Basic Concepts of Chemistry: Scientific Notation

Introduction

• Previous Topics Covered:
  • Introduction to Chemistry
  • Matter and its classification
  • Properties of matter
  • Physical quantities and their units

Importance of Scientific Notation

• Used to handle very small or very large numbers
• Essential for solving numericals in physical chemistry, especially in competitive exams

What is Scientific Notation?

• Definition: A simplified way to represent very large or very small numbers
• Format: n x 10^n
  • n (base) is a number between 1 and 9
  • 10^n (exponent) can be positive or negative

Example: Mole Concept

• Chemical Reaction: 2 moles of H2 + 1 mole of O2 → 2 moles of H2O
• Mole: A counting unit similar to a dozen
• Value of 1 Mole: 6.022 x 10^23
• Scientific Notation Example:
  • Original number: 602200000000000000000000
  • Scientific notation: 6.022 x 10^23

Writing Numbers in Scientific Notation

• Very Large Number:
  • Example: 602200000000000000000000
  • Scientific notation: 6.022 x 10^23
• Very Small Number:
  • Example: 0.000000000000385
  • Scientific notation: 3.85 x 10^-12

Rules for Shifting Decimal Points

• Left Shift: Decimal point to left → positive exponent
• Right Shift: Decimal point to right → negative exponent
• Example:
  • Original: 0.000000000385
  • Shift decimal to get: 3.85 x 10^-12

Examples of Scientific Notation Conversion

1. 4.8 million:
   • Original: 4800000
   • Scientific notation: 4.8 x 10^-5
2. 2340000:
   • Original: 2340000
   • Scientific notation: 2.34 x 10^6
3. 8008:
   • Original: 8008
   • Scientific notation: 8.008 x 10^3
4. 500:
   • Original: 500
   • Scientific notation: 5.0 x 10^2
5. 0.00000060:
   • Original: 0.00000060
   • Scientific notation: 6.0 x 10^8

Arithmetic Operations with Scientific Notation

Multiplication

• Formula: (a x 10^m) x (b x 10^n) = (a x b) x 10^(m+n)
• Example: 2 x 10^5 * 3 x 10^6
  • Solution: (2 x 3) x 10^(5+6) = 6 x 10^11*

Division

• Formula: (a x 10^m) / (b x 10^n) = (a / b) x 10^(m-n)
• Example: 10 x 10^-6 / 2 x 10^5
  • Solution: (10 / 2) x 10^(-6 - 5) = 5 x 10^-11

Addition and Subtraction

• Rule: Exponents must be the same
• Addition Example: 6.1 x 10^4 + 2.2 x 10^3
  • Convert to the same exponent: 6.1 x 10^4 + 0.22 x 10^4
  • Solution: (6.1 + 0.22) x 10^4 = 6.32 x 10^4
• Subtraction Example: 4 x 10^-2 - 2 x 10^-3
  • Convert to the same exponent: 4 x 10^-2 - 0.2 x 10^-2
  • Solution: (4 - 0.2) x 10^-2 = 3.8 x 10^-2

Summary

• Scientific Notation simplifies representation of extremely large or small numbers.
• Essential for dealing with measurements in chemistry.
• Used extensively in physical chemistry for solving numerical problems.

Next Topic

• Significant Figures