Scientific Inquiry and the Scientific Method

Observation, Research, and Experimentation

The scientific method is a systematic approach used in scientific study, including chemistry, to investigate phenomena, acquire new knowledge, or correct and integrate previous knowledge. It involves making observations, forming hypotheses, conducting experiments, and drawing conclusions.

• Observation vs. Inference:

  • Observation: Information gathered by the five senses. Can be qualitative (descriptive, without numbers) or quantitative (with numbers, counts, or measurements).

  • Inference: Assumptions or interpretations based on observations and prior knowledge.

  • Example: "The object is red" (observation); "The object is a book because it has pages" (inference).

• Research: Gathering background information to inform hypotheses and experiments.

• Hypothesis: A proposed, testable explanation for a phenomenon. Must be falsifiable and based on prior observations.

• Theory vs. Law:

  • Theory: A well-substantiated explanation of some aspect of the natural world, based on a body of evidence.

  • Law: A statement that describes an observable occurrence in nature that appears to always be true.

  • Additional info: Theories explain why phenomena occur; laws describe what happens.

• Experiment: A controlled method of testing a hypothesis.

  • Control Group: The group not exposed to the experimental variable; used for comparison.

  • Experimental Group: The group exposed to the variable being tested.

  • Variables:

    • Independent Variable: The variable that is changed or manipulated.

    • Dependent Variable: The variable that is measured or observed; it depends on the independent variable.

  • Example: Testing the effect of room temperature on sleep hours. Temperature is the independent variable; hours of sleep is the dependent variable.

• Conclusion and Report: Summarizing results and communicating findings.

Shortcomings of the "Textbook" Scientific Method

• The steps may not always occur in a strict order.

• Not all steps are required in every investigation.

Measurement in Chemistry

Uncertainty, Accuracy, and Precision

Measurements in chemistry are subject to limitations in accuracy and precision, and always include some degree of uncertainty.

• Uncertainty: The range within which the true value is expected to lie, often determined by the measuring instrument's smallest division.

• Accuracy: How close a measured value is to the accepted or true value.

• Precision: How close repeated measurements are to each other.

• Percent Error: Used to express accuracy: $\%\ \text{error} = \frac{\left| \text{Accepted} - \text{Measured} \right|}{\text{Accepted}} \times 100$

• Standard Deviation: Used to express precision: $\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \overline{x})^2}$

• Types of Error:

  • Random Error: Unavoidable fluctuations affecting precision.

  • Systematic Error: Consistent bias due to faulty equipment or technique, affecting accuracy.

Significant Figures (Sig Figs)

Rules for Counting Significant Figures

• All nonzero digits are significant.

• Zeros between nonzero digits are always significant.

• Leading zeros are never significant.

• Trailing zeros are significant only if there is a decimal point.

• Examples:

  • 2.06 (3 sig figs)

  • 0.0026 (2 sig figs)

  • 30.0 (3 sig figs)

Significant Figures in Calculations

• Addition/Subtraction: The answer is rounded to the same decimal place as the least certain measurement. Example: 3.5670 + 10.304 + 233.1 = 247.0 (rounded to the tenths place)

• Multiplication/Division: The answer is rounded to the same number of significant figures as the measurement with the fewest sig figs. Example: 23.098 × 4.8 = 111 (rounded to 2 sig figs)

SI Units, Prefixes, and Scientific Notation

SI Base Units

• Volume is measured in liters (L), which is not a base SI unit but is commonly used in chemistry.

SI Prefixes

Scientific Notation

• Used to express very large or very small numbers in the form $a \times 10^n$, where $1 \leq |a| < 10$ and $n$ is an integer.

• Example: 0.00000574 meters = $5.74 \times 10^{-6}$ meters

Dimensional Analysis and Unit Conversions

Conversion Factors and Examples

• Conversion Factor: An equality expressed as a fraction to convert between units. Example: $\frac{12\ \text{inches}}{1\ \text{foot}} = 1$

• Example Problem: How many inches are in 128.5 feet? $128.5\ \text{feet} \times \frac{12\ \text{inches}}{1\ \text{foot}} = 1542\ \text{inches}$

• Multi-step Conversion Example: A woman has been alive for 26.5 years. How many hours is this? $26.5\ \text{years} \times \frac{365\ \text{days}}{1\ \text{year}} \times \frac{24\ \text{hours}}{1\ \text{day}} = 232,000\ \text{hours}$

• Dimensional analysis uses unit cancellation to ensure correct conversions.

Summary Table: Types of Error