Some Basic Concepts of Chemistry

Meaning

Matter is anything that occupies space and has mass. From the gigantic mountains to the microscopic dust floating in a sunbeam, everything that has weight and takes up room is matter.

Definitions

1. According to Raymond Chang in his chemistry textbook: "Matter is anything that occupies space and possesses mass; it is the physical material of the universe."
2. According to Linus Pauling: "Matter is made up of particles called atoms and molecules, which are in constant motion and interact with one another through various forces."

Explanation

• Physical Classification: Matter exists primarily in three main states on Earth—solid, liquid, and gas. Solids have a fixed shape and volume because their particles are tightly packed. Liquids have a fixed volume but take the shape of their container because particles can slide past each other. Gases have neither fixed shape nor fixed volume because particles are far apart and move rapidly.
• Chemical Classification: Matter is divided into pure substances and mixtures. Pure substances have a fixed composition (elements and compounds), while mixtures consist of two or more substances combined physically in no fixed ratio (homogeneous and heterogeneous mixtures).

Examples

• Water ($H_2O$): It exists as ice (solid) in your freezer, liquid water in your glass, and water vapor (gas) in the air.
• Air: An invisible mixture of various gases like nitrogen, oxygen, argon, and carbon dioxide.

Real-Life Uses

• Material Science and Packaging: Understanding the states of matter helps engineers design lightweight, durable packaging materials for food to prevent spoilage and protect goods during shipping.
• Air Separation Plants: Industries use the physical properties of matter to separate liquid air into pure oxygen, nitrogen, and argon through fractional distillation for hospitals and welding shops.

Common Misconceptions and Their Corrections

• Misconception: Weight and mass mean the exact same thing in chemistry and physics.
• Correction: Mass is the actual amount of matter present in an object, which remains constant everywhere in the universe. Weight is the gravitational force pulling down on that mass, meaning your weight on the Moon is different from your weight on Earth, but your mass is identical.

Concise Takeaway

Matter is everything around us with mass and volume, classified physically by states and chemically by purity.

Meaning

Dalton's Atomic Theory is the historic proposal that attempts to explain the particulate nature of matter, stating that all matter is made of tiny, indivisible particles called atoms.

Definitions

1. According to John Dalton in his 1808 publication A New System of Chemical Philosophy: "All matter is composed of extremely small, indivisible particles called atoms, which cannot be created or destroyed."
2. According to modern historical chemical definitions: Dalton's theory is a fundamental postulate stating that chemical reactions involve only the rearrangement of atoms into new combinations without altering the atoms themselves.

Explanation

• Elements consist of extremely small particles called atoms.
• All atoms of a given element are identical in mass and properties, whereas atoms of different elements have different masses and properties.
• Compounds are formed when atoms of different elements combine in fixed whole-number ratios.
• Chemical reactions involve only the reorganization of atoms; atoms themselves are neither created nor destroyed.

Examples

• Water formation: Two atoms of hydrogen combine with one atom of oxygen to form one molecule of water, maintaining a fixed 2:1 atom ratio.
• Carbon monoxide and carbon dioxide: Carbon and oxygen can combine in different whole-number ratios to form entirely different substances.

Real-Life Uses

• Industrial Chemical Synthesis: Manufacturing fertilizers and plastics relies on knowing that atoms combine in fixed ratios, ensuring reactants are never wasted.
• Forensic Science: Analyzing the elemental makeup of physical evidence at a crime scene relies on the fact that atoms of specific elements retain their unique identities.

Common Misconceptions and Their Corrections

• Misconception: Dalton's atomic theory is entirely correct and used without changes today.
• Correction: While it laid the groundwork, modern science has proven that atoms are actually divisible into subatomic particles (protons, neutrons, and electrons), and atoms of the same element can have different masses (isotopes).

Concise Takeaway

Dalton stated that matter is built of indivisible atoms, and compounds form from whole-number combinations of these atoms.

Meaning

A molecule is an aggregate of two or more atoms tightly bound together by attractive forces known as chemical bonds, representing the smallest unit of a substance that can exist independently and retain all properties of that substance.

Definitions

1. According to the International Union of Pure and Applied Chemistry (IUPAC): "A molecule is an electrically neutral entity consisting of more than one atom, representing the minimum amount of a chemical substance that retains its chemical identity and properties."
2. According to textbook chemistry definitions: A molecule is formed when atoms share or transfer electrons to achieve a stable electronic configuration.

Explanation

• Molecules can be made of the same type of atoms (homoatomic, like O₂ or N₂) or different types of atoms (heteroatomic, like HCl or H₂O).
• The atomicity of a molecule refers to the total number of atoms present in a single molecule.
• Molecules possess independent existence and determine the physical and chemical properties of the bulk substance.

Examples

• Oxygen gas (O₂): A diatomic molecule made of two oxygen atoms bonded together.
• Glucose (C₆H₁₂O₆): A complex polyatomic molecule made of carbon, hydrogen, and oxygen atoms.

Real-Life Uses

• Pharmacology and Drug Design: Pharmaceutical chemists design drug molecules that fit precisely into biological receptor sites in human cells to cure diseases.
• Atmospheric Chemistry: Monitoring ozone (O₃) molecules in the stratosphere helps scientists protect life on Earth from harmful ultraviolet radiation.

Common Misconceptions and Their Corrections

• Misconception: All molecules are compounds.
• Correction: All compounds are molecules, but not all molecules are compounds. For example, O₂ is a molecule because it has two atoms, but it is an element, not a compound, because both atoms are identical.

Concise Takeaway

Molecules are independent groups of bonded atoms that define the chemical character of a substance.

Meaning

Atomic mass is the mass of a single atom expressed in atomic mass units, while molecular mass is the total sum of the atomic masses of all atoms making up a single molecule of a substance.

Definitions

1. According to standard chemical convention: One atomic mass unit (amu or u) is defined as exactly one-twelfth the mass of an unbound neutral atom of carbon-12 at rest in its ground state.
2. According to IUPAC: Molecular mass is the ratio of the mass of a molecule of a substance to one-twelfth of the mass of an atom of carbon-12.

Explanation

• One atomic mass unit (u) equals $1.66056 \times 10^{-24}$ grams.
• Average atomic mass accounts for the natural isotopic abundance of an element found on Earth.
• Molecular mass is calculated by simply adding up the atomic masses of every individual atom shown in the chemical formula.

Examples

• Atomic mass of Oxygen-16 is roughly 16 u because it is sixteen times heavier than one-twelfth of a carbon-12 atom.
• Molecular mass of Water (H₂O): Two hydrogen atoms ($2 \times 1.008$ u) plus one oxygen atom (16.00 u) gives 18.016 u.

Real-Life Uses

• Pharmaceutical Dosing: Chemists use molecular mass calculations to determine exact active ingredient concentrations in pills and liquid medicines.
• Nutritional Science: Calculating the mass of macronutrients in food labeling relies on accurate molecular mass data.

Common Misconceptions and Their Corrections

• Misconception: Atomic mass on the periodic table is a whole number representing the sum of protons and neutrons.
• Correction: The number on the periodic table is usually a decimal because it is a weighted average of all naturally occurring isotopes of that element, taking their percentage abundances into account.

Concise Takeaway

Atomic and molecular masses measure the relative weight of atoms and molecules using the carbon-12 standard scale.

Meaning

The mole is the fundamental SI unit used to measure the amount of a substance, representing a specific collection of elementary entities, equal to the Avogadro constant.

Definitions

1. According to the 2019 SI unit redefinition by BIPM: "The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly $6.02214076 \times 10^{23}$ elementary entities."
2. According to standard textbooks: A mole is a chemical counting unit equivalent to a dozen, but containing Avogadro's number of particles.

Explanation

• Avogadro's number ($N_A$) is $6.022 \times 10^{23}$ particles per mole.
• Molar mass is the mass of exactly one mole of a substance expressed in grams per mole (g/mol).
• The numerical value of the molar mass in g/mol is identical to the atomic or molecular mass in atomic mass units (u).

Examples

• One mole of carbon atoms has a mass of exactly 12 grams and contains $6.022 \times 10^{23}$ carbon atoms.
• One mole of water molecules weighs 18.02 grams and contains $6.022 \times 10^{23}$ water molecules.

Real-Life Uses

• Chemical Manufacturing Plants: Chemical engineers use moles to measure out exact proportions of raw materials for making thousands of tons of commercial products like ammonia or sulfuric acid.
• Baking and Cooking: While home bakers use cups and spoons, industrial food science uses exact molar ratios of leavening agents like baking soda to ensure consistent bread rising.

Common Misconceptions and Their Corrections

• Misconception: One mole of every substance takes up the exact same physical mass.
• Correction: One mole always contains the same *number* of particles, but because different atoms and molecules have different individual weights, the total mass of one mole varies greatly from substance to substance.

Concise Takeaway

A mole is a collection of $6.022 \times 10^{23}$ particles, and its mass in grams equals the atomic or molecular mass.

Meaning

Percentage composition is the relative measure of the mass of each individual element present in a chemical compound expressed as a percentage of the total molecular mass.

Definitions

1. According to standard chemical definitions: Percentage composition of an element is the mass of that element in a sample of the compound divided by the total mass of the sample, multiplied by one hundred.
2. According to analytical chemistry literature: It represents the quantitative breakdown of a compound's elemental makeup by weight.

Explanation

• Calculated using the formula: Percentage of element = $(\frac{\text{Mass of element in 1 molecule}}{\text{Molar mass of compound}}) \times 100$.
• The sum of the percentage compositions of all elements in a pure compound must always add up to 100 percent.
• It helps chemists verify the purity of synthesized laboratory samples.

Examples

• Percentage of Hydrogen in Water ($H_2O$): Molar mass = 18.02 g/mol. Mass of hydrogen = 2.016 g. Percentage = $(\frac{2.016}{18.02}) \times 100 = 11.19\%$.
• Percentage of Carbon in Carbon Dioxide ($CO_2$): Molar mass = 44.01 g/mol. Mass of carbon = 12.01 g. Percentage = $(\frac{12.01}{44.01}) \times 100 = 27.29\%$.

Real-Life Uses

• Quality Control in Metallurgy: Metallurgists check the percentage composition of carbon in steel to determine if it is hard or ductile.
• Mineral Prospecting: Mining companies analyze rock samples for the percentage composition of metal ores to decide if mining operations will be profitable.

Common Misconceptions and Their Corrections

• Misconception: Percentage composition is based on the number of atoms rather than their mass.
• Correction: Percentage composition is strictly based on mass, not atom count. For example, in water, there are twice as many hydrogen atoms as oxygen atoms, but oxygen makes up roughly 88 percent of the total mass because oxygen atoms are much heavier.

Concise Takeaway

Percentage composition tells you the exact weight share of each element inside a chemical compound.

Meaning

An empirical formula gives the simplest whole-number ratio of atoms of different elements in a compound, while a molecular formula shows the exact actual number of atoms of each element present in a single molecule.

Definitions

1. According to IUPAC: An empirical formula is a chemical formula showing the simplest proportion of elements present in a compound, whereas a molecular formula shows the number of each type of atom in a molecule.
2. According to general chemistry textbooks: The molecular formula is always an integer multiple of the empirical formula.

Explanation

• Relationship equation: $\text{Molecular Formula} = (\text{Empirical Formula})_n$, where $n$ is a whole number integer calculated as $\frac{\text{Molar Mass}}{\text{Empirical Formula Mass}}$.
• Compounds with identical empirical formulas can have completely different molecular formulas and entirely different chemical properties.
• Finding empirical formulas requires starting with percentage composition, converting percentages to grams, dividing by atomic masses to get moles, and finding the simplest mole ratio.

Examples

• Hydrogen Peroxide and Water: The empirical formula for hydrogen peroxide is $HO$, but its molecular formula is $H_2O_2$ ($n=2$).
• Glucose and Formaldehyde: Formaldehyde ($CH_2O$), acetic acid ($C_2H_4O_2$), and glucose ($C_6H_{12}O_6$) all share the exact same empirical formula ($CH_2O$), but have very different molecular formulas.

Real-Life Uses

• Organic Compound Identification: Organic chemists use combustion analysis to find the empirical formulas of newly synthesized carbon-based medicinal compounds.
• Environmental Monitoring: Analyzing pollutant gases in vehicle exhaust to determine their molecular formulas and environmental impact.

Common Misconceptions and Their Corrections

• Misconception: The empirical formula and molecular formula of a substance are always different.
• Correction: For many common substances, such as water ($H_2O$) and carbon dioxide ($CO_2$), the empirical formula and the molecular formula are identical because the simplest ratio is already the actual number of atoms in the molecule.

Concise Takeaway

The empirical formula gives the simplest atom ratio, while the molecular formula gives the true, complete atom count.

Meaning

Stoichiometry is the quantitative study of reactants and products involved in chemical reactions, based on the laws of conservation of mass and chemical balancing.

Definitions

1. According to IUPAC: Stoichiometry is the relationship between the relative quantities of substances taking part in a reaction or forming a compound, typically expressed in ratios of integers.
2. According to standard textbooks: Stoichiometry refers to the calculations of masses, moles, and volumes of reactants and products in a balanced chemical equation.

Explanation

• A chemical equation must always be balanced before doing any stoichiometric calculations to obey the law of conservation of mass.
• Coefficients in a balanced equation represent the mole ratio of reactants and products.
• Limiting reactant: The reactant that is completely consumed first during a chemical reaction, which limits the amount of product that can be formed.
• Excess reactant: The reactant left over in a reaction after the limiting reactant has been completely used up.

Examples

• Balanced Equation for water formation: $2H_2 + O_2 \rightarrow 2H_2O$. This tells us that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water.
• If you have 4 moles of hydrogen and plenty of oxygen, you can produce 4 moles of water.

Real-Life Uses

• Rocket Science and Aerospace: NASA engineers use precise stoichiometric calculations to mix liquid hydrogen and liquid oxygen in rocket engines to ensure complete combustion and maximum thrust without carrying excess dead weight.
• Airbags in Automobiles: Automobile safety systems use the rapid stoichiometric decomposition of sodium azide ($NaN_3$) powder triggered by a crash sensor to instantly fill an airbag with nitrogen gas.

Common Misconceptions and Their Corrections

• Misconception: The reactant you have the smallest physical mass of in grams is always the limiting reactant.
• Correction: The limiting reactant is determined by comparing the *mole* ratio of the available reactants to the balanced equation coefficients, not by comparing their physical masses in grams.

Concise Takeaway

Stoichiometry is the calculation of reactant and product quantities in chemical reactions using balanced equations and mole ratios.

Problem 1: Calculating Percentage Composition

Find the percentage composition of all elements in calcium carbonate ($CaCO_3$). (Atomic masses: Ca = 40.08 u, C = 12.01 u, O = 16.00 u)

Step-by-Step Solution:

• Step 1: Calculate the molar mass of $CaCO_3$. Molar mass = $(1 \times 40.08) + (1 \times 12.01) + (3 \times 16.00) = 40.08 + 12.01 + 48.00 = 100.09 \text{ g/mol}$
• Step 2: Calculate the mass percentage of Calcium (Ca). $\text{Percentage of Ca} = (\frac{40.08}{100.09}) \times 100 = 40.04\%$
• Step 3: Calculate the mass percentage of Carbon (C). $\text{Percentage of C} = (\frac{12.01}{100.09}) \times 100 = 12.00\%$
• Step 4: Calculate the mass percentage of Oxygen (O). $\text{Percentage of O} = (\frac{48.00}{100.09}) \times 100 = 47.96\%$
• Final Check: $40.04 + 12.00 + 47.96 = 100.00\%$. The calculation is correct!

Problem 2: Empirical and Molecular Formula Calculation

A compound contains 82.76 percent carbon and 17.24 percent hydrogen by mass. Its molar mass is 58.12 g/mol. Find its empirical and molecular formulas.

Step-by-Step Solution:

• Step 1: Assume a 100 g sample of the compound (82.76 g C, 17.24 g H).
• Step 2: Convert grams to moles. Moles of C = $\frac{82.76}{12.01} = 6.89 \text{ mol}$. Moles of H = $\frac{17.24}{1.008} = 17.10 \text{ mol}$.
• Step 3: Divide by smallest moles (6.89). C = 1.0, H = 2.48 $\approx 2.5$.
• Step 4: Multiply by 2 to get integers. C = 2, H = 5. Empirical Formula = $C_2H_5$.
• Step 5: Empirical formula mass = $(2 \times 12.01) + (5 \times 1.008) = 29.06 \text{ g/mol}$.
• Step 6: Find $n = \frac{58.12}{29.06} = 2$.
• Step 7: Molecular Formula = $(C_2H_5)_2 = C_4H_{10}$ (Butane).

Problem 3: Stoichiometry and Limiting Reactant Calculation

Calculate the mass of carbon dioxide produced when 50.0 grams of calcium carbonate ($CaCO_3$) is heated until it decomposes completely. Equation: $CaCO_3 \rightarrow CaO + CO_2$.

Step-by-Step Solution:

• Step 1: Check if the equation is balanced ($CaCO_3 \rightarrow CaO + CO_2$). Yes, it is balanced.
• Step 2: Molar masses: $CaCO_3 = 100.09 \text{ g/mol}$, $CO_2 = 44.01 \text{ g/mol}$.
• Step 3: Convert given mass to moles: Moles of $CaCO_3 = \frac{50.0}{100.09} = 0.500 \text{ mol}$.
• Step 4: Mole ratio is 1:1, so 0.500 moles of $CaCO_3$ produce 0.500 moles of $CO_2$.
• Step 5: Convert moles of $CO_2$ to grams: $\text{Mass} = 0.500 \times 44.01 = 22.0 \text{ grams}$.

• Atomic Mass Unit Definition: $1 \text{ u} = \frac{1}{12} \times \text{mass of one } ^{12}\text{C atom} = 1.66056 \times 10^{-24} \text{ g}$
• Number of Moles ($n$): $n = \frac{\text{Given Mass } (m)}{\text{Molar Mass } (M)}$
• Number of Particles ($N$): $N = n \times N_A$ (where $N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$)
• Percentage Composition: $\text{Percentage of Element} = \left(\frac{\text{Mass of element in 1 mol}}{\text{Molar mass of compound}}\right) \times 100$
• Empirical to Molecular Relationship: $\text{Molecular Formula} = (\text{Empirical Formula})_n$, where $n = \frac{\text{Molar Mass}}{\text{Empirical Formula Mass}}$
• Molarity (Concentration): $\text{Molarity } (M) = \frac{\text{Moles of Solute}}{\text{Volume of Solution in Liters}}$

• Gas Chromatography-Mass Spectrometry (GC-MS): Analytical laboratories use GC-MS instruments to separate volatile chemical mixtures and identify unknown compounds by measuring their molecular masses and fragmentation patterns.
• Automated Combustion Analyzers: Modern analytical labs use automated combustion devices to burn organic compounds instantly, measuring carbon dioxide and water vapor to calculate percentage composition and empirical formulas within minutes.
• Computer-Aided Chemical Process Simulators (Aspen Plus / ChemCAD): Chemical engineering industries use advanced software tools to run massive stoichiometric calculations and optimize plant yields before building physical production facilities.
• Spectrophotometers: Used in environmental testing and quality control labs to measure light absorption and determine exact concentrations of chemical solutions using molarity principles.

In the early twentieth century, the world faced a massive agricultural crisis. Natural fertilizers like Chilean saltpeter were running out, and scientists predicted global famine because crops could not get enough nitrogen from the soil to sustain a growing human population. Atmospheric nitrogen was abundant, but nitrogen gas ($N_2$) has a triple covalent bond that makes it extremely unreactive under normal conditions.

German chemist Fritz Haber and chemical engineer Carl Bosch solved this grand challenge by developing an industrial method known as the Haber Process, which relies heavily on stoichiometry, mole concepts, and gas laws. The chemical equation for this reaction is: $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$

Let us examine how the basic concepts of chemistry we studied today made this industrial revolution possible:

1. Mole Concept and Stoichiometric Ratios in Action: The balanced equation tells us that exactly one mole of nitrogen gas must react with three moles of hydrogen gas to produce two moles of ammonia. Industrial plants use massive storage silos calibrated using moles to ensure that nitrogen and hydrogen are pumped into high-pressure reaction vessels in the exact 1 to 3 stoichiometric ratio.
2. Limiting Reactants and Yield Optimization: In industrial reactors, achieving 100 percent conversion of reactants into products is thermodynamically impossible in a single pass. Engineers carefully monitor limiting reactants and recycle unreacted nitrogen and hydrogen gases back into the reaction chamber to maximize the overall percentage yield of ammonia.
3. Molar Mass and Quality Control: Once liquid ammonia is synthesized, quality control chemists take samples and use molar mass calculations and titration techniques to determine the percentage purity of the product before it is shipped out to agricultural fertilizer manufacturing plants.

1. How many atoms are present in exactly one mole of carbon dioxide ($CO_2$)?
   A) $6.022 \times 10^{23}$ atoms
   B) $1.806 \times 10^{24}$ atoms
   C) $3.011 \times 10^{24}$ atoms
   D) $1.204 \times 10^{24}$ atoms
   Answer: B
   Explanation: One molecule of $CO_2$ contains 3 atoms (1 carbon and 2 oxygen). Since one mole contains $6.022 \times 10^{23}$ molecules, the total number of atoms is $3 \times 6.022 \times 10^{23} = 1.806 \times 10^{24}$ atoms.
2. What is the mass of a single atom of carbon-12 in grams?
   A) $1.99 \times 10^{-23} \text{ g}$
   B) $1.66 \times 10^{-24} \text{ g}$
   C) $12.00 \text{ g}$
   D) $6.02 \times 10^{23} \text{ g}$
   Answer: A
   Explanation: One mole of carbon-12 atoms weighs 12.00 grams and contains $6.022 \times 10^{23}$ atoms. The mass of one atom is $\frac{12.00}{6.022 \times 10^{23}} = 1.99 \times 10^{-23} \text{ g}$.
3. Which of the following compounds has the highest percentage of oxygen by mass?
   A) $H_2O$
   B) $CO_2$
   C) $SO_2$
   D) $CO$
   Answer: A
   Explanation: In water ($H_2O$), the molar mass is 18.02 g/mol, and oxygen contributes 16.00 g, which is about 88.8 percent by mass, higher than any of the other listed options.
4. The empirical formula of a compound is $CH_2$ and its molar mass is 42.08 g/mol. What is its molecular formula?
   A) $CH_2$
   B) $C_2H_4$
   C) $C_3H_6$
   D) $C_4H_8$
   Answer: C
   Explanation: The empirical formula mass of $CH_2$ is $14.03 \text{ g/mol}$. Dividing the molar mass gives $n = \frac{42.08}{14.03} \approx 3$. Multiplying gives $C_3H_6$.
5. How many moles of water are produced when 2 moles of hydrogen gas react completely with oxygen?
   A) 1 mole
   B) 2 moles
   C) 3 moles
   D) 4 moles
   Answer: B
   Explanation: From the balanced equation $2H_2 + O_2 \rightarrow 2H_2O$, 2 moles of hydrogen produce 2 moles of water.
6. Which law states that matter can neither be created nor destroyed in a chemical reaction?
   A) Law of Definite Proportions
   B) Law of Multiple Proportions
   C) Law of Conservation of Mass
   D) Avogadro's Law
   Answer: C
   Explanation: The Law of Conservation of Mass, formulated by Antoine Lavoisier, states that total mass remains constant during chemical changes.
7. What is the volume occupied by one mole of any ideal gas at Standard Temperature and Pressure (STP)?
   A) 11.2 liters
   B) 22.4 liters
   C) 44.8 liters
   D) 1.0 liter
   Answer: B
   Explanation: At STP, one mole of any ideal gas occupies a standard molar volume of 22.4 liters.
8. Which of the following is a homogeneous mixture?
   A) Sand and water
   B) Oil and water
   C) Saltwater solution
   D) Granite rock
   Answer: C
   Explanation: A saltwater solution has a uniform composition throughout, making it homogeneous.
9. What is the limiting reactant when 3 moles of $A$ react with 3 moles of $B$ according to the equation $A + 2B \rightarrow AB_2$?
   A) $A$
   B) $B$
   C) Both are limiting
   D) Neither
   Answer: B
   Explanation: For 3 moles of $A$, you would need 6 moles of $B$. Since you only have 3 moles of $B$, $B$ will run out first.
10. What does the coefficient in front of a reactant in a balanced chemical equation represent?
    A) The mass in grams
    B) The number of moles
    C) The temperature
    D) The density
    Answer: B
    Explanation: Stoichiometric coefficients represent the relative number of moles of reactants and products.

1. Define the Law of Definite Proportions and give an example.
   Answer: The Law of Definite Proportions, stated by Joseph Proust, states that a given chemical compound always contains its component elements in a fixed ratio by mass, regardless of its source or method of preparation. For example, pure water always consists of hydrogen and oxygen in a mass ratio of 1 to 8.
2. Calculate the number of molecules present in 0.5 moles of carbon dioxide ($CO_2$).
   Answer: Given moles ($n$) = 0.5 mol. Avogadro's number ($N_A$) = $6.022 \times 10^{23} \text{ molecules/mol}$. Number of molecules = $n \times N_A = 0.5 \times 6.022 \times 10^{23} = 3.11 \times 10^{23}$ molecules.
3. Distinguish between empirical formula and molecular formula with an example.
   Answer: An empirical formula represents the simplest whole-number ratio of atoms, while a molecular formula shows the exact actual number of atoms in a single molecule. For example, acetic acid has the molecular formula $C_2H_4O_2$, but its empirical formula is $CH_2O$.
4. What is a limiting reactant? Explain its role in chemical calculations.
   Answer: The limiting reactant is the reactant completely consumed during a chemical reaction. It determines the maximum amount of product that can be formed because once it is used up, the reaction stops.
5. Calculate the molar mass of sulfuric acid ($H_2SO_4$). (Atomic masses: H = 1.01, S = 32.07, O = 16.00)
   Answer: Molar mass = $(2 \times 1.01) + (1 \times 32.07) + (4 \times 16.00) = 2.02 + 32.07 + 64.00 = 98.09 \text{ g/mol}$.
6. State Dalton's atomic theory and mention one major modification made to it in modern chemistry.
   Answer: Dalton stated matter is made of indivisible atoms, atoms of a given element are identical, and compounds form from fixed ratios. Modern modification: Atoms are divisible into subatomic particles, and isotopes exist.
7. How many grams of sodium hydroxide ($NaOH$) are required to prepare 0.5 liters of a 0.2 M solution?
   Answer: Moles = $M \times \text{Volume} = 0.2 \times 0.5 = 0.1 \text{ moles}$. Mass = $\text{Moles} \times \text{Molar Mass} = 0.1 \times 40.00 = 4.0 \text{ grams}$.
8. Why do fractional atomic masses appear on the periodic table?
   Answer: Fractional atomic masses appear because most naturally occurring elements exist as a mixture of isotopes with different masses. The periodic table lists the weighted average of these isotopes.
9. Calculate the percentage of water of crystallization in blue vitriol, copper sulfate pentahydrate ($CuSO_4 \cdot 5H_2O$).
   Answer: Total molar mass = $249.72 \text{ g/mol}$. Molar mass of $5H_2O = 90.10 \text{ g/mol}$. Percentage of water = $(\frac{90.10}{249.72}) \times 100 = 36.08\%$.
10. State Avogadro's Law.
    Answer: Avogadro's Law states that equal volumes of all gases under the same conditions of temperature and pressure contain an equal number of molecules.

• Matter: Anything with mass and volume, classified physically (solid, liquid, gas) and chemically (pure substances, mixtures).
• Mole Concept: 1 mole = $6.022 \times 10^{23}$ particles. Molar mass in g/mol equals atomic/molecular mass in u.
• Formulas: Empirical formula shows the simplest ratio; molecular formula shows the true count.
• Stoichiometry: Always balance equations first; use mole ratios and identify limiting reactants.

Mnemonic (M-G-V): To convert from Moles to Grams, multiply by molar mass. To convert from Moles to Volume at STP, multiply by 22.4 L. To convert from Moles to Particles, multiply by Avogadro's number ($6.022 \times 10^{23}$).