Unit 3: Composition of Substances & Solutions

The Mole

  • Identity of a Substance

    • Defined not only by composition but also by the quantity of each type of atom or ion.

    • Example: Water (H2O) vs. Hydrogen Peroxide (H2O2)

    • Composed of hydrogen and oxygen.

    • Water has 1 oxygen atom, whereas hydrogen peroxide has 2, leading to different properties.

  • Measurement Tools

    • Modern instruments directly measure microscopic traits.

    • Traditionally, macroscopic properties (mass and volume) were measured using simple tools (balances and volumetric glassware).

  • The Mole

    • New unit for amount of substance necessary for chemical measurements.

    • Similar to other units (pair, dozen, gross).

    • Defined as the amount of substance containing the same number of entities as the number of atoms in 12 g of pure 12C.

    • One Latin connotation of "mole" is "large mass" or "bulk".

    • Links macroscopic features (mass) with microscopic properties (number of atoms/molecules).

  • Stoichiometry

    • Refers to ratios of substances in a chemical reaction.

    • Stoichiometric coefficients represent the ratio in which molecules react or the number of moles that react.

    • Mole allows conversion between atomic mass units and grams:

    • 1 mole contains 6.02214076imes10236.02214076 imes 10^{23} discrete entities (Avogadro's number, NAN_A).

  • Avogadro's Number

    • Defined as 6.022imes1023/extmol6.022 imes 10^{23}/ ext{mol} (approximately).

    • Each mole of any element contains the same number of atoms.

    • Molar mass defined as the mass in grams of 1 mole of a substance, expressed in grams per mole (g/mol).

  • Comparison of Atomic Mass and Molar Mass

    • While atomic mass (amu) and molar mass (g/mol) are numerically equivalent, they differ in scale:

    • Example: 1 mole of 12C weighs 12 g, atomic mass = 12 amu.

    • A small drop of water (0.03 g) contains more molecules than can be imagined, despite being only a fraction of 1 mole (~18 g).

  • Empirical Formula Determination

    • Relative numbers, not masses, of atoms in a compound.

    • Requires conversion of experimentally measured masses to moles.

    • Ratios derived yield the compound's empirical formula.

Deriving the Number of Atoms and Molecules From Mass

  • Application of Formula Mass, Mole, and Avogadro's Number

    • In calculating the number of moles from a substance's mass, we can derive the number of atoms or molecules.

  • Example Problem

    • Given: 40.0 mg of saccharin (C7H5NO3S).

    • Molar mass = 183.18 g/mol.

    • To find number of saccharin molecules:

    • Convert mass to grams: 0.0400 g (40.0 mg).

    • Calculate number of moles:

      • extMoles=racextmassextmolarmass=rac0.0400g183.18g/molext{Moles} = rac{ ext{mass}}{ ext{molar mass}} = rac{0.0400 g}{183.18 g/mol}

      • Result: Number of moles derived, then multiply by Avogadro's number to find molecules.

Determining Empirical Formulas From Masses of Elements

  • Determination Method

    • Measure the masses of constituent elements from which a compound is formed.

    • Convert these masses to number of moles.

    • Calculate whole-number ratios for empirical formula.

  • Example Calculation

    • For a given compound with:

    • 1.71 g C, 0.287 g H.

    • Convert to moles:

      • extMolesofC=rac1.71g12.01g/molext{Moles of C} = rac{1.71 g}{12.01 g/mol}

      • extMolesofH=rac0.287g1.008g/molext{Moles of H} = rac{0.287 g}{1.008 g/mol}

    • Yield ratios yielding unrounded formula, then adjust to whole number.

    • Final empirical formula obtained (CH2).

  • Another Example

    • Given masses of Cl and O in a compound determined:

    • 5.31 g Cl and 8.40 g O.

    • Calculate tentative empirical formula.

    • Normalize subscripts to resolve decimal values by multiplication.

    • Final empirical formula (Cl2O7).

Moles and Volumes from Molar Concentrations

  • Molarity Definition

    • Molarity is defined as moles of solute divided by liters of solution.

    • Rearrangement for moles of solute yields:

    • extMolesofsolute=MimesLext{Moles of solute} = M imes L

  • Example Problem

    • How much sugar in 10 mL of soft drink containing 0.133 mol of sucrose?

    • Calculate molarity:

      • M=rac0.133mol0.355LM = rac{0.133 mol}{0.355 L}

      • Then use relation (extmolesofsolute=MimesL)( ext{moles of solute} = M imes L) to find amount.

      • Determine amount in moles from 10 mL.

Dilution of Solutions

  • Concept of Dilution

    • Dilution decreases concentration through addition of solvent.

    • Example: Iced tea diluted as ice melts.

  • Mathematical Relationship

    • The equation relating before and after dilution:

    • M<em>1V</em>1=M<em>2V</em>2M<em>1V</em>1 = M<em>2V</em>2

Mass Percentage

  • Definition

    • Mass percentage is ratio of component mass to total solution mass, expressed as a percentage.

    • Alternate terms: percent mass, weight percent, etc.

  • Example

    • Liquid bleach with 7.4% sodium hypochlorite:

    • In 100.0 g of bleach, correspondingly 7.4 g of NaClO.

Parts per Million (ppm) and Parts per Billion (ppb)

  • Definition

    • Used to express low concentrations, defined in mass, volume, or both.

    • Mass-based definitions are typical for pollutants in environmental science.

  • Example

    • Maximum safe level of fluoride in drinking water is 4 ppm

Formula Mass

  • Concept

    • Formula mass is the sum of average atomic masses as per a chemical formula,

    • Expressed typically in atomic mass units (amu).

  • Chemical Identity

    • Chemical identity relies on the types and relative numbers of atoms present.

    • Percent composition aids in determining empirical formula and eventually the molecular formula.

Conclusion

  • Mole as a Unit

    • Fundamental for discussing concentrations and conversions in chemical science.

    • Crucial for all measurements involving atomic-level quantities in a macroscopic context.