecules formed by two or more atoms of the same element (e.g., H₂, N₂, O₂ molecules are formed by two atoms).
• Compounds: Formed when atoms of two or more different elements combine in a definite ratio.
  • Have a fixed composition.
  • Properties are typically very different from their constituent elements (e.g., Hydrogen gas burns, Oxygen gas supports combustion, but Water, H₂O, is a liquid used to extinguish fires).
  • Constituents can only be separated by chemical methods.
  • Examples: Water (H₂O), Ammonia (NH₃), Carbon dioxide (CO₂). A molecule of water has 2 H atoms and 1 O atom; a molecule of carbon dioxide has 1 C atom and 2 O atoms.

Mixtures:

• Contain particles of two or more pure substances (called components).
• The components can be present in any ratio, so their composition is variable.
• Components can be separated by physical methods (e.g., hand-picking, filtration, crystallization, distillation).
• Examples: Sugar solution in water, air, tea, salt and sugar mixture.

Mixtures are classified into:

• Homogeneous Mixtures:
  • Components completely mix with each other.
  • Particles are uniformly distributed throughout the mixture.
  • Composition is uniform throughout.
  • Examples: Sugar solution, air.
• Heterogeneous Mixtures:
  • Composition is not uniform throughout.
  • Different components are often visible separately.
  • Examples: Mixture of salt and sugar, grains and pulses with dirt/stones.

Properties Of Matter And Their Measurement

Each substance possesses unique characteristics called properties. These are categorized into physical and chemical properties.

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Physical And Chemical Properties

Physical Properties:

• Can be measured or observed without changing the chemical identity or composition of the substance.
• Examples: Color, odor, melting point, boiling point, density.

Chemical Properties:

• Require a chemical change to occur during measurement or observation.
• Describe how a substance reacts or changes into other substances.
• Examples: Composition, combustibility, reactivity with acids or bases, acidity, basicity.

Chemists use both physical and chemical properties, determined by careful measurement and experimentation, to understand and predict the behavior of substances.

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Measurement Of Physical Properties

Quantitative measurement is crucial in scientific investigations. Any measurement consists of two parts: a number and a unit. For example, 6 meters ($6 \text{ m}$) means the quantity is 6 and the unit is meters.

Historically, different measurement systems like the English System and the Metric System were used. The decimal-based Metric System was more convenient. Eventually, the need for a universal standard led to the establishment of the International System of Units (SI) in 1960.

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The International System Of Units (Si)

The SI system (Le Système International d’Unités) was established by the General Conference on Weights and Measures (CGPM). It is based on seven fundamental base units representing seven basic physical quantities.

These base units are precisely defined and serve as the foundation for deriving other units (e.g., speed, volume, density). National Metrology Institutes (like NPL in India) maintain these standards, which are periodically compared internationally.

Base Physical Quantity	Symbol for Quantity	Name of SI Unit	Symbol for SI Unit
Length	$l$	metre	m
Mass	$m$	kilogram	kg
Time	$t$	second	s
Electric current	$I$	ampere	A
Thermodynamic temperature	$T$	kelvin	K
Amount of substance	$n$	mole	mol
Luminous intensity	$I_v$	candela	cd

The definitions of these base units are highly precise, based on fundamental constants or properties of nature (e.g., speed of light for meter, caesium frequency for second, Planck constant for kilogram, Avogadro constant for mole).

The SI system also uses prefixes to denote multiples or submultiples of units, making it easier to express very large or very small values.

Multiple	Prefix	Symbol
$10^{24}$	yotta	Y
$10^{21}$	zeta	Z
$10^{18}$	exa	E
$10^{15}$	peta	P
$10^{12}$	tera	T
$10^9$	giga	G
$10^6$	mega	M
$10^3$	kilo	k
$10^2$	hecto	h
$10^1$	deca	da
$10^{-1}$	deci	d
$10^{-2}$	centi	c
$10^{-3}$	milli	m
$10^{-6}$	micro	μ
$10^{-9}$	nano	n
$10^{-12}$	pico	p
$10^{-15}$	femto	f
$10^{-18}$	atto	a
$10^{-21}$	zepto	z
$10^{-24}$	yocto	y

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Mass And Weight

Mass is the measure of the amount of matter in a substance. It is a fundamental property and remains constant regardless of location.

Weight is the force exerted by gravity on an object. It can vary depending on the local gravitational acceleration.

In laboratories, mass is accurately determined using an analytical balance.

The SI unit of mass is the kilogram (kg). For convenience in chemistry labs, the gram (g) is often used, where $1 \text{ kg} = 1000 \text{ g}$.

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Volume

Volume is the amount of space occupied by a substance. Its units are derived from length units, e.g., $(\text{length})^3$. The SI unit for volume is cubic meter ($m^3$).

In chemistry, smaller volumes are common, so units like cubic centimeter ($\text{cm}^3$) and cubic decimeter ($\text{dm}^3$) are frequently used.

A common non-SI unit for liquid volume is the liter (L).

The relationships between these units are:

$$1 \text{ L} = 1000 \text{ mL}$$ $$1000 \text{ cm}^3 = 1 \text{ dm}^3$$ $$1 \text{ L} = 1 \text{ dm}^3$$ $$1 \text{ mL} = 1 \text{ cm}^3$$

Volume of liquids is measured using graduated cylinders, burettes, and pipettes. Volumetric flasks are used for preparing solutions with precise volumes.

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Density

Density is an intrinsic property of a substance defined as its mass per unit volume.

The formula is: $D = \frac{\text{Mass}}{\text{Volume}}$.

The SI unit of density is kilogram per cubic meter ($kg \text{ m}^{-3}$). Chemists often use gram per cubic centimeter ($g \text{ cm}^{-3}$) or gram per milliliter ($g \text{ mL}^{-1}$) for convenience.

Density provides insight into how closely particles are packed; higher density indicates closer packing.

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Temperature

Temperature is a measure of the degree of hotness or coldness of an object. There are three common scales for measuring temperature:

• Celsius scale (°C): Water freezes at 0°C and boils at 100°C (at standard atmospheric pressure).
• Fahrenheit scale (°F): Water freezes at 32°F and boils at 212°F.
• Kelvin scale (K): This is the SI unit of temperature. It is an absolute scale where 0 K is absolute zero.

Relationships between the scales:

Celsius to Fahrenheit: $^\circ\text{F} = \frac{9}{5}(^\circ\text{C}) + 32$

Celsius to Kelvin: $\text{K} = ^\circ\text{C} + 273.15$

A key difference is that negative temperatures are possible on the Celsius and Fahrenheit scales, but not on the Kelvin scale, which starts from absolute zero (0 K).

Uncertainty In Measurement

Scientific measurements always involve some degree of uncertainty due to limitations of measuring instruments and the skill of the person performing the measurement. Proper handling and representation of this uncertainty are crucial.

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Scientific Notation

Chemistry often deals with extremely large or small numbers (e.g., number of atoms in a sample, mass of an electron). To manage these numbers conveniently, scientific notation (exponential notation) is used.

A number in scientific notation is expressed in the form $N \times 10^n$, where:

• $N$ is the digit term (a number between 1.000... and 9.999...).
• $n$ is the exponent (a positive or negative integer).

Example:

• $232.508$ is written as $2.32508 \times 10^2$ (decimal moved 2 places left, exponent is +2).
• $0.00016$ is written as $1.6 \times 10^{-4}$ (decimal moved 4 places right, exponent is -4).

Mathematical Operations with Scientific Notation:

Multiplication and Division: Exponents are added during multiplication and subtracted during division, while digit terms are multiplied or divided normally.

$(5.6 \times 10^5) \times (6.9 \times 10^8) = (5.6 \times 6.9) \times 10^{(5+8)} = 38.64 \times 10^{13} = 3.864 \times 10^{14}$

$(9.8 \times 10^{-2}) \div (2.5 \times 10^{-6}) = (9.8 \div 2.5) \times 10^{(-2 - (-6))} = 3.92 \times 10^{(-2+6)} = 3.92 \times 10^4$

Addition and Subtraction: Numbers must have the same exponent before adding or subtracting the digit terms.

$(6.65 \times 10^4) + (8.95 \times 10^3) = (6.65 \times 10^4) + (0.895 \times 10^4) = (6.65 + 0.895) \times 10^4 = 7.545 \times 10^4$

$(2.5 \times 10^{-2}) - (4.8 \times 10^{-3}) = (2.5 \times 10^{-2}) - (0.48 \times 10^{-2}) = (2.5 - 0.48) \times 10^{-2} = 2.02 \times 10^{-2}$

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Significant Figures

Significant figures are the meaningful digits in a measured number. They include all digits known with certainty plus one estimated or uncertain digit. The uncertainty is typically understood to be $\pm 1$ in the last significant digit.

For example, a measurement of $11.2 \text{ mL}$ means the 11 is certain, and the 2 is uncertain (could be 11.1 or 11.3).

Rules for Determining Significant Figures:

1. All non-zero digits are significant. (e.g., $285 \text{ cm}$ has 3 s.f., $0.25 \text{ mL}$ has 2 s.f.).
2. Zeros preceding the first non-zero digit are NOT significant. They only indicate the decimal point's position. (e.g., $0.03$ has 1 s.f., $0.0052$ has 2 s.f.).
3. Zeros between two non-zero digits ARE significant. (e.g., $2.005$ has 4 s.f.).
4. Zeros at the end or right of a number ARE significant if they are after the decimal point. (e.g., $0.200 \text{ g}$ has 3 s.f., $100.0$ has 4 s.f.).
5. Terminal zeros are NOT significant if there is no decimal point. (e.g., $100$ has 1 s.f.). Scientific notation helps clarify this: $1 \times 10^2$ (1 s.f.), $1.0 \times 10^2$ (2 s.f.), $1.00 \times 10^2$ (3 s.f.).
6. Exact numbers (from counting or definitions) have infinite significant figures. (e.g., 2 balls, 20 eggs, $1 \text{ inch} = 2.54 \text{ cm}$).

In scientific notation ($N \times 10^n$), all digits in the digit term ($N$) are significant figures.

Precision and Accuracy:

• Precision refers to the closeness of agreement between multiple measurements of the same quantity.
• Accuracy refers to the agreement of a measured value to the true or accepted value.

Measurements can be precise but not accurate, accurate but not precise (less common), neither precise nor accurate, or both precise and accurate.

Student	Measurement 1 (g)	Measurement 2 (g)	Average (g)	Evaluation (True Value = 2.00 g)
A	1.95	1.93	1.940	Precise, but not accurate
B	1.94	2.05	1.995	Neither precise nor accurate
C	2.01	1.99	2.000	Both precise and accurate

Calculations with Significant Figures:

The result of a calculation should reflect the uncertainty of the measurements used.

• Addition and Subtraction: The result should have no more decimal places than the number with the fewest decimal places.

  Example: $12.11 + 18.0 + 1.012 = 31.122$. Since $18.0$ has only one decimal place, the result is rounded to $31.1$.

• Multiplication and Division: The result should have no more significant figures than the number with the fewest significant figures used in the calculation.

  Example: $2.5 \times 1.25 = 3.125$. Since $2.5$ has two significant figures, the result is rounded to $3.1$.

Rounding Off Numbers:

When rounding a number to the required number of significant figures:

1. If the digit to be removed is greater than 5, increase the preceding digit by one (e.g., $1.386$ rounded to 3 s.f. becomes $1.39$).
2. If the digit to be removed is less than 5, the preceding digit remains unchanged (e.g., $4.334$ rounded to 3 s.f. becomes $4.33$).
3. If the digit to be removed is exactly 5:
   • If the preceding digit is even, it remains unchanged (e.g., $6.25$ rounded to 2 s.f. becomes $6.2$).
   • If the preceding digit is odd, it is increased by one (e.g., $6.35$ rounded to 2 s.f. becomes $6.4$).

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Dimensional Analysis

Dimensional analysis (also known as the factor label method or unit factor method) is a technique used to convert units from one system to another by using conversion factors.

A conversion factor is a ratio derived from an equality between different units (e.g., $1 \text{ in} = 2.54 \text{ cm}$) that is equal to one. These factors can be written as $\frac{2.54 \text{ cm}}{1 \text{ in}}$ or $\frac{1 \text{ in}}{2.54 \text{ cm}}$. Multiplying a quantity by a conversion factor doesn't change its value, only its units.

The correct conversion factor is chosen so that the original unit cancels out, leaving the desired unit.

Answer:

Answer:

Answer:

Dimensional analysis allows units to be treated like algebraic quantities that can be cancelled.

Laws Of Chemical Combinations

The formation of compounds from elements follows several fundamental laws, established based on experimental observations.

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Law Of Conservation Of Mass

Proposed by Antoine Lavoisier in 1789.

Statement: Matter can neither be created nor destroyed.

This means that in any physical or chemical change, the total mass of the reactants before the change is equal to the total mass of the products after the change. Lavoisier's precise measurements of masses in combustion reactions supported this law.

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Law Of Definite Proportions

Given by French chemist Joseph Proust.

Statement: A given compound always contains exactly the same proportion of elements by weight (mass), regardless of its source or method of preparation.

Proust's work on cupric carbonate samples (natural and synthetic) showed the percentage composition of copper, carbon, and oxygen was identical in both cases. This law is also known as the Law of Definite Composition.

Sample	% of Copper	% of Carbon	% of Oxygen
Natural	51.35	9.74	38.91
Synthetic	51.35	9.74	38.91

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Law Of Multiple Proportions

Proposed by John Dalton in 1803.

Statement: If two elements can combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element are in a ratio of small whole numbers.

Example: Carbon and oxygen can form Carbon Monoxide (CO) and Carbon Dioxide (CO₂).

• In CO, 12 g of Carbon combines with 16 g of Oxygen.
• In CO₂, 12 g of Carbon combines with 32 g of Oxygen.

With a fixed mass of Carbon (12 g), the masses of Oxygen that combine are 16 g and 32 g. The ratio of these masses is $16:32$, which simplifies to a simple whole number ratio of $1:2$.

Another example from the text: Hydrogen and Oxygen form Water (H₂O) and Hydrogen Peroxide (H₂O₂).

• In Water, 2 g of Hydrogen combines with 16 g of Oxygen.
• In Hydrogen Peroxide, 2 g of Hydrogen combines with 32 g of Oxygen.

With a fixed mass of Hydrogen (2 g), the masses of Oxygen that combine are 16 g and 32 g. The ratio is $16:32$, or $1:2$.

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Gay Lussac’s Law Of Gaseous Volumes

Given by Joseph Louis Gay Lussac in 1808.

Statement: When gases combine or are produced in a chemical reaction, they do so in a simple ratio by volume, provided all gases are at the same temperature and pressure.

Example: The reaction between hydrogen and oxygen to form water vapor:

Hydrogen (g) + Oxygen (g) → Water vapor (g)

Experimentally, 100 mL of hydrogen reacts with 50 mL of oxygen to produce 100 mL of water vapor.

The volumes of reactants (Hydrogen and Oxygen) are 100 mL and 50 mL, giving a simple ratio of $100:50$, which simplifies to $2:1$. The volumes of reactants and products (Hydrogen, Oxygen, and Water vapor) are 100 mL, 50 mL, and 100 mL, giving a simple ratio of $100:50:100$, or $2:1:2$.

Gay Lussac's law is a specific case of the Law of Definite Proportions applied to volumes of gases.

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Avogadro’s Law

Proposed by Amedeo Avogadro in 1811.

Statement: Equal volumes of all gases at the same temperature and pressure should contain equal numbers of molecules.

Avogadro's crucial contribution was distinguishing between atoms and molecules. Applying his law explains Gay Lussac's observations.

Considering the reaction: Hydrogen (g) + Oxygen (g) → Water vapor (g)

Based on experiments, it's a 2:1 volume ratio of reactants:

2 volumes Hydrogen + 1 volume Oxygen → 2 volumes Water vapor

According to Avogadro's Law, if volumes are equal, the number of molecules must be equal (at the same T and P).

So, 2 molecules of Hydrogen + 1 molecule of Oxygen → 2 molecules of Water vapor

This only works if hydrogen and oxygen exist as diatomic molecules (H₂ and O₂) and water as H₂O, as shown below:

$2\text{H}_2\text{(g)} + 1\text{O}_2\text{(g)} \rightarrow 2\text{H}_2\text{O(g)}$

This explanation was consistent with experimental results and solidified the concept of molecules.

Dalton’s Atomic Theory

Building upon the Laws of Chemical Combination and the ancient concept of indivisible particles (like Democritus's 'a-tomio' and Kanda's 'Paramanu'), John Dalton published his atomic theory in 1808.

Postulates of Dalton's Atomic Theory:

1. Matter consists of indivisible particles called atoms.
2. All atoms of a given element are identical in properties, including mass. Atoms of different elements have different properties and masses.
3. Compounds are formed when atoms of different elements combine in a fixed, simple whole-number ratio.
4. Chemical reactions involve the reorganization of atoms. Atoms are neither created nor destroyed during a chemical reaction.

Dalton's theory successfully explained the Law of Conservation of Mass, the Law of Definite Proportions, and the Law of Multiple Proportions. However, it could not fully explain Gay Lussac's Law of Gaseous Volumes or why atoms combine.

Atomic And Molecular Masses

Atoms and molecules are extremely small, so their masses are also very small. Chemists use specific units and concepts to deal with these masses.

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Atomic Mass

Measuring the absolute mass of a single atom is difficult. Initially, atomic masses were determined relative to the lightest atom, hydrogen. The modern standard system is based on Carbon-12 (¹²C), agreed upon in 1961.

In this system, a ¹²C atom is assigned a mass of exactly 12 atomic mass units (amu).

An atomic mass unit (amu) is defined as exactly one-twelfth ($1/12$th) of the mass of one carbon-12 atom.

Today, 'amu' is replaced by 'u', which stands for unified mass.

$1 \text{ amu} = 1 \text{ u} \approx 1.66056 \times 10^{-24} \text{ g}$

The mass of any other atom is expressed relative to this standard.

Example: Mass of a hydrogen atom $\approx 1.0080 \text{ u}$. Mass of an oxygen-16 atom $\approx 15.995 \text{ u}$.

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Average Atomic Mass

Many elements found in nature exist as isotopes, which are atoms of the same element with different numbers of neutrons (and thus different masses).

The average atomic mass of an element is the weighted average of the masses of its naturally occurring isotopes, taking into account their relative abundances.

Average atomic mass = $\sum (\text{isotopic mass}_i \times \text{relative abundance}_i)$

Example: Carbon exists as ¹²C (98.892% abundance, 12 u), ¹³C (1.108% abundance, 13.00335 u), and ¹⁴C (very low abundance).

Average atomic mass of Carbon = $(0.98892 \times 12 \text{ u}) + (0.01108 \times 13.00335 \text{ u}) + (\approx 0) = 12.011 \text{ u}$.

The atomic masses listed in the periodic table are typically these average atomic masses.

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Molecular Mass

The molecular mass is the sum of the atomic masses of all the atoms present in a molecule of a substance. It is calculated by multiplying the atomic mass of each element by the number of its atoms in the molecule and adding these values together.

Answer:

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Formula Mass

Some substances, particularly ionic compounds like sodium chloride (NaCl), do not exist as discrete molecules but as a network of ions arranged in a crystal lattice.

For such compounds, a formula unit (like NaCl) represents the simplest ratio of ions in the structure. We calculate the formula mass by summing the atomic masses of the atoms in the formula unit, rather than calling it molecular mass.

Example: Sodium Chloride (NaCl)

Atomic mass of Na = 23.0 u, Atomic mass of Cl = 35.5 u

Formula mass of NaCl = Atomic mass of Na + Atomic mass of Cl = $23.0 \text{ u} + 35.5 \text{ u} = 58.5 \text{ u}$.

Mole Concept And Molar Masses

Atoms and molecules are incredibly small and exist in vast numbers. To count them conveniently, chemists use the mole concept.

The mole (mol) is the SI unit for the amount of substance. It is defined based on a fixed number of elementary entities.

Definition: One mole contains exactly $6.02214076 \times 10^{23}$ elementary entities.

This number is called the Avogadro constant or Avogadro number ($N_A$).

These elementary entities can be atoms, molecules, ions, electrons, or any other specified particles.

Examples:

• 1 mol of hydrogen atoms = $6.022 \times 10^{23}$ hydrogen atoms.
• 1 mol of water molecules = $6.022 \times 10^{23}$ water molecules.
• 1 mol of sodium chloride = $6.022 \times 10^{23}$ formula units of sodium chloride.

The number $6.022 \times 10^{23}$ was determined by experiments, such as finding the mass of a carbon-12 atom and relating it to the molar mass of carbon (12 g/mol). One mole of carbon-12 atoms weighs exactly 12 grams.

The mass of one mole of a substance in grams is called its molar mass.

Numerically, the molar mass in grams per mole ($g \text{ mol}^{-1}$) is equal to the atomic mass, molecular mass, or formula mass in unified atomic mass units (u).

Examples:

• Molar mass of hydrogen atoms = 1.008 g mol⁻¹ (from atomic mass 1.008 u)
• Molar mass of water (H₂O) = 18.02 g mol⁻¹ (from molecular mass 18.02 u)
• Molar mass of sodium chloride (NaCl) = 58.5 g mol⁻¹ (from formula mass 58.5 u)

The molar mass allows conversion between the mass of a substance and the number of moles (and thus the number of entities).

Percentage Composition

Knowing the composition of a compound is important. The percentage composition of a compound tells us the mass percentage of each element present in it. This is useful for identifying unknown compounds or checking the purity of known ones.

The mass percentage of an element in a compound is calculated using the formula:

$$\text{Mass \% of an element} = \frac{\text{Mass of that element in the compound}}{\text{Molar mass of the compound}} \times 100$$

Example: Water (H₂O)

Molar mass of H₂O = 18.02 g/mol (2 $\times$ 1.008 g/mol for H + 1 $\times$ 16.00 g/mol for O)

Mass % of Hydrogen = $\frac{\text{Mass of H in 1 mol H₂O}}{\text{Molar mass of H₂O}} \times 100 = \frac{(2 \times 1.008 \text{ g})}{18.02 \text{ g}} \times 100 = \frac{2.016 \text{ g}}{18.02 \text{ g}} \times 100 \approx 11.19 \%$

Mass % of Oxygen = $\frac{\text{Mass of O in 1 mol H₂O}}{\text{Molar mass of H₂O}} \times 100 = \frac{16.00 \text{ g}}{18.02 \text{ g}} \times 100 \approx 88.79 \%$

(Note: The sum of percentages should be close to 100%).

Example: Ethanol (C₂H₅OH)

Molar mass of C₂H₅OH = $(2 \times 12.01) + (6 \times 1.008) + (1 \times 16.00) = 24.02 + 6.048 + 16.00 = 46.068$ g/mol

• Mass % of Carbon = $\frac{2 \times 12.01}{46.068} \times 100 = \frac{24.02}{46.068} \times 100 \approx 52.14 \%$
• Mass % of Hydrogen = $\frac{6 \times 1.008}{46.068} \times 100 = \frac{6.048}{46.068} \times 100 \approx 13.13 \%$
• Mass % of Oxygen = $\frac{1 \times 16.00}{46.068} \times 100 = \frac{16.00}{46.068} \times 100 \approx 34.73 \%$

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Empirical Formula For Molecular Formula

The percentage composition data can be used to determine the empirical and molecular formulas of a compound.

• An empirical formula shows the simplest whole-number ratio of atoms of each element in a compound.
• A molecular formula shows the actual number of atoms of each element in a molecule of the compound.

The molecular formula is a whole-number multiple of the empirical formula: Molecular Formula = (Empirical Formula)$_n$, where $n$ is a whole number.

The relationship between molar mass and empirical formula mass is: $n = \frac{\text{Molar Mass}}{\text{Empirical Formula Mass}}$.

Steps to Determine Empirical and Molecular Formulas from Mass %:

1. Assume 100 g of the compound. The mass % of each element is equal to its mass in grams.
2. Convert the mass of each element to moles by dividing by its atomic mass.
3. Divide the number of moles of each element by the smallest number of moles calculated in step 2 to find the simplest mole ratio.
4. If the ratios are not whole numbers, multiply all ratios by the smallest whole number that converts them into whole numbers.
5. Write the empirical formula using these whole-number ratios as subscripts.
6. Calculate the empirical formula mass.
7. Divide the given molar mass by the empirical formula mass to find the multiplier, $n$.
8. Multiply the empirical formula subscripts by $n$ to get the molecular formula.

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Stoichiometry And Stoichiometric Calculations

Stoichiometry is the study of the quantitative relationships between reactants and products in a balanced chemical reaction. It deals with calculations of masses, volumes, or moles involved.

A balanced chemical equation provides key stoichiometric information:

• It uses chemical formulas to represent reactants and products.
• States of matter (solid (s), liquid (l), gas (g), aqueous (aq)) are often indicated.
• The coefficients in front of the formulas (stoichiometric coefficients) indicate the relative number of moles and molecules involved.

Example: Combustion of methane

CH₄ (g) + 2O₂ (g) → CO₂ (g) + 2H₂O (g)

This balanced equation tells us:

• One molecule of CH₄ reacts with two molecules of O₂ to produce one molecule of CO₂ and two molecules of H₂O.
• One mole of CH₄ reacts with two moles of O₂ to produce one mole of CO₂ and two moles of H₂O.
• Since equal volumes of gases at the same T and P contain equal moles (Avogadro's Law), we can also say: 22.7 L of CH₄ reacts with 45.4 L of O₂ to produce 22.7 L of CO₂ and 45.4 L of H₂O (at STP, standard temperature and pressure, slightly different from older definitions).
• Using molar masses: 16 g of CH₄ reacts with $2 \times 32 = 64$ g of O₂ to produce 44 g of CO₂ and $2 \times 18 = 36$ g of H₂O.

Stoichiometric calculations allow us to predict the amount of product formed from a given amount of reactant, or vice versa, using molar ratios from the balanced equation and molar masses.

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Limiting Reagent

In many reactions, reactants are not present in the exact stoichiometric ratio required by the balanced equation. One reactant might be present in a smaller amount than needed to react completely with the other(s).

The limiting reagent (or limiting reactant) is the reactant that is completely consumed first in a reaction. It determines or limits the maximum amount of product that can be formed.

The other reactant(s) are in excess.

To identify the limiting reagent and calculate product yield, you compare the mole ratio of reactants available to the mole ratio required by the balanced equation. The reactant that produces the least amount of product (based on its available quantity) is the limiting reagent.

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Reactions In Solutions

Many chemical reactions, especially in the laboratory, occur in solutions. The concentration of a solution describes the amount of solute dissolved in a specific amount of solvent or solution.

Common ways to express concentration:

1. Mass per cent (or weight per cent, w/w %)

$\text{Mass per cent} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 100$

(Mass of solution = Mass of solute + Mass of solvent)

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2. Mole Fraction ($x$)

The mole fraction of a component is the ratio of the number of moles of that component to the total number of moles of all components in the solution.

For a solution with components A and B with moles $n_A$ and $n_B$:

Mole fraction of A, $x_A = \frac{n_A}{n_A + n_B}$

Mole fraction of B, $x_B = \frac{n_B}{n_A + n_B}$

The sum of mole fractions of all components in a solution is always 1 ($x_A + x_B + ... = 1$). Mole fraction is unitless.

3. Molarity (M)

Molarity is one of the most common concentration units. It is defined as the number of moles of solute per liter of solution.

$\text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}}$

Molarity depends on temperature because volume changes with temperature. A 1 M solution contains 1 mole of solute dissolved to make a total volume of 1 liter of solution.

When diluting a solution, the number of moles of solute remains constant. The relationship between the molarity ($M$) and volume ($V$) of a concentrated solution ($M_1, V_1$) and a diluted solution ($M_2, V_2$) is:

$M_1 V_1 = M_2 V_2$

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4. Molality (m)

Molality is defined as the number of moles of solute per kilogram of solvent.

$\text{Molality (m)} = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kilograms}}$

Molality is independent of temperature because it is based on mass, which does not change with temperature.

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