Ch 01 - Some Basic Concepts of Chemistry11th Chemistry

• Cisplatin and Taxol: Highly effective in cancer therapy.
• AZT (Azidothymidine): Used specifically for helping patients with AIDS.

• Philosopher's stone (Paras): An alchemical substance that was historically believed to convert baser metals, such as iron and copper, into gold.
• Paramanu: Acharya Kanda (born 600 BCE, originally known as Kashyap) formulated the theory of very small indivisible particles, conceptualizing atomic theory approximately 2500 years before John Dalton.

• Solids: Definite shape and definite volume; particles are tightly packed in an ordered fashion with no freedom of movement.
• Liquids: Definite volume but no definite shape (takes the shape of the container); particles are close together but can move around each other.
• Gases: Neither definite shape nor definite volume; particles are far apart with easy, fast, and random movement.

• Mixture: Contains two or more pure substances present in any ratio, leading to a variable composition. Examples include air and sugar solutions.
• Pure Substance: The constituent particles are of the same chemical nature and possess a fixed composition. Examples include copper metal, water, and pure glucose.

• Homogeneous Mixture: Components completely mix with each other, resulting in a uniform composition throughout the entire sample with no visible boundaries (e.g., completely dissolved sugar solution, clean air).
• Heterogeneous Mixture: Composition is not uniform throughout, and the different components or phases are often visually distinct (e.g., mixtures of salt and sugar, or grains and dirt).

• Fixed Ratio: Water ($H_2O$) always contains hydrogen and oxygen in a fixed, definite ratio by mass (1:8).
• Different Properties: The properties of a compound differ entirely from its constituent elements. For instance, $H_2$ gas burns with a pop sound, $O_2$ gas supports combustion, but the resulting compound $H_2O$ is used as a fire extinguisher.
• Separation Methods: The constituents of a compound cannot be separated by simple physical methods; they require chemical or electrochemical methods of separation.

• Physical Properties: Can be measured or observed without changing the basic chemical identity or composition of the substance. Examples include color, odor, melting point, boiling point, and density.
• Chemical Properties: Measurement or observation absolutely requires a chemical change (reaction) to occur. Examples include combustibility, acidity, basicity, and chemical reactivity.

• Mass ($m$): The absolute amount of matter present in a substance. It remains constant regardless of the object's location in the universe.
• Weight ($W$): The force exerted by gravity on an object ($W = m \cdot g$). It may vary from one place to another due to localized changes in gravitational acceleration ($g$).
• Note: While the SI unit of mass is the kilogram (kg), chemists predominantly use grams (g) for practical laboratory measurements.

Variables & Units:

• Mass = Amount of matter (kg or g)
• Volume = Space occupied ($m^3$ or $cm^3$)

Conditions/Notes:

• SI Unit: $kg\ m^{-3}$
• Chemist Unit: $g\ cm^{-3}$ (or $g\ mL^{-1}$)
• Density indicates how closely particles of a substance are packed.

1. Length: metre (m)
2. Mass: kilogram (kg)
3. Time: second (s)
4. Electric Current: ampere (A)
5. Thermodynamic Temperature: kelvin (K)
6. Amount of Substance: mole (mol)
7. Luminous Intensity: candela (cd)

Variables & Units:

• $^\circ F$ = Temperature in degrees Fahrenheit
• $^\circ C$ = Temperature in degrees Celsius

Conditions/Notes:

• The Celsius scale is calibrated from $0^\circ C$ (freezing point of water) to $100^\circ C$ (boiling point of water).
• The Fahrenheit scale represents this range between $32^\circ F$ and $212^\circ F$.

• femto (f): $10^{-15}$
• pico (p): $10^{-12}$
• nano (n): $10^{-9}$
• micro ($\mu$): $10^{-6}$
• mega (M): $10^{6}$
• giga (G): $10^{9}$

Variables & Units:

• K = Temperature in Kelvin (SI Unit)
• $^\circ C$ = Temperature in degrees Celsius

Conditions/Notes:

• Negative temperatures are NOT possible on the Kelvin scale, unlike the Celsius scale. $0\ K$ is absolute zero.

• The Kilogram is no longer defined by a physical artifact (the International Prototype of the Kilogram).
• It is now strictly defined by taking the fixed numerical value of the Planck constant ($h$) as $6.62607015 \times 10^{-34}\ J\ s$, and is realized in practice using an advanced electromechanical instrument called a Kibble balance.

• Format: $N \times 10^n$
• N (Digit Term): Must be a number between $1.000...$ and $9.999...$ (meaning there must be exactly one single non-zero digit to the left of the decimal point).
• n (Exponent): An integer (positive or negative).
• Purpose: Used to conveniently and accurately handle extremely large (e.g., Avogadro's number) or extremely small numbers in chemical calculations without losing track of decimal places.

• Precision: Refers to the closeness of various measurements of the same physical quantity to each other. It indicates the consistency and reproducibility among multiple trials, regardless of whether they are correct.
• Accuracy: Refers to the agreement of a particular measured value to the true or accepted correct value. It indicates how 'right' the measurement is.

1. Preceding zeros: NEVER significant (e.g., $0.03$ has 1 sig fig). They strictly indicate the position of the decimal point.
2. Trapped zeros: ALWAYS significant (e.g., $2.005$ has 4 sig figs).
3. Terminal/Trailing zeros: Significant ONLY IF they are on the right side of a decimal point (e.g., $0.200$ has 3 sig figs; $100$ has 1 sig fig, but $100.0$ has 4).
4. Exact numbers: Counting discrete objects (e.g., 2 balls, 20 eggs) have infinite significant figures because they are exact counts, not measurements.

• Addition & Subtraction: The final result cannot have more digits to the right of the decimal point than the original number with the least number of decimal places (Focus strictly on decimal places).
• Multiplication & Division: The final result must be reported with no more significant figures than the measurement with the fewest total significant figures (Focus strictly on total significant figures).

• If the preceding number is even, it is not changed (e.g., $6.25$ rounded to one decimal place becomes $6.2$).
• If the preceding number is odd, it is increased by one to make it even (e.g., $6.35$ rounded to one decimal place becomes $6.4$).

Variables & Units:

• $m$ = Mass of the substances (g or kg)

Conditions/Notes:

• Statement: "Matter can neither be created nor destroyed in a physical or chemical change."
• Scientist: Antoine Lavoisier (1789).
• Valid strictly for ordinary chemical reactions, tested inside an isolated/closed system to accurately account for gaseous products.

• Definition: A highly reliable method used to convert physical quantities from one system of units to another.
• Principle: It relies on systematically multiplying the given measurement by a Unit Factor (a ratio physically equal to 1, such as $\frac{1\ kg}{1000\ g}$).
• Because the ratio mathematically equals 1, multiplying the original measurement by it safely changes the units without altering the actual underlying physical amount.

Variables & Units:

• $m_A, m_B$ = Masses of constituent elements A and B

Conditions/Notes:

• Statement: "A given compound always contains exactly the same proportion of elements by weight, irrespective of the source."
• Scientist: Joseph Proust (1799).
• Example: Pure water always contains Hydrogen and Oxygen in a 1:8 mass ratio.

Variables & Units:

• $m_{B1}, m_{B2}$ = Different masses of element B that combine with a fixed mass of element A.

Conditions/Notes:

• Statement: "If two elements combine to form more than one compound, the different masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers."
• Scientist: John Dalton (1803).
• Example: In $CO$ and $CO_2$, oxygen combining with 12g Carbon is 16g and 32g (Ratio 1:2).

Variables & Units:

• $V$ = Volume of reacting and product gases (L or mL)

Conditions/Notes:

• Statement: "When gases combine or are produced in a chemical reaction, they do so in a simple ratio by volume."
• Strict Condition: All gases must be measured at the same temperature and pressure.
• This is effectively the law of definite proportions applied by volume.

Variables & Units:

• V = Volume of the gas (L or $m^3$)
• N = Number of molecules
• T, P = Temperature, Pressure

Conditions/Notes:

• Statement: "Equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules."
• Avogadro made a crucial distinction between atoms and molecules (e.g., recognizing diatomic $H_2$ and $O_2$), which Dalton's theory initially couldn't explain.

1. Matter consists of extremely small, indivisible particles called atoms.
2. All atoms of a given specific element possess identical properties and identical mass; conversely, atoms of different elements differ in mass.
3. Chemical compounds are formed when atoms of different elements combine in a fixed, simple whole-number ratio.
4. Chemical reactions exclusively involve the reorganization of atoms (they are neither fundamentally created nor destroyed in a chemical process).

Variables & Units:

• $M_{avg}$ = Average atomic mass (u or amu)
• $\%\ \text{Abundance}_i$ = Percentage natural abundance of the $i^{th}$ isotope
• $M_i$ = Exact atomic mass of the $i^{th}$ isotope (u)

Conditions/Notes:

• This calculation accounts for the existence of multiple isotopes in nature. The atomic masses listed in the periodic table are always average atomic masses.

• The law is explicitly not valid for non-stoichiometric compounds.
• Example: Transition metal oxides such as Iron(II) oxide ($FeO$) often vary slightly in actual composition (forming compounds like $Fe_{0.95}O$) due to microscopic crystal lattice defects. Because of these defects, the constituent elements are not present in a perfectly fixed, integer whole-number ratio by mass.

• Statement: If two different elements combine separately with the same fixed weight of a third element, the ratio of the masses in which they do so are either the same or a simple whole-number multiple of the mass ratio in which they combine directly with each other.
• Example: In $CH_4$ and $H_2O$, Carbon and Oxygen combine separately with a fixed mass of Hydrogen. When C and O combine with each other to form $CO_2$, their mass ratio ($3:8$) is a simple mathematical multiple of their respective combination ratios with Hydrogen.

Variables & Units:

• Mass of element = Total mass of the specific element in one mole of the compound (g)
• Molar mass = Total mass of one mole of the entire compound ($g\ mol^{-1}$)

Conditions/Notes:

• Useful for determining the purity of a given sample by cross-checking experimental percentage composition with theoretical values.

• Definition: One atomic mass unit is defined as a mass exactly equal to one-twelfth ($1/12$) of the mass of one pure Carbon-12 ($^{12}C$) atom.
• Value: $1\ amu = 1.66056 \times 10^{-24}\ g$.
• It serves as the universal standard reference point for measuring the relative atomic and molecular masses of all other elements and compounds.

Variables & Units:

• n = A simple integer (1, 2, 3...)
• Molar Mass = Actual mass of one mole of the compound (g/mol)
• Empirical Formula Mass = Mass calculated from the empirical formula (g/mol)

Conditions/Notes:

• The value of n must be a whole number. If the calculation yields a fraction closely approaching an integer, it is rounded off.

• Mass: Exactly $1.992648 \times 10^{-23}\ g$.
• Derivation: It was determined experimentally using a mass spectrometer. It also aligns theoretically with dividing the molar mass of Carbon-12 ($12\ g\ mol^{-1}$) by Avogadro's number ($N_A = 6.022 \times 10^{23}\ mol^{-1}$).

• Reason: Ionic compounds like $NaCl$ do not exist as discrete, independent single molecules.
• Instead, they exist as a continuously repeating three-dimensional crystal lattice (e.g., in $NaCl$, one $Na^+$ ion is surrounded symmetrically by six $Cl^-$ ions, and vice versa).
• Therefore, 'Formula Mass' is calculated using the simplest whole-number empirical ratio of the ions (the empirical formula unit) rather than a non-existent discrete molecule.

Variables & Units:

• Mass of solute = Amount of substance dissolved (g)
• Mass of solution = Total mass of mixture (g)

Conditions/Notes:

• Mass of solution = Mass of solute + Mass of solvent.
• Often used in industrial chemistry and indicating purity (e.g., 10% NaCl by mass means 10g NaCl in 90g water).

• Definition: One mole is the amount of substance containing exactly $6.02214076 \times 10^{23}$ elementary entities (which can be atoms, molecules, ions, electrons, etc.).
• Reference: It is formally defined relative to the number of atoms present in exactly $12\ g$ ($0.012\ kg$) of the Carbon-12 ($^{12}C$) isotope.
• Avogadro's Constant ($N_A$): The fixed, accepted numerical value used for standard calculations is $6.022 \times 10^{23}\ \text{mol}^{-1}$.

Variables & Units:

• $n_A$ = Number of moles of component A
• $n_B$ = Number of moles of component B

Conditions/Notes:

• Unitless: It is a ratio of moles to moles, so it has no units.
• Sum Property: The sum of mole fractions of all components in a solution is always exactly 1 ($X_A + X_B = 1$).

• Definition: The mass of exactly one mole of a substance, universally expressed in units of grams per mole ($g\ mol^{-1}$).
• Relationship: It is numerically identical to the substance's atomic, molecular, or formula mass expressed in unified mass units (u) or amu.
• Example: A single Water ($H_2O$) molecule has a molecular mass of $18.02\ u$, meaning its molar mass (the mass of $6.022 \times 10^{23}$ water molecules) is exactly $18.02\ g\ mol^{-1}$.

Variables & Units:

• Number of moles of solute = $n = \frac{\text{Given Mass}}{\text{Molar Mass}}$
• Volume of solution = Measured in Litres (L) or $dm^3$.

Conditions/Notes:

• Unit: $mol\ L^{-1}$ or M.
• The most widely used unit of concentration in laboratories.

• Old STP ($0^\circ C$ or $273.15\ K$, $1\ atm$): 1 mole of gas occupies exactly $22.4\ L$.
• New STP ($0^\circ C$ or $273.15\ K$, $1\ bar$): 1 mole of gas occupies exactly $22.7\ L$.
• Note: Always verify whether a stoichiometric problem provides pressure in atmospheres (atm) or bars to choose the correct corresponding molar volume.

Variables & Units:

• $M_1, V_1$ = Molarity and Volume of the initial concentrated stock solution.
• $M_2, V_2$ = Molarity and Volume of the final diluted solution.

Conditions/Notes:

• This works because adding solvent (like water) does not change the total number of moles of the solute in the container ($n = M \times V$).

Variables & Units:

• Number of moles of solute = $n$ (mol)
• Mass of solvent = Measured strictly in Kilograms (kg)

Conditions/Notes:

• Unit: $mol\ kg^{-1}$ or m.
• Crucial Distinction: The denominator is mass of the solvent only, not the total solution.

• Empirical Formula: Represents the simplest whole-number ratio of various atoms present in a compound. For example, the empirical formula for benzene is $CH$.
• Molecular Formula: Shows the exact, actual number of different types of atoms physically present in a single discrete molecule of the compound. For example, the molecular formula for benzene is $C_6H_6$.

• Molarity ($M$) depends on the volume of the solution. Since liquids expand/contract with heating/cooling, volume changes with temperature, making Molarity temperature-dependent.
• Molality ($m$) depends entirely on the mass of the solvent. Since mass is unaffected by temperature variations, Molality is completely independent of temperature.

• Definition: Derived from the Greek words stoicheion (element) and metron (measure), stoichiometry deals mathematically with calculating the exact masses (and sometimes volumes) of reactants consumed and products formed in a chemical reaction.
• Information Provided: The stoichiometric coefficients (the numbers in front of the molecules) indicate the exact molar ratios, molecular ratios, and mass/volume relationships of the reacting entities.
• Note: Under STP conditions, these coefficients directly correlate to standard gas volumes (e.g., 1 mole = $22.7\ L$ at 1 bar).

• Definition: The limiting reagent is the reactant that gets completely consumed first during a chemical reaction.
• Significance: It strictly limits and determines the maximum theoretical amount of product that can be formed. Once the limiting reagent is entirely exhausted, the chemical reaction stops immediately, regardless of how much of the other reactants (excess reagents) are left over in the vessel.
• Caution: The limiting reagent is NOT necessarily the reactant with the lowest physical mass; it is completely determined by the required molar stoichiometric ratio.

Variables & Units:

• Mass of solute = Amount of trace substance (g)
• Mass of solution = Total mass of the mixture (g)

Conditions/Notes:

• Primarily used for extremely dilute solutions, such as expressing the hardness of water or trace atmospheric pollution levels.

Variables & Units:

• Actual Yield = The experimentally obtained amount of product (g or mol)
• Theoretical Yield = The maximum calculated amount of product predicted by stoichiometry (g or mol)

Conditions/Notes:

• The actual yield is almost always less than the theoretical yield due to incomplete reactions, side reactions, or loss of product during physical recovery.