Chapter 1: Introduction to Matter, Energy, and Measurement – General Chemistry Study Notes

Introduction: Matter, Energy, and Measurement

This chapter introduces foundational concepts in chemistry, focusing on the measurement of matter and energy, the use of units, and the importance of precision and accuracy in scientific work. Mastery of these topics is essential for all subsequent studies in chemistry.

Units of Measurement

• Metric System: The metric system is the standard system of measurement in science and most countries worldwide.

• SI Units: The Système International d'Unités (SI) defines seven base units from which all other units are derived.

Physical Quantity	Name of Unit	Abbreviation
Mass	Kilogram	kg
Length	Meter	m
Time	Second	s
Temperature	Kelvin	K
Amount of substance	Mole	mol
Electric current	Ampere	A
Luminous intensity	Candela	cd

Be able to recognize these units and their associated quantities.

Metric System and Prefixes

Prefixes are used to convert base units into units appropriate for the quantity being measured. The base unit can be any unit (e.g., meter, gram, liter).

Prefix	Abbreviation	Meaning	Example
Giga	G	109	1 gigameter (Gm) = 1 × 109 m
Mega	M	106	1 megameter (Mm) = 1 × 106 m
Kilo	k	103	1 kilometer (km) = 1 × 103 m
Deci	d	10-1	1 decimeter (dm) = 0.1 m
Centi	c	10-2	1 centimeter (cm) = 0.01 m
Milli	m	10-3	1 millimeter (mm) = 0.001 m
Micro	μ	10-6	1 micrometer (μm) = 1 × 10-6 m
Nano	n	10-9	1 nanometer (nm) = 1 × 10-9 m
Pico	p	10-12	1 picometer (pm) = 1 × 10-12 m
Femto	f	10-15	1 femtometer (fm) = 1 × 10-15 m

Example: 1 Gbyte = 1 × 109 bytes; 1 mL = 1 × 10-3 L; 1 kg = 1 × 103 g

Temperature

Temperature is a measure of the average kinetic energy of the particles in a sample. The Celsius and Kelvin scales are most commonly used in scientific measurements.

• Kelvin (K) is the SI unit for temperature.

• Conversion formulas:

  • $K = ^ ext{o}C + 273.15$

  • $^ ext{o}C = K - 273.15$

• The change in temperature ($\Delta T$) is the same in both Celsius and Kelvin.

Example: $\Delta T(^\text{o}C) = 100 - 0 = 100$; $\Delta T(K) = 373 - 273 = 100$

Volume

Volume is the amount of space occupied by a substance. The most commonly used metric units for volume are the liter (L) and the milliliter (mL).

• 1 L = 1 dm3

• 1 mL = 1 cm3 = 1 cc

Equivalence Statements:

• 1 dm3 = 1 × 10-3 m3

• 1 cm3 = 1 × 10-6 m3

Measuring Volume

• Graduated Cylinder, Syringe, Burette: Used to deliver variable volumes (have graduations/markings).

• Pipette, Volumetric Flask: Used to deliver or hold a specific volume (one marking).

The more markings, the greater the accuracy.

Density

Density is a physical property defined as mass divided by volume:

$d = \frac{m}{V}$

• Common units: g/mL or g/cm3

• To solve for volume: $V = \frac{m}{d}$

• To solve for mass: $m = dV$

Example: If 65.0 g of methanol has a density of 0.791 g/mL, $V = \frac{65.0\ g}{0.791\ g/mL} = 82.2\ mL$

Uncertainty in Measurement

• Exact Numbers: Known values with no uncertainty (e.g., 12 eggs in a dozen).

• Inexact Numbers: Values obtained by measurement, always with some uncertainty.

• All measurements have some degree of uncertainty, typically in the last digit reported.

Example: 2.49 mL ± 0.01 mL; 809 g ± 1 g; 1.3 cm ± 0.1 cm

Accuracy versus Precision

• Accuracy: How close a measurement is to the true value.

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

Example:

Trial	Mass (g)
1	3.52
2	3.56
3	3.49
4	3.51
Average	3.52

This data set is precise (values are close together) but not accurate (far from the true value of 2.50 g).

Significant Figures

• Significant figures are the digits in a measurement that are known with certainty plus one estimated digit.

• When rounding, do not overstate the accuracy of your answer.

Rules for Determining Significant Figures

1. All nonzero digits are significant (e.g., 3.25 has 3 s.f.).

2. Zeroes between significant digits are significant (e.g., 3.005 has 4 s.f.).

3. Zeroes at the beginning are never significant (e.g., 0.0057 has 2 s.f.).

4. Zeroes at the end are significant if a decimal point is present (e.g., 8000. has 4 s.f.).

Significant Figures in Calculations

• Addition/Subtraction: The answer should have the same number of decimal places as the measurement with the fewest decimal places.

• Multiplication/Division: The answer should have the same number of significant figures as the measurement with the fewest significant figures.

Example (Addition):

$106.7\ g + 0.25\ g + 0.195\ g = 107.145\ g$ (report as 107.1 g, 1 decimal place)

Example (Multiplication):

$(7.3\ cm) \times (0.002\ cm) = 0.0146\ cm^2$ (report as 0.01 cm2, 1 s.f.)

Scientific Notation

Used to express very large or very small numbers. The number is written as a product of a number between 1 and 10 and a power of ten:

$D.DD \times 10^n$

• Large numbers (greater than 1): positive exponent

• Small numbers (less than 1): negative exponent

Example: 3820 = $3.82 \times 10^3$; 0.0478 = $4.78 \times 10^{-2}$

Dimensional Analysis

Dimensional (unit) analysis is used to convert one quantity to another using conversion factors based on equivalence statements.

• Example equivalence: 1 in = 2.54 cm

• Conversion factor: $\frac{1\ in}{2.54\ cm}$ or $\frac{2.54\ cm}{1\ in}$

General formula:

$\text{given unit} \times \frac{\text{desired unit}}{\text{given unit}} = \text{desired unit}$

Example: Convert 8.00 m to inches: $8.00\ m \times \frac{1\ cm}{1 \times 10^{-2}\ m} \times \frac{1\ in}{2.54\ cm} = 315\ in.$

Metric Conversion and Practice Problems

• Apply dimensional analysis and significant figures to solve practical problems.

• Examples include converting units of mass, volume, and speed, and calculating density and mass using given data.

Example: What is the mass in grams of a 325 mg aspirin tablet? $325\ mg \times \frac{1 \times 10^{-3}\ g}{1\ mg} = 0.325\ g$

Ladder Method

The ladder method is a visual tool for converting between metric units by moving the decimal point or adjusting the exponent in scientific notation.

• Move left for smaller to larger units (subtract from exponent).

• Move right for larger to smaller units (add to exponent).

Additional info: These foundational skills are essential for all laboratory and theoretical work in chemistry, as they ensure accurate communication and calculation of scientific data.