Fundamental Concepts in General Chemistry: Units, Measurement, Moles, and Molecular Structure

Base Units and Measurement

SI Base Units

The International System of Units (SI) provides standard base units for scientific measurement, forming the foundation for all quantitative work in chemistry.

• Mass: kilogram (kg)

• Length: meter (m)

• Time: second (s)

• Temperature: kelvin (K)

Mass, Length, and Time

These fundamental quantities are essential for describing physical properties and changes in chemical systems.

• Weight: The force exerted by an object due to gravity.

• Mass: The measure of the amount of matter in an object or sample.

• Conversions:

  • 1 kg = 1000 g

  • 1 km = 1000 m

  • "kilo" prefix = 1000

Metric Multipliers

Metric prefixes are used to express measurements at different scales, from very large to very small.

• Giga: $10^9$ (1 billion)

• Mega: $10^6$ (1 million)

• Kilo: $10^3$ (1 thousand)

• Deci: $10^{-1}$ (1 tenth)

• Centi: $10^{-2}$ (1 hundredth)

• Milli: $10^{-3}$ (1 thousandth)

• Micro: $10^{-6}$ (1 millionth)

• Nano: $10^{-9}$ (1 billionth)

Each prefix multiplies the base unit by the indicated factor.

Temperature

Temperature is measured in kelvin in scientific contexts. The kelvin scale is related to the Celsius scale by:

• $\text{Kelvin} = \text{Celsius} + 273$

Scientific Notation and Significant Figures

Scientific Notation

Scientific notation is used to express very large or very small numbers in a compact form.

• Example: $1,000,000,000 = 1 \times 10^9$

• Example: $6500 = 6.5 \times 10^3$

• Example: $0.00065 = 6.5 \times 10^{-4}$

Significant Figures

Significant figures indicate the precision of a measured value.

• Any digit that is not zero is significant.

• Zeros between nonzero digits are significant.

• Zeros to the left of the first nonzero digit are not significant.

• Zeros to the right of the last nonzero digit are significant if the number contains a decimal point.

Calculations with Measured Numbers

• Addition/Subtraction: The answer should have no more digits after the decimal point than the original number with the smallest number of digits after the decimal point.

• Multiplication/Division: The answer should have no more significant figures than the original number with the smallest amount of significant figures.

The Mole and Molar Mass

The Mole ("Chemist's Dozen")

The mole is a counting unit in chemistry, representing a specific number of particles (atoms, molecules, or formula units).

• Avogadro's Number: $6.022 \times 10^{23}$ items per mole

• Used to relate macroscopic amounts of substances to the number of particles.

Molar Mass

Molar mass is the mass in grams of one mole of a substance.

• For elements, the molar mass (g/mol) is numerically equal to the atomic mass (amu).

• Example: One mole of helium ($6.022 \times 10^{23}$ atoms) has a mass of 4.003 g.

• $6.022 \times 10^{23}$ amu = 1 g

Counting Molecules by Weighing

Calculating the Molar Mass of a Compound

To determine the molar mass of a compound, sum the molar masses of all atoms in its formula.

• Example: $\text{H}_2\text{O}$: $2 \times 1.008$ (H) $+ 16$ (O) $= 18.016$ g/mol

Converting Mass to Moles and Molecules

• $\text{moles of compound} = \frac{\text{mass of compound (g)}}{\text{molar mass of compound (g/mol)}}$

• Example: 500g $\text{H}_2\text{O}$: $\frac{500}{18.016} = 27.753$ mol $\text{H}_2\text{O}$

• To find molecules: $\text{moles} \times 6.022 \times 10^{23}$

Mass Percent Composition

Calculating Mass Percent

Mass percent composition shows the percentage by mass of each element in a compound.

• $\text{Percent by mass of an element} = \left( \frac{n \times \text{molar mass of element}}{\text{molar mass of compound}} \right) \times 100\%$

• Where $n$ is the number of moles of the element in one mole of the compound.

• Example: In $\text{H}_2\text{O}_2$, two moles of H and two moles of O:

  • $\text{Mass percent H} = \frac{2 \times 1.008}{34.016} \times 100\% = 5.92\%$

  • $\text{Mass percent O} = \frac{2 \times 16.00}{34.016} \times 100\% = 94.07\%$

Using Mass Percent Composition to Determine Empirical Formula

Empirical Formula from Mass Percent

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

• Percent composition is the same regardless of sample size.

• Example: 92.26% C and 7.74% H in a 100g sample:

  • 92.26g C $\rightarrow \frac{92.26}{12.01} = 7.682$ mol C

  • 7.74g H $\rightarrow \frac{7.74}{1.008} = 7.682$ mol H

  • Empirical formula: $\text{C}_{7.682}\text{H}_{7.682}$, which simplifies to CH

Using Empirical Formula and Molar Mass to Determine Molecular Formula

Finding the Molecular Formula

The molecular formula shows the actual number of atoms of each element in a molecule.

• $n = \frac{\text{molar mass}}{\text{molar mass of empirical formula}}$

• Round $n$ to the nearest whole number.

• Multiply the subscripts in the empirical formula by $n$.

• Example: If CH has a molar mass of 13.01 and the compound's molar mass is 78, $n = \frac{78}{13.01} \approx 6$, so the molecular formula is $\text{C}_6\text{H}_6$.

Lewis Structures and Molecular Shape

Drawing Simple Lewis Structures

Lewis structures represent the arrangement of atoms and electrons in a molecule, showing covalent bonds and lone pairs.

• Atoms of main group elements achieve stability by becoming isoelectronic with noble gases (octet rule).

• Hydrogen is an exception, holding only two electrons.

• Steps for drawing Lewis structures:

  1. Write the symbol for each atom in the expected arrangement (skeletal structure).

  2. Count the total number of valence electrons.

  3. Distribute electrons to form bonds and complete octets.

Lewis Structures of Molecules with a Central Atom

• Central atom is usually the least electronegative.

• Pairs of shared electrons are called bonds; unshared pairs are lone pairs.

Lewis Structures of Polyatomic Ions and Resonance

• Polyatomic ions have charges shown in brackets.

• Resonance structures represent delocalized electrons.

Exceptions to the Octet Rule

• Some atoms (e.g., Be, B) have fewer than 8 electrons.

• Atoms in the third period or beyond can have more than 8 electrons (expanded octet).

Molecular Shape

The shape of a molecule is determined by the arrangement of atoms and electron pairs around the central atom, influencing chemical properties and reactivity.

*Additional info: Some context and examples have been expanded for clarity and completeness, including stepwise procedures and formula derivations for empirical and molecular formulas, as well as Lewis structure conventions.*