Compounds and Stoichiometry

Stink Bug Compounds

• Stink bugs produce a solution of volatile compounds that smells bad.
• The main compounds are hydrogen cyanide (toxic, inhibits cytochrome c oxidase, blocking aerobic respiration) and benzoyl benzaldehyde.
• Benzaldehyde vaporizes at room temperature.
• At low concentrations, benzaldehyde smells like toasted almonds, but at high concentrations, it smells like rotten almonds and irritates the skin, eyes, and respiratory tract.
• Benzaldehyde is a compound with 7 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom.
• One mole of benzaldehyde has a mass of about 106 grams.

Compounds

• Compounds are pure substances composed of two or more elements in a fixed proportion.
• Compounds can be broken down chemically.
• Compounds are characterized by their physical and chemical properties.

Topics Covered

• Representing compounds using empirical and molecular formulas and percent composition is covered.
• Major classes of chemical reactions are briefly reviewed and will be examined more closely later.
• Balancing chemical equations, identifying limiting reagents, and calculating reaction yields are recapped.

Molecules and Moles

• A molecule is a combination of two or more atoms held together by covalent bonds.
• Molecules are the smallest units of compounds that display their identifying properties.
• Molecules can be composed of two or more atoms of the same element (e.g., $N<em>2$, $O</em>2$) or different elements (e.g., $CO<em>2$, $COCl</em>2$, $C<em>6H</em>5CHO$).
• Reactions usually involve a large number of molecules, so compounds are measured in moles or grams.
• Molar mass is used to interconvert between moles and grams.

Ionic Compounds

• Ionic compounds do not form true molecules because of how oppositely charged ions arrange in the solid state.
• Solid NaCl is a coordinated lattice where each $Na^+$ ion is surrounded by $Cl^-$ ions, and each $Cl^-$ ion is surrounded by $Na^+$ ions.
• The term formula unit, representing the empirical formula, is used instead of molecule.
• Molecular weight is meaningless, so the term formula weight is used instead.

Molecular Weight

• Atomic weight is a weighted average of the masses of naturally occurring isotopes.
• Molecular weight is the sum of the atomic weights of all atoms in a molecule, measured in atomic mass units (amu) per molecule.
• The formula weight of an ionic compound is found by adding the atomic weights of the constituent ions according to its empirical formula, also in AMU per molecule.

Example: Molecular Weight of $SOCl_2$

• One S: $1 \, \times \, 32.1 \, \text{AMU} = 32.1 \, \text{AMU}$
• One O: $1 \, \times \, 16 \, \text{AMU} = 16 \, \text{AMU}$
• Two Cl: $2 \, \times \, 35.5 \, \text{AMU} = 71 \, \text{AMU}$
• Total: $32.1 + 16 + 71 = 119.1 \, \text{AMU per molecule}$

Mole

• A mole is a quantity of any substance equal to the number of particles in 12 grams of carbon-12 ($\frac{12}{6}C$).
• This number is Avogadro's number ($N_A = 6.022 \times 10^{23} \, mol^{-1}$).
• One mole of a compound has a mass in grams equal to the molecular or formula weight in AMU.
  • Example: One molecule of carbonic acid ($H<em>2CO</em>3$) has a mass of 62 AMU, and one mole has a mass of 62 grams.
• The mass of one mole of a compound is called its molar mass, in grams per mole.
• Molecular weight is measured in amu/molecule, not grams/mol.
• Formula for determining the number of moles:
  • $\text{Moles} = \frac{\text{Mass of Sample (g)}}{\text{Molar Mass (g/mol)}}$

Example: Moles in 9.53 grams of $MgCl_2$

1. Find the molar mass of $MgCl_2$: $1 \times 24.3 \, g/mol + 2 \times 35.5 \, g/mol = 95.3 \, g/mol$
2. Solve for the number of moles: $\frac{9.53 \, g}{95.3 \, g/mol} = 0.1 \, mol \, MgCl_2$

Equivalent Weight

• Certain elements or compounds act more potently in certain reactions.
• One mole of HCl donates one mole of $H^+$ ions.
• One mole of $H<em>2SO</em>4$ donates two moles of $H^+$ ions.
• One mole of $H<em>3PO</em>4$ donates three moles of $H^+$ ions.
• One mole of sodium donates one mole of electrons.
• One mole of magnesium donates two moles of electrons.
• Equivalence: How many moles of protons, hydroxide ions, electrons, or ions will one mole of a given compound produce?
• Gram equivalent weight: The mass of a compound (in grams) that produces one equivalent of the particle of interest.
• Formula:
  • $\text{Gram Equivalent Weight} = \frac{\text{Molar Mass}}{n}$, where n is the number of particles of interest produced or consumed per molecule.
  • Example: Need $31 \, g$ of $H<em>2CO</em>3$ (molar mass $62 \, g/mol$) to produce one equivalent of hydrogen ions because each molecule donates two hydrogen ions ($n = 2$).
• The equivalent weight of a compound is the mass that provides one mole of the particle of interest.
• Formula to determine equivalents:
  • $\text{Equivalents} = \frac{\text{Mass of Compound (g)}}{\text{Gram Equivalent Weight (g)}}$

Normality

• Normality (N) is a measure of concentration in units of equivalents per liter ($\frac{\text{equivalents}}{L}$).
• Commonly used for hydrogen ion concentration.
• A 1 N solution of acid contains 1 mole of $H^+$ ions per liter.
• A 2 N solution of acid contains 2 moles of $H^+$ ions per liter.
• The actual concentration of the acidic compound may differ due to varying numbers of donatable hydrogen ions.
  • In 1 N HCl, the molarity of HCl is 1 M (monoprotic).
  • In 1 N $H<em>2CO</em>3$, the molarity of $H<em>2CO</em>3$ is 0.5 M (diprotic).
• Normality calculations assume a reaction proceeds to completion.
  • Even though carbonic acid doesn't fully dissociate, it can react with enough base to give up both protons.
• Conversion from normality to molarity:
  • $\text{Molarity} = \frac{\text{Normality}}{n}$, where n is the number of protons, hydroxide ions, electrons, or ions produced or consumed.

Benefit of Using Equivalents and Normality

• Allows direct comparison of quantities of interest (e.g.,$H^+$ or $OH^-$).
• One equivalent of acid ($H^+$) neutralizes one equivalent of base ($OH^-$).
• One mole of HCl will not completely neutralize one mole of $Ca(OH)<em>2$ because one mole of HCl donates one equivalent of acid, but $Ca(OH)</em>2$ donates two equivalents of base.

Example: Gram Equivalent Weight of Sulfuric Acid ($H<em>2SO</em>4$)

1. Find the molar mass of $H<em>2SO</em>4$:
   • $(2 \times 1.0) + (1 \times 32.1) + (4 \times 16) = 98.1 \, g/mol \, H<em>2SO</em>4$
2. Identify the equivalents (protons, $H^+$), since these are transferred in acid-base reactions. The number of protons in sulfuric acid ($n$) is 2.
3. Calculate the gram equivalent weight:
   • $\text{Gram Equivalent Weight} = \frac{\text{Molar Mass}}{n} = \frac{98.1 \, g/mol \, H<em>2SO</em>4}{2 \, mol \, H^+/mol \, H<em>2SO</em>4} = 49.05 \, g/mol \, H^+$

Example: Normality of a 2 M $Mg(OH)_2$ Solution

1. Identify the number of equivalents ($n$). There are two hydroxide ions ($OH^-$) for each molecule of $Mg(OH)_2$.
2. Calculate the normality:
   • $\text{Normality} = \text{Molarity} \times n = 2 \, M \times 2 \, equiv \, OH^-/mol \, Mg(OH)<em>2 = 4 \, N \, Mg(OH)</em>2$