GOB Chemistry: Measurement, Significant Figures, and Scientific Reasoning Study Guide

Measurement and Significant Figures

Understanding Significant Figures

Significant figures are the digits in a measurement that are known with certainty plus one digit that is estimated. They reflect the precision of a measured or calculated quantity.

• Definition: Significant figures are all the nonzero digits, zeros between nonzero digits, and trailing zeros in the decimal portion.

• Example: The number 1.250100 has 7 significant figures.

• Application: When performing calculations, the result should be rounded to the correct number of significant figures based on the operation (multiplication/division: least number of sig figs; addition/subtraction: least number of decimal places).

Rounding and Expressing Numbers in Scientific Notation

Scientific notation is used to express very large or very small numbers in a compact form. Rounding to a specified number of significant figures is essential for reporting measurements accurately.

• Example: 0.00222755 rounded to four significant figures is $2.228 \times 10^{-3}$.

• Formula: $a \times 10^n$ where a is a number between 1 and 10, and n is an integer.

Measured vs. Exact Numbers

Measured numbers are obtained from instruments and have uncertainty, while exact numbers are counted or defined and have no uncertainty.

• Measured Number: 10 cm/in (from a ruler)

• Exact Number: 12 eggs/dozen (by definition)

Conversion Factors and Dimensional Analysis

Conversion factors are ratios used to express a quantity in different units. Dimensional analysis is a method to convert units using these factors.

• Example: 1 gal = 4 qt = 3.7854 L

• Application: To convert 22.0 gal to liters: $22.0 \text{ gal} \times \frac{3.7854 \text{ L}}{1 \text{ gal}} = 83.3 \text{ L}$

Calculating Volume and Mass

Volume and mass calculations often require conversion between units and application of density.

• Formula for Volume: $V = \frac{m}{d}$ where m is mass and d is density.

• Example: To find the mass of 2.00 L of a solution with density 1.15 g/mL: $2.00 \text{ L} \times \frac{1000 \text{ mL}}{1 \text{ L}} \times 1.15 \text{ g/mL} = 2300 \text{ g}$

Scientific Reasoning and Experimental Design

Steps in the Scientific Method

The scientific method is a systematic approach to investigation.

• Observation: Gathering data through senses or instruments.

• Hypothesis: A tentative explanation for observations.

• Experiment: Testing the hypothesis under controlled conditions.

• Theory: A well-substantiated explanation based on repeated experiments.

Classification of Substances

In chemistry, substances are classified as chemicals or non-chemicals based on their composition and properties.

• Chemical: A substance with a definite composition (e.g., sugar).

• Non-chemical: Forms of energy or mixtures without definite composition (e.g., heat, light, wave).

Application of Mathematical Relationships in Chemistry

Equations and Rearrangement

Chemical and physical relationships are often expressed as equations that can be rearranged to solve for unknowns.

• Example: From $P_1 V_1 = P_2 V_2$, to solve for $V_2$:

$V_2 = \frac{P_1 V_1}{P_2}$

Specific Gravity and Density

Specific gravity is the ratio of the density of a substance to the density of water.

• Formula: $\text{Specific gravity} = \frac{\text{Density of sample}}{\text{Density of water}}$

• Application: If urine has a density of 1.014 g/mL, its specific gravity is $\frac{1.014}{1.00} = 1.014$

Tables

Sample Table: Significant Figures in Numbers

This table compares the number of significant figures in various numbers.

Number	Significant Figures
0.04300	4
0.003002	4
1.04	3
3.050	4

Sample Table: Conversion Factors

This table lists common conversion factors used in chemistry.

Conversion	Factor
1 gal to L	3.7854 L
1 kg to lb	2.20 lb
1 in to cm	2.54 cm

Additional info:

• Some questions involve practical applications such as dosage calculations and unit conversions, which are essential skills in GOB Chemistry.

• Understanding significant figures and scientific notation is foundational for all laboratory and clinical measurements.