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

Chapter 1: Matter, Measurement, and Problem Solving

1.6 The Units of Measurement

Measurement is fundamental to chemistry, requiring standard units to ensure consistency and accuracy. The two most common unit systems are the Metric system and the English system. Scientists use the International System of Units (SI), which is based on the metric system.

• Unit: A standard quantity used to specify measurements.

• SI Units: Derived from the French phrase Système International d’Unités.

• Metric system: Used globally; English system is used mainly in the United States.

The Standard Units

The SI system defines seven base units for fundamental quantities.

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. It is slightly longer than a yard (1 yard = 36 inches, 1 meter = 39.37 inches).

• Defined as 1/10,000,000 of the distance from the equator to the North Pole (through Paris).

• Modern definition: The distance light travels in a vacuum in 1/299,792,458 seconds.

The Kilogram: A Measure of Mass

The kilogram (kg) is the SI unit of mass.

• 1 kg = 2.205 lb

• The gram (g) is a secondary unit: 1 g = 1/1000 kg.

• Mass measures the quantity of matter; weight measures the gravitational pull on matter.

The Second: A Measure of Time

The second (s) is the SI unit of time, measuring the duration of events.

• Defined as the period of time for a specific number of radiation events of a specific transition from cesium-133.

The Kelvin: A Measure of Temperature

The kelvin (K) is the SI unit of temperature, measuring the average kinetic energy of particles in a substance.

• Temperature determines the direction of thermal energy transfer (heat).

• Thermal energy flows from hot to cold objects.

Kelvin Scale and Absolute Zero

• Kelvin scale: Assigns 0 K (absolute zero) to the coldest temperature possible.

• Absolute zero: $0~K = -273.15~^ ext{o}C$; the temperature at which molecular motion virtually stops.

Temperature Scale Conversions

• The Fahrenheit degree is five-ninths the size of a Celsius degree.

• The Celsius and Kelvin degrees are the same size.

Conversion formulas:

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

• $K = ^ ext{o}C + 273.15$

Example: To convert 85.6°F to Celsius and Kelvin:

• $^ ext{o}C = \frac{(85.6 - 32)}{1.8} = 29.8^ ext{o}C$

• $K = 29.8 + 273.15 = 302.95~K$

Prefix Multipliers

SI units use prefix multipliers to indicate powers of ten, similar to scientific notation.

Prefix	Symbol	Multiplier
kilo	k	1,000 ($10^3$)
centi	c	0.01 ($10^{-2}$)
milli	m	0.001 ($10^{-3}$)
micro	μ	0.000001 ($10^{-6}$)
nano	n	0.000000001 ($10^{-9}$)
mega	M	1,000,000 ($10^6$)
giga	G	1,000,000,000 ($10^9$)
tera	T	1,000,000,000,000 ($10^{12}$)
pico	p	0.000000000001 ($10^{-12}$)

Example: 1 kilometer (km) = 1,000 meters (m).

Derived Units: Volume and Density

Derived units are combinations of base units. Volume and density are common derived units in chemistry.

• Volume: Measure of space; SI unit is cubic meter ($m^3$), but liter (L) and milliliter (mL) are commonly used.

• Density: Ratio of mass to volume; $d = \frac{m}{V}$

Substance	Density (g/cm3)
Water	1.00
Mercury	13.6
Iron	7.87
Gold	19.3
Air	0.0012

Example: If a sample has a mass of 3.15 g and a volume of 0.233 cm3, its density is:

• $d = \frac{3.15~g}{0.233~cm^3} = 13.5~g/cm^3$

Intensive and Extensive Properties

Properties of matter can be classified as intensive or extensive.

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

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

1.7 The Reliability of a Measurement

Reliability in measurement is ensured by understanding significant figures, exact numbers, and the concepts of precision and accuracy.

• Significant Figures: Digits in a measurement that are known with certainty plus one estimated digit.

• Exact Numbers: Numbers with unlimited significant figures, such as counted objects or defined quantities.

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

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

Counting Significant Figures

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

• Interior zeros (between nonzero digits) are significant (e.g., 408 has 3 significant figures).

• Leading zeros are not significant (e.g., 0.0032 has 2 significant figures).

• Trailing zeros after a decimal point are significant (e.g., 45.00 has 4 significant figures).

• Trailing zeros before a decimal point may or may not be significant (e.g., 1400 may have 2, 3, or 4 significant figures depending on context).

Exact Numbers

• Have unlimited significant figures.

• Examples: Counting objects, defined conversion factors (e.g., 1 inch = 2.54 cm exactly).

• Do not affect the number of significant figures in calculations.

Significant Figures in Calculations

• For multiplication/division: The result has the same number of significant figures as the measurement with the fewest significant figures.

• For addition/subtraction: The result has the same number of decimal places as the measurement with the fewest decimal places.

Example: $2.84 \times 0.32 = 0.91$ (rounded to 2 significant figures)

Precision and Accuracy

• Precision: Consistency among repeated measurements.

• Accuracy: Closeness to the true or accepted value.

• High precision does not guarantee high accuracy.

Example Calculations

• Density Calculation: $d = \frac{m}{V}$

• Temperature Conversion: $^ ext{o}C = \frac{(^ ext{o}F - 32)}{1.8}$, $K = ^ ext{o}C + 273.15$

Visual Aids

• Percent transmittance and absorbance scales are used in spectrophotometry.

• Reading a meniscus in graduated cylinders is important for accurate volume measurement.

Additional info: These notes summarize the main concepts from the provided textbook slides, including SI units, measurement reliability, and calculation rules. For more advanced study, students should review dimensional analysis and unit conversions in detail.