If you are preparing for Class 11/12 Chemistry, NEET, JEE, TNPSC, SSC or other competitive exams, understanding Chemical Arithmetic is absolutely essential.

This chapter forms the foundation of:

• Mole Concept
• Atomic & Molecular Mass
• Equivalent Mass
• Stoichiometry
• Volumetric Analysis
• Laws of Chemical Combination

In this detailed guide, we explain all concepts in a simple and exam-oriented way.

What is Chemical Arithmetic?

Chemical Arithmetic deals with numerical calculations in chemistry based on measurements, atomic masses, molecular masses, and chemical equations.

It mainly focuses on:

• Measurement & Significant Figures
• Units & SI System
• Mole Concept
• Stoichiometric Calculations
• Titration & Volumetric Analysis

Measurement in Chemistry

Chemistry is an experimental science. Every measurement involves:

• Arithmetic number
• Unit of measurement

🔹 Accuracy vs Precision

Significant Figures (Very Important for Exams)

Significant figures represent the accuracy of measurement.

Rules for Counting Significant Figures

1. All non-zero digits are significant
2. Zeros between digits are significant
3. Leading zeros are NOT significant
4. Trailing zeros after decimal are significant
5. Trailing zeros in whole numbers are NOT significant

Rounding Off Rules

• Digit < 5 → Ignore
• Digit > 5 → Increase previous digit
• Digit = 5 → Follow even/odd rule

Systems of Units in Chemistry

1️⃣ CGS System

Centimetre, Gram, Second

2️⃣ MKS System

Metre, Kilogram, Second

3️⃣ FPS System

Foot, Pound, Second

4️⃣ SI System (International System)

🔹 7 SI Base Units

Laws of Chemical Combination

These laws explain how elements combine.

1. Law of Conservation of Mass

Mass is neither created nor destroyed.

2. Law of Definite Proportion

Elements combine in fixed ratio.

3. Law of Multiple Proportion

Elements combine in simple whole-number ratios.

4. Gay-Lussac’s Law

Gases combine in simple volume ratios.

Atomic Theory & Hypotheses

Dalton’s Atomic Theory

• Matter consists of atoms
• Atoms combine in simple ratios
• Atoms are indivisible (old concept)

Modern Atomic Theory

• Atom is divisible
• Isotopes exist
• Nuclear reactions possible

Avogadro’s Hypothesis

Equal volumes of gases (same T & P) contain equal number of molecules.

Important Formula:

$$Molecular\ Mass = 2 × Vapour\ Density$$

Mole Concept (Most Important Topic)

Definition

1 mole contains 6.022 × 10²³ particles

Formula

$$Number\ of\ moles = \frac{Given\ Mass}{Molar\ Mass}$$

Important Fact

1 mole gas at STP = 22.4 litres

Atomic Mass & Molecular Mass

Atomic Mass

Relative mass compared to Carbon-12.

Average Atomic Mass Formula

$$\frac{(m×a + n×b)}{m+n}$$

Molecular Mass

Sum of atomic masses in a molecule.

Equivalent Mass

Equivalent mass depends on reaction type.

General Formula

$$Equivalent\ Mass = \frac{Molecular\ Mass}{n-factor}$$

For:

• Element → Atomic mass / Valency
• Acid → Molecular mass / Basicity
• Base → Molecular mass / Acidity
• Salt → Formula mass / Total charge

Percentage Composition & Empirical Formula

Percentage Formula

$$\% = \frac{Mass\ of\ Element}{Molecular\ Mass} × 100$$

Steps to Find Empirical Formula

1. Convert % into grams
2. Divide by atomic weight
3. Find simplest ratio
4. Write empirical formula

$$Molecular\ Formula = n × Empirical\ Formula$$

Chemical Stoichiometry

Stoichiometry means quantitative relationship in chemical reactions.

Two Types:

1️⃣ Gravimetric Analysis

Mass–Mass calculations

2️⃣ Volumetric Analysis

Titration-based calculations

Types of Titrations

• Acid–Base Titration
• Redox Titration
• Iodometric Titration
• Precipitation Titration

Important Formula

$$N_1V_1 = N_2V_2$$

Limiting Reagent

The reactant that gets completely consumed first is called Limiting Reagent.

It determines the maximum amount of product formed.

Important Quick Revision Points

• 1 mole = 6.022 × 10²³ particles
• 1 mole gas at STP = 22.4 L
• Molecular Mass = 2 × Vapour Density
• Equivalent Mass = Molecular Mass / n-factor
• N₁V₁ = N₂V₂

🎯 Why Chemical Arithmetic is Important for Competitive Exams?

This chapter is the foundation for:

• NEET Physical Chemistry
• JEE Main & Advanced
• TNPSC Chemistry Questions
• SSC & Railway Exams

Strong understanding ensures accuracy in numerical problems.