Chapter 1: Matter, Measurement, and Problem Solving – General Chemistry Study Notes

Chapter 1: Matter, Measurement, and Problem Solving

Numbers and Chemistry

Chemistry is a quantitative science, meaning that numbers and measurements are fundamental to understanding chemical concepts and solving problems. This chapter introduces the foundational concepts of measurement, units, and problem-solving strategies in chemistry.

• Quantitative topics involve numerical values and calculations.

• Key concepts include: units of measurement, uncertainty in measurement, significant figures, and dimensional analysis.

The Standard Units

SI Base Units

The International System of Units (SI) is the standard for scientific measurements. Each physical quantity has a base unit:

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

The Meter: A Measure of Length

• The meter (m) is the SI unit of length, slightly longer than a yard (1 m = 39.37 inches).

• Originally defined as 1/10,000,000 of the distance from the equator to the North Pole; now defined as the distance light travels in a vacuum in 1/299,792,458 seconds.

The Kilogram: A Measure of Mass

• Mass measures the quantity of matter in an object.

• SI unit: kilogram (kg); 1 kg = 2.205 lb.

• 1 gram (g) = 1/1000 kg.

• Weight is the gravitational pull on an object's mass.

The Second: A Measure of Time

• Second (s) is the SI unit of time.

• Defined as the duration of 9,192,631,770 periods of radiation from a cesium-133 atom.

A Measure of Temperature

• Temperature can be measured in Celsius (°C), Kelvin (K), or Fahrenheit (°F).

• Conversion formulas:

  • $^\circ C = \frac{(^\circ F - 32)}{1.8}$

  • $K = ^\circ C + 273.15$

Prefix Multipliers

SI units can be modified by prefixes to represent powers of ten. Common prefixes include:

Prefix	Symbol	Multiplier
kilo	k	103
centi	c	10-2
milli	m	10-3
micro	μ	10-6
nano	n	10-9
pico	p	10-12

Example: 23.5 m = 0.0235 km = 2,350 cm = 23,500,000,000 nm

Volume and Derived Units

Volume

• Volume is a derived unit (not a base SI unit), calculated as length × width × height.

• Common units: liter (L) and milliliter (mL).

• 1 L = 1 dm3; 1 mL = 1 cm3 = 1 cc

Glassware for Measuring Volume

• Graduated cylinder: measures variable volumes.

• Syringe: delivers variable volumes, often with a stopcock.

• Burette: delivers a specific volume, used in titrations.

• Pipette: delivers a specific volume accurately.

• Volumetric flask: holds a specific volume for solution preparation.

Practice: Choosing the Correct Unit

• 100 cm (not mm or m) for a baseball bat length.

• 230 mL for a glass of milk.

• 50 kg for a person's weight.

• 50 mg for a paper clip.

• 15 mL for a tablespoon.

Density

• Density is a derived unit: $\text{Density} = \frac{\text{mass}}{\text{volume}}$

• Units: g/cm3 or g/mL.

• Density determines if a substance will sink or float in another substance.

Substance	Density (g/cm3)
Charcoal	0.57
Ethanol	0.789
Ice (0°C)	0.917
Water (4°C)	1.00
Aluminum	2.70
Iron	7.86
Gold	19.3

Intensive and Extensive Properties

• Intensive property: Independent of the amount of substance (e.g., density).

• Extensive property: Dependent on the amount of substance (e.g., mass).

Numbers in Science: Exact and Inexact

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

• Inexact (measured) numbers: Obtained by measurement, subject to error (equipment or human error).

Significant Figures and Measurement Reliability

Significant Figures

• All digits in a measurement are certain except the last, which is estimated.

• Significant figures reflect the precision of a measurement.

Rules for Counting Significant Figures

• All nonzero digits are significant (e.g., 28.03 has 4 sig figs).

• Interior zeroes (between nonzero digits) are significant (e.g., 7.0301 has 5 sig figs).

• Leading zeroes (to the left of the first nonzero digit) are not significant (e.g., 0.0032 has 2 sig figs).

• Trailing zeroes:

  • After a decimal point: always significant (e.g., 3.5600 has 5 sig figs).

  • Before a decimal point and after a nonzero number: significant (e.g., 120.0 has 4 sig figs).

  • Before an implied decimal point: ambiguous, use scientific notation to clarify.

Significant Figures in Calculations

• Multiplication/Division: Result has the same number of significant figures as the factor with the fewest significant figures.

• Addition/Subtraction: Result has the same number of decimal places as the quantity with the fewest decimal places.

Rules for Rounding

• Round down if the last digit dropped is four or less.

• Round up if the last digit dropped is five or more.

• In multistep calculations, round only the final answer.

Example: Density Calculation with Rounding

• Find the density of a cube with sides of 2.5 cm and a mass of 5.0 g.

• Volume = $(2.5\,\text{cm})^3 = 15.625\,\text{cm}^3$

• Density = $\frac{5.0\,\text{g}}{15.625\,\text{cm}^3} = 0.32\,\text{g/cm}^3$ (rounded to 2 significant figures)

Scientific Notation

• Used to express very large or very small numbers.

• Examples:

  • 0.000135 = $1.35 \times 10^{-4}$

  • 0.004753 = $4.753 \times 10^{-3}$

  • 785,000 = $7.85 \times 10^{5}$

Solving Chemical Problems: Dimensional Analysis

Dimensional Analysis

• Unit conversion problems are solved using dimensional analysis.

• Units are treated as algebraic quantities and can be multiplied, divided, and canceled.

• A unit equation states two equivalent quantities (e.g., 2.54 cm = 1 in).

• A conversion factor is a fraction derived from a unit equation (e.g., $\frac{2.54\,\text{cm}}{1\,\text{in}}$ or $\frac{1\,\text{in}}{2.54\,\text{cm}}$).

General Problem Solving Strategy

1. Identify the starting point (given information).

2. Identify the end point (what you must find).

3. Devise a conceptual plan to connect the starting and end points using known relationships or conversion factors.

4. Sort, strategize, solve, and check your answer for reasonableness.

Units Raised to a Power

• When converting units raised to a power, raise both the number and the unit to that power.

• Example: $(2.54\,\text{cm})^2 = (1\,\text{in})^2$ so $6.45\,\text{cm}^2 = 1\,\text{in}^2$

Common Conversion Factors

• 1 pound = 453.6 g

• 1 inch = 2.54 cm (exactly)

• 3.8 L = 1 gallon

• 1 mile = 1.609 km

• 1 atm = 760 mmHg = 760 torr

Example: Convert 23.5 m to km, cm, nm

• $23.5\,\text{m} \times \frac{1\,\text{km}}{10^3\,\text{m}} = 0.0235\,\text{km}$

• $23.5\,\text{m} \times \frac{1\,\text{cm}}{10^{-2}\,\text{m}} = 2,350\,\text{cm}$

• $23.5\,\text{m} \times \frac{1\,\text{nm}}{10^{-9}\,\text{m}} = 2.35 \times 10^{10}\,\text{nm}$

Additional info:

• Dimensional analysis is a universal problem-solving method in chemistry, applicable to all unit conversions and many equation-based problems.