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

Chapter 1: Matter, Measurement, and Problem Solving

1.6 The Units of Measurement

In chemistry, units are standard quantities used to specify measurements. Consistent use of units is essential for clear scientific communication.

• Metric system: Used in most of the world.

• English system: Used mainly in the United States.

• International System of Units (SI): The modern form of the metric system, used globally in science. The abbreviation SI comes from the French phrase Système International d’Unités.

The Standard Units

The SI system defines seven base units for fundamental physical 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. 1 meter is slightly longer than a yard (1 yard = 36 inches, 1 meter ≈ 39.37 inches).

• Originally defined as 1/10,000,000 of the distance from the equator to the North Pole through Paris.

• Currently, 1 meter is defined as the distance light travels in a vacuum in 1/299,792,458 second.

The Kilogram: A Measure of Mass

• The kilogram (kg) is the SI unit of mass. 1 kg ≈ 2.205 lb.

• The gram (g) is 1/1000 of a kilogram.

• Mass is a measure of the quantity of matter in an object.

• Weight is the measure of the gravitational pull on an object’s mass.

The Second: A Measure of Time

• The second (s) is the SI unit of time.

• 1 second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom.

The Kelvin: A Measure of Temperature

• The kelvin (K) is the SI unit of temperature.

• Temperature measures the average kinetic energy of the particles in a substance.

• Temperature also determines the direction of heat transfer (from hot to cold).

• The Kelvin scale assigns 0 K (absolute zero) to the lowest possible temperature, where molecular motion stops.

• Absolute zero: $0\ \text{K} = -273.15\ ^\circ\text{C}$

Temperature Scales and Conversions

• The Celsius (°C) and Kelvin (K) scales have the same size degree.

• The Fahrenheit (°F) degree is 5/9 the size of a Celsius degree.

• Temperature conversions:

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

• $\text{K} = ^\circ\text{C} + 273.15$

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

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

• $\text{K} = 29.8 + 273.15 = 302.95\ \text{K}$

Prefix Multipliers

SI units use prefix multipliers to indicate multiples or fractions of units by powers of ten.

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
mega	M	106
giga	G	109
tera	T	1012

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

Derived Units: Volume and Density

Derived units are combinations of base units. Two important derived units in chemistry are volume and density.

• Volume: A measure of space. SI unit is the cubic meter ($\text{m}^3$), but liters (L) and milliliters (mL) are commonly used in chemistry.

• Density: The ratio of mass to volume. SI unit is $\text{kg}/\text{m}^3$, but $\text{g}/\text{cm}^3$ is often used for solids and liquids.

Formula:

• $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

Example: If a metal sample has a mass of 3.15 g and a volume of 0.233 cm3:

• $\text{Density} = \frac{3.15\ \text{g}}{0.233\ \text{cm}^3} = 13.5\ \text{g}/\text{cm}^3$

Substance	Density (g/cm3)
Water (at 20°C)	0.998
Aluminum	2.70
Iron	7.87
Gold	19.3
Mercury	13.6

Intensive and Extensive Properties

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

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

1.7 The Reliability of a Measurement

Measurements in chemistry must be reliable and precise. This section covers significant figures, exact numbers, and the concepts of precision and accuracy.

Counting Significant Figures

• Significant figures reflect the precision of a measured quantity.

• All digits in a measurement are significant except for leading and trailing zeros (with some exceptions).

• The more significant figures, the greater the certainty of the measurement.

Rules for Significant Figures:

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

2. Interior zeros (zeros between nonzero digits) are significant (e.g., 408, 7.0301).

3. Leading zeros (zeros to the left of the first nonzero digit) are not significant (e.g., 0.0032 has 2 significant figures).

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

5. Trailing zeros before a decimal point (and after a nonzero digit) are significant (e.g., 140.00 has 5 significant figures).

6. Trailing zeros in a whole number with no decimal point are ambiguous and should be avoided by using scientific notation.

Exact Numbers

• Exact numbers have an infinite number of significant figures.

• Examples: Counting discrete objects (e.g., 3 apples), defined quantities (e.g., 1 dozen = 12), and integral numbers in equations.

• Conversion factors are often exact (e.g., 1 inch = 2.54 cm exactly).

• Exact numbers do not affect the number of significant figures in a calculation.

Significant Figures in Calculations

• For multiplication and division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

• For addition and subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.

• Rounding should be done at the end of a multi-step calculation to avoid rounding errors.

Example: $3.25 \times 2.1 = 6.8$ (rounded to 2 significant figures)

Precision and Accuracy

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

• Precision: How close a series of measurements are to one another.

• It is possible for measurements to be precise but not accurate, or accurate but not precise.

Example: If repeated measurements of a mass yield values very close to each other but far from the true value, the measurements are precise but not accurate.

1.8 Solving Chemical Problems

Solving problems in chemistry often involves unit conversions and dimensional analysis.

Dimensional Analysis

• Dimensional analysis is a method of converting between units using conversion factors.

• Conversion factors are ratios that express how many of one unit are equal to another unit (e.g., $1\ \text{in} = 2.54\ \text{cm}$).

• Set up the calculation so that units cancel, leaving the desired unit.

Example: Convert 2.54 cm to inches:

• $2.54\ \text{cm} \times \frac{1\ \text{in}}{2.54\ \text{cm}} = 1\ \text{in}$

Example: Convert 6450 mm2 to cm2:

• $6450\ \text{mm}^2 \times \left(\frac{1\ \text{cm}}{10\ \text{mm}}\right)^2 = 64.5\ \text{cm}^2$

Additional info: These notes are based on standard introductory General Chemistry content and have been expanded for clarity and completeness.