General Chemistry Study Notes: Measurement, Units, Moles, and Chemical Formulas

Measurement and Units in Chemistry

SI Prefixes and Their Uses

In chemistry, measurements often require the use of prefixes to express very large or very small quantities. The International System of Units (SI) uses standard prefixes to indicate powers of ten.

Prefix	Symbol	Multiplier	Exponent	Example of Use
tera	T	1,000,000,000,000	1012	terabyte
giga	G	1,000,000,000	109
mega	M	1,000,000	106	megawatt
kilo	k	1,000	103
deci	d	0.1	10-1
centi	c	0.01	10-2
milli	m	0.001	10-3
micro	μ	0.000001	10-6
nano	n	0.000000001	10-9
pico	p	0.000000000001	10-12
femto	f	0.000000000000001	10-15	femtometer

Basic SI Units

Chemistry relies on several fundamental units for measurement:

• Time: second (s)

• Distance: meter (m)

• Mass: kilogram (kg)

• Frequency: hertz (Hz)

• Moles: mole (mol)

• Temperature: kelvin (K)

Derived Units and Physical Quantities

Many physical quantities in chemistry are expressed using combinations of SI base units:

• Acceleration: $\text{m/s}^2$

• Force: $\text{kg} \cdot \text{m/s}^2$ (newton, N)

• Pressure: $\text{N/m}^2$ (pascal, Pa)

• Energy: $\text{kg} \cdot \text{m}^2/\text{s}^2$ (joule, J)

• Density: $\text{kg/m}^3$

• Volume: $\text{m}^3$

Significant Figures and Measurement Uncertainty

Rules for Significant Figures

Significant figures (sig figs) indicate the precision of a measured value. The following rules apply:

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Trailing zeros after a decimal point are significant.

• Leading zeros are not significant.

• Exact numbers (from counting or defined conversions) have infinite significant figures.

Examples:

• 377 (3 sig figs)

• 0.006790 (4 sig figs)

• 100 cm (infinite sig figs, exact conversion)

Calculations with Significant Figures

• For multiplication/division: The result should have the same number of sig figs as the value with the fewest sig figs.

• For addition/subtraction: The result should be rounded to the least precise decimal place among the values.

Accuracy vs. Precision

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

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

Random Error

Random errors cause measurements to fluctuate unpredictably. They affect precision but not accuracy.

Conversions and Dimensional Analysis

Unit Conversions

Converting between units is essential in chemistry. Use conversion factors to relate different units.

• 1 cm3 = 1 mL

• 2.54 cm = 1 inch

Example:

Convert 0.0000071 sec to scientific notation: $7.1 \times 10^{-6}$ s

The Mole and Molar Mass

Counting Atoms by Weighing

Atoms are counted by weighing samples and using the concept of molar mass. The mole is a counting unit for atoms, molecules, or other particles.

• Molar Mass: The mass of one mole of a substance, usually expressed in g/mol.

• Avogadro's Number: $6.022 \times 10^{23}$ particles/mol

Example:

If a bundle of pencils weighs 27,950 g and each pencil weighs 5.6 g, the number of pencils is:

$\text{Number of pencils} = \frac{27,950}{5.6} \approx 4,991$

Relative Atomic Mass and the Mole

The mole is defined based on the number of atoms in 12.000 grams of carbon-12 ($^{12}C$):

$1 \text{ mole} = 6.022 \times 10^{23}$ atoms

Molar Masses Listed on the Periodic Table

The molar mass of an element is a weighted average based on the natural abundance of its isotopes.

Isotope	Abundance (%)	g/mol (amu)
$^{28}$Si	92.21	27.977
$^{29}$Si	4.70	28.976
$^{30}$Si	3.09	29.974

The average atomic mass is calculated as:

$\text{Average atomic mass} = \sum (\text{fractional abundance} \times \text{isotope mass})$

Formula Mass and Moles of Compounds

Calculating Molar Mass of Compounds

The molar mass of a compound is the sum of the molar masses of its constituent elements, multiplied by their subscripts in the chemical formula.

• For $\text{CCl}_2\text{F}_2$: $\text{Molar mass} = 1 \times \text{C} + 2 \times \text{Cl} + 2 \times \text{F}$

Example:

If you have $6.022 \times 10^{23}$ molecules of $\text{CCl}_2\text{F}_2$, you have 1 mole, and the mass is equal to the molar mass in grams.

Mass Percent and Empirical Formulas

Mass Percent in Compounds

Mass percent expresses the composition of a compound as the percentage by mass of each element.

$\text{Mass percent} = \frac{\text{mass of element in 1 mole of compound}}{\text{molar mass of compound}} \times 100$

Example:

Calculate the percent N in ammonium nitrate ($\text{NH}_4\text{NO}_3$):

• Molar mass of $\text{NH}_4\text{NO}_3$ = 80.04 g/mol

• Mass of N = 2 × 14.01 g = 28.02 g

• Percent N = $(28.02/80.04) \times 100 \approx 35.0\%$

Empirical Formulas

The empirical formula gives the simplest whole-number ratio of atoms in a compound.

Name	Molecular Formula	Multiplier	Empirical Formula
benzene	C6H6	6	CH
water	H2O	1	H2O
nitrogen dioxide	NO2	1	NO2
phosphorus pentoxide	P2O5	2	P2O5
sodium carbonate	Na2CO3	1	Na2CO3
terephthalic acid	C8H6O4	2	C4H3O2

Example:

For $\text{P}_2\text{O}_5$, calculate the percent composition of P and O:

• Molar mass of $\text{P}_2\text{O}_5$ = $2 \times 30.97 + 5 \times 16.00 = 141.94$ g/mol

• Percent P = $(2 \times 30.97 / 141.94) \times 100 \approx 43.6\%$

• Percent O = $(5 \times 16.00 / 141.94) \times 100 \approx 56.4\%$

Summary Table: Key Concepts

Concept	Definition	Example
SI Prefix	Multiplier for units	kilo = 1,000
Significant Figures	Digits that reflect measurement precision	0.00450 (3 sig figs)
Mole	Counting unit for atoms/molecules	$6.022 \times 10^{23}$ atoms
Molar Mass	Mass of 1 mole of substance	H2O: 18.02 g/mol
Empirical Formula	Simplest ratio of atoms	CH for benzene

Additional info: Some context and examples have been expanded for clarity and completeness.