4.1 Chemical Formulas, Molecular Structures, and Formula Mass Calculations

Representations of Chemical Compounds

• Chemical composition and structure can be symbolized using various types of formulas and models, including molecular formulas, empirical formulas, and structural formulas.
• Atoms within molecules are arranged through bonding, which can be depicted visually or symbolically to represent the molecule's three-dimensional shape.
• A single compound can be represented in multiple ways, such as the formula for methane, which is written as $CH_4$.

Molecular Formulas and Structural Formulas

• Molecular Formula: This is a representation of a molecule that uses chemical symbols to identify the types of atoms present. Subscripts are used following the chemical symbol to indicate the specific number of each type of atom in the molecule.
• Structural Formula: This representation shows the same information as a molecular formula but also illustrates how the atoms are connected (bonded) within the molecule.
• Chemical Symbols and Subscripts:
  • Subscripts are numbers written to the right and slightly below a chemical symbol (e.g., the $2$ in $H_2$).
  • They indicate that the atoms are part of a discrete molecular structure and are bonded together.
• Coefficients:
  • A coefficient is a number written in front of an element symbol or chemical formula (e.g., the $2$ in $2H_2$).
  • Coefficients indicate that the element or molecule is being multiplied as separate units; they are not combined into a single larger molecule.
• Comparison of Hydrogen Representations:
  • $H$: Represents one single, discrete atom of hydrogen.
  • $2H$: Represents two separate, discrete single atoms of hydrogen.
  • $H_2$: Represents a single molecule consisting of two hydrogen atoms bonded together.
  • $2H_2$: Represents two separate molecules of diatomic hydrogen ($H_2$).

Three-Dimensional Molecular Models

• Ball-and-Stick Model: In this model, atoms are represented as spheres ("balls") and chemical bonds are represented as rods ("sticks"). This model helps visualize the geometry and bond angles between atoms.
• Space-Filling Model: This model depicts atoms as spheres that are connected directly to one another without visible sticks. It provides a better representation of the relative sizes of atoms and the space the molecule occupies.
• Case Study: Water ($H_2O$):
  • Water can be depicted via its molecular formula ($H_2O$), a structural formula showing the $O-H$ bonds, a ball-and-stick model, or a space-filling model.
• Case Study: Sulfur ($S_8$):
  • In its natural state, sulfur tends to form octatomic molecules ($S_8$).
  • The structural formula shows eight sulfur atoms connected in a ring.
  • The ball-and-stick model reveals that this ring is not a flat octagon but a "disorganized" or puckered shape.
  • The space-filling model shows only the clustered atoms, with the internal bonds obscured.

Empirical Formulas

• Definition: An empirical formula is a representation that uses chemical symbols and subscripts to show the simplest whole-number ratio of the atoms or ions present in a compound.
• Function: It provides the relative number of atoms rather than the absolute number found in a single molecule.
• Example: Benzene:
  • Benzene is a volatile liquid with a molecular structure consisting of six carbon atoms in a ring and six hydrogen atoms.
  • Molecular Formula: $C_6H_6$
  • Empirical Formula: $CH$ (since the $6:6$ ratio reduces to $1:1$).
• Example: Acetic Acid:
  • Acetic acid is the primary component of vinegar.
  • It can be written in several equivalent ways based on the information the chemist wants to convey:
    • $CH_3COOH$: Highlights the functional groups (methyl and carboxyl).
    • $HCH_3COO$: Often used in acid-base chemistry to show the acidic hydrogen first.
    • $HC_2H_3O_2$: Another common representation for the acid.
    • $C_2H_4O_2$: Shows the total count of all atoms ($2$ carbons, $4$ hydrogens, $2$ oxygens).
  • Empirical Formula: $CH_2O$ (the $2:4:2$ ratio reduces to $1:2:1$).
• Example: Glucose:
  • Glucose contains $6$ carbon atoms, $12$ hydrogen atoms, and $6$ oxygen atoms.
  • Molecular Formula: $C_6H_{12}O_6$
  • Empirical Formula: $CH_2O$
  • Note: Glucose and acetic acid share the same empirical formula ($CH_2O$), yet they are entirely different substances with different properties.

Isomers

• Definition: Isomers are compounds that have the same chemical/molecular formula but different molecular structures and spatial arrangements of atoms.
• Properties: Because their structures differ, isomers possess different physical and chemical properties.
• Comparison: Acetic Acid vs. Methyl Formate:
  • Both share the molecular formula $C_2H_4O_2$.
  • Acetic Acid: The two carbon atoms are bonded directly to each other ($C-C$), and an oxygen atom is bonded to a hydrogen atom ($O-H$).
  • Methyl Formate: There is an oxygen atom situated between the two carbon atoms ($C-O-C$), and there is no oxygen-hydrogen bond.

Formula Mass and Molecular Mass

• The mass of a substance is defined as the sum of the average atomic masses of all atoms represented in the substance's formula.
• Molecular Mass (Covalent Compounds):
  • Since covalent molecules exist as discrete particles, the formula mass is identical to the molecular mass.
• Formula Mass (Ionic Compounds):
  • Ionic compounds do not exist as discrete molecules; instead, they form vast, three-dimensional crystalline lattices containing millions of cations and anions.
  • The formula used (e.g., $NaCl$) represents the simplest ratio (formula unit), not a single molecule.
  • Chemists use the term "formula mass" specifically for ionic compounds and "molecular mass" for molecular/covalent compounds.
• Calculation Rules and Significant Figures:
  • Atomic masses are pulled from the periodic table in units of $amu$ (atomic mass units).
  • When adding masses, the result must follow the rules of significant figures for addition: the answer is rounded to the same number of decimal places as the least precise measurement.
  • Rounding Note: In multi-step laboratory calculations, the unrounded number should be used in intermediate steps to prevent rounding errors in the final result.

Calculating Masses: Worked Examples

• Chloroform ($CHCl_3$):

  • $1 \times \text{mass of C} = 12.01138 \times 1 = 12.01138$
  • $1 \times \text{mass of H} = 1.00794 \times 1 = 1.00794$
  • $3 \times \text{mass of Cl} = 35.45 \times 3 = 106.35$
  • Sum: $12.01 + 1.008 + 106.35 = 119.368$
  • Rounded Result: $119.378$ (or $119.37$ based on specific table precision).
  • Note: Per the transcript, the result was given as $119.368$ but rounded to the second decimal place as $119.37$ due to the precision of carbon ($12.01$) and chlorine ($106.35$).

• Aspirin ($C_9H_8O_4$):

  • $9 \times \text{C} (12.01138) = 108.10242$
  • $8 \times \text{H} (1.00794) = 8.06352$
  • $4 \times \text{O} (15.9994) = 63.9976$
  • Sum: $180.15402$
  • Formula Mass: $180.15402 \rightarrow 180.15228$ (The transcript provides the rounded value as $180.15 \text{ amu}$).

• Ibuprofen ($C_{13}H_{18}O_2$):

  • Atomic masses: $C = 12.01 \text{ amu}$, $H = 1.008 \text{ amu}$, $O = 16 \text{ amu}$.
  • Calculation:
    • Carbon: $13 \times 12.01 = 156.13 \text{ amu}$
    • Hydrogen: $18 \times 1.008 = 18.144 \text{ amu}$
    • Oxygen: $2 \times 16 = 32 \text{ amu}$
  • Sum: $206.274 \rightarrow 206.27 \text{ amu}$.

• Sodium Chloride ($NaCl$):

  • The mass of the neutral atoms is used for ions because the electron lost by sodium is gained by chlorine; the total mass remains conserved.
  • $1 \times Na (22.99) = 22.99 \text{ amu}$
  • $1 \times Cl (35.45) = 35.45 \text{ amu}$
  • Formula Mass: $58.44 \text{ amu}$.

• Aluminum Sulfate ($Al_2(SO_4)_3$):

  • Used in paper manufacturing and water purification.
  • Interpreting the Formula: The subscript $3$ outside the parentheses applies to the entire sulfate group ($SO_4^{2-}$).
    • Aluminum ($Al$): $2$ atoms.
    • Sulfur ($S$): $1 \times 3 = 3$ atoms.
    • Oxygen ($O$): $4 \times 3 = 12$ atoms.
  • Atomic Masses: $Al = 26.98 \text{ amu}$, $S = 32.06 \text{ amu}$, $O = 16.00 \text{ amu}$.
  • Calculation:
    • $2 \times 26.98 = 53.96 \text{ amu}$
    • $3 \times 32.06 = 96.18 \text{ amu}$
    • $12 \times 16.00 = 192.00 \text{ amu}$
  • Formula Mass: $342.14 \text{ amu}$.