Chemistry Basic Concepts and Calculations - Lecture 2 Notes

Overview

• Topic: Scientific Notations, Mathematical Operations, Significant Figures
• Importance: Useful for handling large and small numbers in chemistry.

Scientific Notations

Definition

• Scientific notations are a way to express very large or very small numbers in a compact form.
• Format: n × 10^k
  • n is a number with one non-zero digit to the left of the decimal point.
  • k is the exponent indicating the power of ten.

Why Use Scientific Notations?

• Easier representation of large/small numbers.
• Simplifies mathematical calculations (addition, subtraction, multiplication, division).

Examples of Writing in Scientific Notation

1. Large Number Example: 4300000 = 4.3 × 10^6
   • Decimal moves 6 places to the left (positive exponent).
2. Small Number Example: 0.0000345 = 3.45 × 10^-5
   • Decimal moves 5 places to the right (negative exponent).

Mathematical Operations with Scientific Notation

Multiplication

• Multiply the coefficients and add the exponents.
  Example: (0.05 × 10^5) × (2.5 × 10^8) = (0.125 × 10^13) = 1.25 × 10^12

Division

• Divide the coefficients and subtract the exponents.
  Example: (1.0 × 10^3) / (1.0 × 10^5) = 1.0 × 10^(3-5) = 1.0 × 10^-2

Addition and Subtraction

• Convert to the same power of ten before performing the operation.
  Example: (6.65 × 10^4) + (8.95 × 10^3) = (6.65 × 10^4) + (0.895 × 10^4) = 7.55 × 10^4

Precision and Accuracy

Definitions

• Accuracy: How close a measured value is to the correct value.
• Precision: How closely individual measurements agree with each other.

Example of Accuracy and Precision

• Measurements: 1.94 g (not accurate), 2.00 g (accurate), etc.
• Precision can be assessed by how close the measurements are to each other, regardless of their accuracy.

Significant Figures

Definition

• Significant figures include all non-zero digits, zeros between non-zero digits, and trailing zeros in decimal numbers.

Rules for Identifying Significant Figures

1. All non-zero digits are significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros are not significant.
4. Trailing zeros in a decimal number are significant.
5. Trailing zeros in a whole number without a decimal point may or may not be significant.
6. Exact numbers have unlimited significant figures.

Examples

• 24.5 m has 3 significant figures.
• 2002 has 4 significant figures.
• 0.0025 has 2 significant figures.
• 1500 (no decimal) may have 2, 3, or 4 significant figures depending on context.

Rounding Numbers

Rounding Rules

1. If the digit to be dropped is less than 5, the last retained digit stays the same.
2. If the digit to be dropped is 5 or more, the last retained digit increases by 1.
3. For rounding to significant figures, keep the least number of significant figures from the input values in calculations.

Example

• Rounding 2.345 to 2 significant figures: 2.3
• Rounding 2.675 to 3 significant figures: 2.68

Dimensional Analysis

Definition

• A method for converting units using conversion factors.

Example Problem

• Convert 1.47 miles to inches using:
  • 1 mile = 5280 feet
  • 1 foot = 12 inches
  Calculation:
  1.47 miles × (5280 feet/mile) × (12 inches/foot) = total inches.

Conclusion

• In this lecture, we covered scientific notations, mathematical operations, significant figures, and dimensional analysis.
• Understanding these concepts is essential for accurately performing calculations in chemistry.