Atoms and Molecules — NCERT Solutions, AI Tutor & Practice

Law of conservation of mass: In any physical or chemical change, mass can neither be created nor destroyed. The total mass of the reactants is always equal to the total mass of the products.

Law of constant proportions (definite proportions): In a chemical compound, the elements are always present in a fixed ratio by mass, irrespective of the source or method of preparation of the compound.

Example: In water ($H_2O$), hydrogen and oxygen are always present in the mass ratio $1:8$.

Total mass of reactants: $5.3\ \text{g} + 6.0\ \text{g} = 11.3\ \text{g}$

Total mass of products: $2.2\ \text{g} + 0.9\ \text{g} + 8.2\ \text{g} = 11.3\ \text{g}$

Since total mass of reactants $=$ total mass of products $= 11.3$ g, the observations agree with the law of conservation of mass.

Atomic mass unit (u): One atomic mass unit is defined as exactly one-twelfth ($\frac{1}{12}$) of the mass of one atom of carbon-12 ($^{12}C$).

$1\ \text{u} = \frac{1}{12} \times \text{mass of one } ^{12}C\ \text{atom}$

The carbon-12 isotope is taken as the standard reference. The atomic masses of all other elements are expressed relative to this standard.

(a) Water, $H_2O$: $= (2 \times 1) + (1 \times 16)$ $= 2 + 16 = 18\ \text{u}$

(b) Nitric acid, $HNO_3$: $= (1 \times 1) + (1 \times 14) + (3 \times 16)$ $= 1 + 14 + 48 = 63\ \text{u}$

Calcium chloride is an ionic compound, so we calculate its formula unit mass.

$\text{Formula unit mass of } CaCl_2 = (1 \times 40) + (2 \times 35.5)$ $= 40 + 71 = 111\ \text{u}$

Use the criss-cross method: the valency of one ion becomes the subscript of the other.

(a) Aluminium oxide: $Al^{3+}$ and $O^{2-}$ $\Rightarrow Al_2O_3$

(b) Sodium sulphate: $Na^{+}$ and $SO_4^{2-}$ $\Rightarrow Na_2SO_4$

(c) Magnesium nitride: $Mg^{2+}$ and $N^{3-}$ $\Rightarrow Mg_3N_2$

One mole is the amount of a substance that contains as many elementary particles (atoms, molecules, or ions) as there are atoms in exactly 12 g of carbon-12.

One mole of any substance contains Avogadro's number of particles: $N_A = 6.022 \times 10^{23}\ \text{particles}$

Also, the mass of one mole of a substance is equal to its atomic or molecular mass expressed in grams (molar mass).

Step 1 — Molar mass of $CO_2$: $= 12 + (2 \times 16) = 12 + 32 = 44\ \text{g/mol}$

Step 2 — Number of moles: $n = \frac{\text{given mass}}{\text{molar mass}} = \frac{22}{44}$ $n = 0.5\ \text{mol}$

Step 1 — Number of moles of water: $n = \frac{\text{given mass}}{\text{molar mass}} = \frac{9}{18} = 0.5\ \text{mol}$

Step 2 — Number of molecules: $N = n \times N_A = 0.5 \times 6.022 \times 10^{23}$ $N = 3.011 \times 10^{23}\ \text{molecules}$

Step 1 — Number of moles of atoms: $n = \frac{\text{number of atoms}}{N_A} = \frac{3.011 \times 10^{23}}{6.022 \times 10^{23}} = 0.5\ \text{mol}$

Step 2 — Mass of sodium: $\text{mass} = n \times \text{molar mass} = 0.5 \times 23$ $= 11.5\ \text{g}$

In the criss-cross method, the subscript of one element equals the valency of the other element.

For $X_2Y_3$:

• Subscript of $X$ = 2, which comes from the valency of $Y$.
• Subscript of $Y$ = 3, which comes from the valency of $X$.

Given valency of $X = 3$ (matches subscript of Y = 3).

Since subscript of X = 2 comes from valency of Y: $\text{Valency of } Y = 2$

Check: $X^{3+}$ and $Y^{2-}$ → criss-cross gives $X_2Y_3$. ✓

(a) Moles from number of atoms: $n = \frac{12.044 \times 10^{23}}{6.022 \times 10^{23}} = 2\ \text{mol of atoms}$

(b) Moles from mass of $O_2$ gas:

Molar mass of $O_2 = 2 \times 16 = 32\ \text{g/mol}$ $n = \frac{\text{given mass}}{\text{molar mass}} = \frac{32}{32} = 1\ \text{mol of } O_2$