Chemca Formula Sheet - Some Basic Concepts of Chemistry (Mole Concept)

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EXAM MASTER FORMULA SHEET

Some Basic Concepts of Chemistry (Mole Concept)

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1. Laws of Chemical Combination

Law of Conservation of Mass (Lavoisier): Total mass of reactants = Total mass of products. (Not strictly valid for nuclear reactions).

Law of Definite Proportions (Proust): A given compound always contains exactly the same proportion of elements by weight.

Law of Multiple Proportions (Dalton): If two elements form more than one compound, the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers.

Gay Lussac's Law of Gaseous Volumes: Gases combine in simple whole number ratios by volume (at same T & P).

2. Atomic, Molecular Masses & V.D.

Average Atomic Mass (Isotopes):

\[ A_{\text{avg}} = \frac{A_1x_1 + A_2x_2 + \dots}{x_1 + x_2 + \dots} \]

\(x_i\) = % abundance or molar ratio

Average Molar Mass of Gaseous Mixture:

\[ M_{\text{mix}} = \frac{M_1n_1 + M_2n_2 + \dots}{n_1 + n_2 + \dots} \]

Vapour Density (V.D.):

\[ \text{Molar Mass} = 2 \times \text{V.D.} \] \[ \text{V.D.} = \frac{\text{Density of Gas}}{\text{Density of H}_2} \text{ (at same T, P)} \]

Dulong & Petit's Law (Solid Elements):

\[ \text{Atomic Weight} \times \text{Specific Heat} \approx 6.4 \]

Specific heat must be in \(\text{cal/g-}\!^\circ\text{C}\)

3. Fundamental Mole Relations (The Y-Map)

Avogadro's Number (\(N_A\)) = \(6.022 \times 10^{23}\) particles/mol.

Calculating Number of Moles (\(n\)):

\[ n = \frac{\text{Mass } (W)}{\text{Molar Mass } (M_w)} = \frac{\text{Number of Particles } (N)}{N_A} = \frac{\text{Volume of Gas at STP } (V)}{22.4 \text{ L}} \]

Note for Modern STP: Standard pressure is now 1 bar. At 273.15 K and 1 bar, molar volume is 22.7 L. However, for most traditional JEE/NEET problems, 22.4 L (at 1 atm) is still widely used unless 1 bar is specifically mentioned.

4. Stoichiometry & Advanced Computations

Limiting Reagent (L.R.):

For reaction \(aA + bB \rightarrow cC\), calculate ratio: \(\frac{\text{Moles given}}{\text{Stoichiometric Coefficient}}\)
The reactant with the minimum value of this ratio is the Limiting Reagent. It completely dictates the amount of product formed.

% Yield: \[ \% \text{ Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100 \]

% Purity: \[ \% \text{ Purity} = \frac{\text{Mass of pure chemical}}{\text{Total mass of sample}} \times 100 \]

Principle of Atom Conservation (POAC):

Mass of atoms of an element is conserved. Useful when chemical equation cannot be easily balanced.

For \(A \rightarrow B\): \[ (\text{No. of atoms of element in 1 molecule of A}) \times (\text{Moles of A}) = (\text{No. of atoms of element in 1 molecule of B}) \times (\text{Moles of B}) \]

5. Percentage Composition & Formulas

Mass Percentage of an Element:

\[ \% \text{ of Element} = \frac{n \times \text{Atomic Mass of Element}}{\text{Molar Mass of Compound}} \times 100 \]

Molecular vs Empirical Formula:

\(\text{Molecular Formula} = n \times (\text{Empirical Formula})\)

Where \(n = \frac{\text{Molecular Mass}}{\text{Empirical Formula Mass}}\) (n is an integer)

6. Concentration Terms & Dilution

Temperature Dependent (Volume Based): Molarity (M), Normality (N), Formality (F), % w/v, % v/v

Temperature Independent (Mass Based): Molality (m), Mole Fraction (\(\chi\)), % w/w, ppm, ppb

Term	Formula	Unit
Molarity (M)	\( \frac{\text{Moles of Solute}}{\text{Volume of Solution (L)}} \)	mol/L (M)
Molality (m)	\( \frac{\text{Moles of Solute}}{\text{Mass of Solvent (kg)}} \)	mol/kg (m)
Mole Fraction (\(\chi_A\))	\( \frac{n_A}{n_A + n_B} \) (\(\chi_A + \chi_B = 1\))	Unitless
Parts Per Million (ppm)	\( \frac{\text{Mass of Solute}}{\text{Total Mass}} \times 10^6 \)	ppm

Chemca Master Interconversions:

\[ M = \frac{10 \times d \times (\% w/w)}{M_{\text{solute}}} \]

d = density of solution (g/mL)

\[ m = \frac{1000 \times M}{1000 \times d - (M \times M_{\text{solute}})} \]

\[ m = \frac{1000 \times \chi_{\text{solute}}}{\chi_{\text{solvent}} \times M_{\text{solvent}}} \]

Dilution Formula:

\[ M_1 V_1 = M_2 V_2 \]

Mixing of Solutions (Same Solute):

\[ M_{mix} = \frac{M_1 V_1 + M_2 V_2}{V_1 + V_2} \]

7. Advanced & Special Concepts

Volume Strength of H₂O₂ (V):

\( \text{Volume Strength (V)} = 11.2 \times \text{Molarity} \)
\( \text{Volume Strength (V)} = 5.6 \times \text{Normality} \)
\( \% \text{ Strength (w/v)} = \frac{17}{56} \times V \)

*Based on STP (273K, 1 atm). If 1 bar is used, factor is 11.35.

Oleum (H₂S₂O₇) Labelling:

Oleum is labeled as \((100 + x)\%\), where \(x\) is the mass of water required to fully react with free \(SO_3\) in 100g sample.

\[ \% \text{ of Free } SO_3 = \frac{80}{18} \times x \]

Hardness of Water:

\[ \text{Degree of Hardness (ppm)} = \frac{\text{Mass of } CaCO_3 \text{ equivalent}}{\text{Total Mass of Water}} \times 10^6 \]

\( \text{Moles of } CaCO_3 \text{ eq.} = \text{Moles of } Ca^{2+}/Mg^{2+} \text{ salt} \times \frac{n\text{-factor of salt}}{2} \)

8. Equivalent Concept & Titration

Equivalent Weight (\(E\)):

\[ E = \frac{\text{Molar Mass } (M)}{\text{n-factor (Valency factor)}} \]

Number of Equivalents (\(Eq\)):

\[ Eq = \frac{\text{Mass}}{E} = \text{Moles} \times \text{n-factor} = N \times V(L) \]

How to calculate n-factor:

Acids: Basicity (No. of replaceable \(H^+\) ions). E.g., \(H_2SO_4 \rightarrow 2\), \(H_3PO_4 \rightarrow 3\), \(H_3PO_3 \rightarrow 2\).
Bases: Acidity (No. of replaceable \(OH^-\) ions).
Salts: Total magnitude of positive or negative charge on ions.
Redox Agents: Number of electrons exchanged per molecule OR Change in oxidation state \(\times\) number of atoms.

Law of Chemical Equivalence:

In any reaction \(aA + bB \rightarrow cC + dD\), substances react in equal equivalents:

\[ \text{Equivalents of A} = \text{Equivalents of B} = \text{Equivalents of C} = \text{Equivalents of D} \] \[ N_1 V_1 = N_2 V_2 \]

9. Eudiometry (Gas Analysis)

General Combustion Equation of Hydrocarbons:

\[ C_xH_y + \left(x + \frac{y}{4}\right)O_2 \longrightarrow xCO_2(g) + \frac{y}{2}H_2O(l) \]

Crucial Point: At room temperature, water formed is considered liquid. Therefore, its volume contribution to the gaseous mixture is taken as zero. Contraction in volume (\(V_c\)) = \(V_{\text{reactants}} - V_{\text{products}}\).

Gas to be absorbed	Absorbent Used
\(CO_2, SO_2, Cl_2\) (Acidic Gases)	Aqueous KOH or NaOH solution
\(O_2\) (Oxygen)	Alkaline Pyrogallol solution
\(O_3\) (Ozone)	Turpentine Oil
\(CO\) (Carbon Monoxide)	Ammoniacal Cuprous Chloride (\(Cu_2Cl_2\))
\(H_2O\) vapour (Moisture)	Anhydrous \(CaCl_2\), Conc. \(H_2SO_4\), or \(P_2O_5\)
\(NH_3\) (Ammonia)	Water or Dilute acid / Nessler's Reagent

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Chemca Formula Sheet - Mole Concept