Atoms and Molecules Class 9 NCERT: Laws, Formulas & Mole Concept

The Laws of Chemical Combination

Antoine L. Lavoisier and Joseph L. Proust established the foundation of chemical sciences by introducing two crucial laws after extensive experimentation:

1. Law of Conservation of Mass: This law states that mass can neither be created nor destroyed in a chemical reaction. In simple terms, the total mass of the reactants before a reaction is always equal to the total mass of the products formed after the reaction.

Example: If $100\text{ g}$ of Calcium Carbonate ($CaCO_3$) is heated, it decomposes to produce $56\text{ g}$ of Calcium Oxide ($CaO$) and $44\text{ g}$ of Carbon Dioxide ($CO_2$). The sum of product masses ($56 + 44 = 100\text{ g}$) perfectly matches the initial reactant mass.

1. Law of Constant Proportions: Established by Proust, this law states that in a chemical substance, the elements are always present in definite proportions by mass.

Example: Pure water ($H_2O$) obtained from any source will always contain hydrogen and oxygen in a fixed mass ratio of $1:8$. If you decompose $9\text{ g}$ of water, you will always get $1\text{ g}$ of hydrogen gas and $8\text{ g}$ of oxygen gas.

Dalton's Atomic Theory

Postulate 1: Indivisibility

All matter is made up of very tiny particles called atoms, which participate in chemical reactions. Atoms are indivisible particles, which cannot be created or destroyed in a chemical reaction.

Postulate 2: Identical Nature

Atoms of a given element are identical in mass and chemical properties, while atoms of different elements have different masses and chemical properties.

Postulate 3: Compound Formation

Atoms combine in the ratio of small whole numbers to form compounds. The relative number and kinds of atoms are constant in a given compound.

How to Write Chemical Formulas (Criss-Cross Method)

1. Step 1: Write Symbols — Write down the symbols of the combining elements or ions side-by-side. Write the positive ion (cation/metal) on the left and the negative ion (anion/non-metal) on the right. E.g., for Aluminium Oxide, write Al and O.
2. Step 2: Write Valencies — Write the respective valency or charge below each element's symbol. The valency of Aluminium (Al) is 3+, and Oxygen (O) is 2-.
3. Step 3: Criss-Cross the Valencies — Cross-over the valency numbers (ignoring the charges) to write them as subscripts for the opposite element. The valency of O (2) goes to Al, and the valency of Al (3) goes to O.
4. Step 4: Write Final Formula — Combine them to write the chemical formula. For Aluminium Oxide, it becomes Al₂O₃. For polyatomic ions, remember to use parentheses if the subscript is greater than 1 (e.g., Ca(OH)₂).

Understanding the Mole Concept & Molar Mass

• What is a Mole?: Just as one dozen means 12 items, one mole of any substance is defined as that quantity which contains exactly $6.022 \times 10^{23}$ particles (atoms, molecules, or ions). This number is known as the Avogadro Constant ($N_A$).
• Molar Mass: The mass of 1 mole of a substance is called its molar mass. It is numerically equal to the atomic or molecular mass of that substance but written with grams ($g$) as the unit instead of $u$.
• Formula 1: Number of moles ($n$) = Given Mass ($m$) / Molar Mass ($M$)
• Formula 2: Number of moles ($n$) = Given number of particles ($N$) / Avogadro's Number ($N_A$)

CBSE Board Exam Tips & Common Pitfalls

• Unit Alert: Do not confuse Unified Mass ($u$) with Molar Mass ($g$). $u$ represents the mass of a single molecule, whereas $g$ represents the mass of $6.022 \times 10^{23}$ molecules.
• Formula Parentheses: When writing formulas with polyatomic ions like Nitrate ($NO_3^-$) or Carbonate ($CO_3^{2-}$), always use brackets if there's more than one ion. For example, Calcium Nitrate is $Ca(NO_3)_2$. Writing $CaNO_{32}$ is a highly penalized error!
• Diatomic Elements: Elements like Nitrogen, Oxygen, Hydrogen, and Chlorine naturally exist as diatomic molecules ($N_2, O_2, H_2, Cl_2$). While calculating their molecular mass, always multiply their atomic masses by 2.

Practice Questions with Solutions

• Q: In a reaction, $5.3\text{ g}$ of sodium carbonate reacted with $6\text{ g}$ of ethanoic acid. The products were $2.2\text{ g}$ of carbon dioxide, $0.9\text{ g}$ water and $8.2\text{ g}$ of sodium ethanoate. Show that these observations are in agreement with the law of conservation of mass. A: Step 1: Write down the reaction equation: $\text{Sodium carbonate} + \text{Ethanoic acid} \rightarrow \text{Sodium ethanoate} + \text{Carbon dioxide} + \text{Water}$ Step 2: Calculate the total mass of the reactants before the reaction: $\text{Mass of Reactants} = 5.3\text{ g} (\text{Sodium carbonate}) + 6.0\text{ g} (\text{Ethanoic acid}) = 11.3\text{ g}$ Step 3: Calculate the total mass of the products formed after the reaction: $\text{Mass of Products} = 8.2\text{ g} (\text{Sodium ethanoate}) + 2.2\text{ g} (\text{Carbon dioxide}) + 0.9\text{ g} (\text{Water}) = 11.3\text{ g}$ Step 4: Compare both masses. Since the total mass of the reactants ($11.3\text{ g}$) equals the total mass of the products ($11.3\text{ g}$), the law of conservation of mass is verified. Final answer: The reaction strictly obeys the Law of Conservation of Mass.
• Q: Write the chemical formulas for (i) Magnesium Chloride, (ii) Calcium Oxide, and (iii) Ammonium Sulfate. A: Step 1: For Magnesium Chloride: Symbols: $Mg$ (valency 2+) and $Cl$ (valency 1-). Criss-cross the numbers to get $MgCl_2$. Step 2: For Calcium Oxide: Symbols: $Ca$ (valency 2+) and $O$ (valency 2-). The ratio simplifies from $Ca_2O_2$ to $CaO$. Step 3: For Ammonium Sulfate: Symbols: $NH_4$ (valency 1+) and $SO_4$ (valency 2-). Since there are multiple ammonium ions, we use parentheses: $(NH_4)_2SO_4$. Final answer: (i) $MgCl_2$, (ii) $CaO$, (iii) $(NH_4)_2SO_4$
• Q: Calculate the molecular mass of Nitric Acid ($HNO_3$). (Atomic masses: $H = 1\text{ u}$, $N = 14\text{ u}$, $O = 16\text{ u}$). A: Step 1: Identify the number of atoms of each element in $HNO_3$: Hydrogen = 1, Nitrogen = 1, Oxygen = 3. Step 2: Multiply the number of atoms of each element by its respective atomic mass: $\text{Mass of } H = 1 \times 1 = 1\text{ u}$ $\text{Mass of } N = 1 \times 14 = 14\text{ u}$ $\text{Mass of } O = 3 \times 16 = 48\text{ u}$ Step 3: Add the masses together: $\text{Total molecular mass} = 1 + 14 + 48 = 63\text{ u}$ Final answer: The molecular mass of Nitric Acid is $63\text{ u}$.
• Q: Calculate the number of moles in $52\text{ g}$ of Helium ($He$) gas. (Atomic mass of $He = 4\text{ u}$). A: Step 1: Identify the given values: Given mass ($m$) = $52\text{ g}$ Molar mass of Helium ($M$) = $4\text{ g/mol}$ Step 2: Use the formula for calculating number of moles: $n = \frac{m}{M}$ Step 3: Substitute the values into the formula: $n = \frac{52}{4} = 13\text{ moles}$ Final answer: There are 13 moles of Helium in $52\text{ g}$ of Helium gas.

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