Chemistry I Study Notes

Introduction

• Course: Foundation Chemistry I (CHEM 113)

• Textbook: Chemistry: The Central Science (13th Edition)

• University: University of Ghana, Department of Chemistry

Importance of Numbers in Chemistry

• Numbers are crucial in chemistry.

• Scientific phenomena are described using small units to represent various quantities.

• Key Concepts in Chemistry include:

  • Units of measurement

  • Quantities to be measured and calculated

  • Uncertainty in measurement

  • Significant figures

  • Dimensional analysis

Units of Measurement (SI Units)

• Definition: Système International d’Unités (International System of Units) is the standard for measurement.

• Each physical quantity has a different base unit, e.g., length, mass, time, etc.

Metric System Prefixes

• Prefixes modify base units for convenient use.

Table of SI Prefixes

• Examples:

  • Nanogram: ng (10^-9 g)

  • Microsecond: μs (10^-6 s)

  • Millimeter: mm (10^-3 m)

Practice Exercise

1. Weighing Suitable Items on a Bathroom Scale:

   • (a) 2.0 ✕ 10^7 mg

   • (b) 2500 mg

   • (c) 5 ✕ 10^{-4} kg

   • (d) 4 ✕ 10^6 cg

   • (e) 5.5 ✕ 10^8 dg

2. Identify SI Units:

   • (a) 10^-9 gram (nanogram)

   • (b) 10^-6 second (microsecond)

   • (c) 10^-3 meter (millimeter)

Common Non-SI Metric Units Used in Chemistry

Useful Unit Conversions

Decimal Multipliers in SI Units

• Prefixes serve to express exceptionally large or small numbers more conveniently:

  • 1 mL = 10^{-3} L

  • 1 km = 1000 m

  • 1 ng = 10^{-9} g

  • Example: 1,130,000 m = 1.13 × 10^6 m = 1.13 Mm

Fundamental Measurements, Mass, and Length

• Mass and Length as Basic Units

  • Mass: A measure of material amount, base unit in SI is kilogram (kg) but grams (g) are often used in laboratories.

  • 1 kg = 1000 g

  • Mass measurement involves comparing sample weight with known mass units using a balance.

  • Length: Measure of distance, with base unit meter (m).

Laboratory Measurements of Length

• SI unit = meter (m)

• Common laboratory units:

  • Centimeter (cm) = 10^{-2} m = 0.01 m

  • Millimeter (mm) = 10^{-3} m = 0.001 m

Volume Measurement

• Volume is derived from length (V = length³) with the SI unit as m³.

• More commonly used metric units for volume:

  • 1 L = 1 dm³ (exactly)

  • Laboratory glassware measures in L or mL:

  • 1 L = 1000 mL

  • 1 mL = 1 cm³

Volume Conversion Table

• Relationships:

  • 10 mm = 1 cm

  • 10 cm = 1 dm

  • 10 dm = 1 m

  • 1 cm³ = (1 x 10^{-2} m)³ = 1 x 10^{-6} m³

  • 1 dm³ = (1 x 10^{-1} m)³ = 1 x 10^{-3} m³

Volume Measurement Units

• Volume is not a base unit in SI; it is derived from the cubic meter (m³).

• Commonly used metric units:

  • Liter (L), derived as 1 decimeter cubed (dm³).

  • Milliliter (mL), equivalent to 1 centimeter cubed (cm³).

Example Problem: Volume Calculations

• Earth’s oceans contain approximately 1.36 ✕ 10^9 km³ of water.

• Convert to liters:

  • Using 1 L = 10^{-3} m³ and 1 km = 10^{3} m, we find a conversion factor for volumes.

Density Calculation

• Definition: Density is a physical property defined by the formula: $Density = \frac{mass}{volume}$

  • Common units: g/mL or g/cm³.

Example Density Calculations

1. Calculate density of mercury with 1.00 ✕ 10² g occupying 7.36 cm³.

2. Calculate volume of 65.0 g of liquid methanol with density 0.791 g/mL.

3. Calculate mass of a cube of gold with density 19.32 g/cm³ and length of 2.00 cm.

4. Volume of the cube: $Volume = (2.00 cm)³ = 8.00 cm³$

5. $Mass = volume \times density = (8.00 cm³)(19.32 g/cm³) = 155 g$

Numbers in Science

• Exact numbers: Counted or defined (e.g., 12 eggs in a dozen).

• Inexact numbers: Depend on measurement methods and instrument limitations (e.g., balances with different precisions).

Uncertainty in Measurements

• Subject to differences in device accuracy and precision.

• A good measurement provides a range of uncertainty.

Importance of Uncertainty

• Measurements should include uncertainty:

  • Example: 152 cm may have an uncertainty of +/- 1 cm.

Types of Measurement Instruments

• Pipettes, volumetric flasks, graduated cylinders, syringes, and burettes each deliver variable volumes.

Measurement Precision and Accuracy

• Good measurements require clarity in uncertainty understanding.

• Understanding systematic (determinate) and random (indeterminate) errors is critical for precision and reproducibility.

Systematic Errors

• Caused by instrument malfunction, methodology, or operator error (e.g., calibration issues, improper measurement techniques).

• Detectable and usually correctable.

Random Errors

• Arise from variations in measurements due to instrument precision limits and environmental changes.

• Cannot be eliminated but can be minimized through improved technique and averaging repeated measurements.

Key Definitions and Differences

• Precision: Reproducibility of measurements across trials.

• Accuracy: Closeness of measured value to known true value.

Significant Figures

• Definition: The digits in a number that carry meaning contributing to its precision.

• Guidelines for significant figures include:

  1. All non-zero numbers are significant.

  2. Any zeros between non-zero digits are significant.

  3. Trailing zeros in a decimal number are significant.

  4. Leading zeros are not significant.

Rules for Addition and Subtraction

• The result is limited to the decimal place of the number with the fewest decimal places.

Rules for Multiplication and Division

• The answer has the same number of significant figures as the number with the least significant figures among input values.

Logarithmic Calculations

• Logarithm: If n = 10⁰, then log n = a.

  • Examples: log 100 = 2; antilog 2 = 100.

Examples of Logarithmic Calculations

• Combine log and antilog to find measurements with significant digits.

Error Analysis and Propagation

• Incorporate errors and uncertainties when operating with combinations of data:

  • Addition or subtraction: $σ<em>{z} = σ</em>{x} + σ_{y}$

  • Multiplication or division yields percentages: $$

Final Exercises

1. Calculate mean, standard deviation, and variance from datasets to compare measurements.

2. Utilize the empirical rule to justify the accuracy of data in scientific contexts.