Moles

Quiz Information

  • Quiz#6
    • Date: Wednesday (10/8) – 2pm
    • Retake Round 1: Friday (10/10)
    • Location: STEM 216
    • Duration: Last 30 minutes in Lecture
    • Retake Round 2: Monday (10/13)
    • Location: Harris Hall 101
    • Time: 3PM
  • No Quiz Next Week
  • Trivia during Recitation

Lecture Presentation

  • Text: Eight Edition Chemistry
  • Authors: Robinson McMurry | Fay
  • Chapter: 2
    • Title: Atoms, Molecules, and Ions
  • Prepared by: W. Guo
  • Department: Chemistry, Virginia Commonwealth University

The Mole Concept

  • Definition of a Mole:
    • The mole is a unit that represents the amount of matter.
    • Denoted as mol.
  • Terms:
    • The mole is often referred to as chemists' dozen, in the same way that 1 dozen = 12.
    • 1 mole = $6.022 imes 10^{23}$ (This quantity is known as Avogadro's number, named in honor of Italian scientist Amedeo Avogadro.)
    • The term MOLEcule is derived from the mole concept.

Mole Equivalence

  • Examples of One Mole:
    • 1 mole of carbon (C) = $6.022 imes 10^{23}$ C atoms
    • 1 mole of gold (Au) = $6.022 imes 10^{23}$ Au atoms
    • 1 mole of water (H2O) = $6.022 imes 10^{23}$ H2O molecules

Atomic and Molar Mass

  • Definitions:
    • Atomic Mass: The mass of 1 single C atom in atomic mass units (amu).
    • Molar Mass: The mass of 1 mole of carbon in grams.
    • Example: 1 mole of carbon weighs 12.011 grams.
  • The relationship between atomic mass and molar mass:
    • The molar mass in grams is numerically equivalent to its atomic weight in amu.
    • For carbon: 1 C atom weighs 12.011 amu.

Learning Checks

  • Question: In the case of 1 mol of Cu, Ag, and Au, which contains the most number of atoms?
    • Options:
      A. 1 mol of Cu
      B. 1 mol of Ag
      C. 1 mol of Au
      D. They contain the same number of atoms.
  • Analogy: This question is comparable to a household question: among 1 dozen eggs, 1 dozen books, and 1 dozen pencils, which contains the most items?

Grams Comparison Learning Check

  • Question: Comparing 1 mol of Cu, Ag, and Au for the most number of grams:
    • Options:
      A. 1 mol of Cu
      B. 1 mol of Ag
      C. 1 mol of Au
      D. They contain the same weight.
  • Analogy: This is similar to asking which is the heaviest item out of 1 dozen eggs, 1 dozen books, and 1 dozen pencils.

Mole to Mass Conversion Factor

  • Conversion Factors:
    • 1 mole = $6.022 imes 10^{23}$ particles
    • 1 mole = (Molar Mass) grams

Lecture #21: Learning Objectives

  • Understanding the following:
    • How to find the molar mass of an element.
    • Calculate the molar mass of a compound.
    • Convert between mass (grams), moles, and number of atoms or molecules.

Molar Mass (MM) of Compounds

  • Definition: Molar mass of a compound = sum of the Molar Masses (MMs) of all its elements.
    • Unit: grams/mole (g/mol)
  • Synonyms: Molar mass is also referred to as formula mass, molecular weight, or formula weight.
  • Examples of Molar Mass Calculation:
    • O2: $16.00 imes 2 = 32.00 ext{ g/mol}$
    • H2O: $1.01 imes 2 + 16.00 imes 1 = 18.02 ext{ g/mol}$
    • NaCl: $22.99 imes 1 + 35.45 imes 1 = 58.44 ext{ g/mol}$
    • CO2: $12.01 imes 1 + 16.00 imes 2 = 44.01 ext{ g/mol}$

Counting Atoms

  • Subscripts:
    • Subscripts indicate the number of times to count the atom immediately before the subscript.
    • Example: In H2O, there are 2 hydrogen (H) atoms and 1 oxygen (O) atom (the “1” is omitted as a subscript).
  • Practice Example:
    • For BaSO4, there are:
    • Ba: 1 atom
    • S: 1 atom
    • O: 4 atoms

Parenthesis in Chemical Formulas

  • Usage of Parentheses:
    • If elements are inside parentheses, the subscript behind the parentheses applies to all contained elements.
  • Example Calculation:
    • For compound Ba(NO3)2, count the atoms:
    • Ba: 1
    • N: 2
    • O: 6
  • Tip: Counting atoms inside parentheses is similar to using the distributive property in mathematics.

Additional Examples

  • Practice:
    • For MgCl2:
    • Atoms of Magnesium: 1
    • Atoms of Chlorine: 2
    • For Al₂S3:
    • Atoms of Aluminum: 2
    • Atoms of Sulfur: 3
  • This Could Be A Little Tricky…:
    • For Ca3(PO4)2:
    • Atoms of Calcium: 3
    • Atoms of Phosphorus: 2
    • Atoms of Oxygen: 8
  • Note: There are two phosphate groups (PO₄), leading to calculations of 2 × 1 = 2 P atoms and 2 × 4 = 8 O atoms.

One More Practice

  • For the compound (NH2)2CO:
    • With the atom structure shown:
    • N: 2
    • H: 4
    • C: 1
    • O: 1

Molar Mass Practice

  • Calculation Example:
    • Molar mass of urea (NH2)2CO:
    • MM of (NH2)2CO = 2N + 4H + C + O
    • Calculation: 2(14.01) + 4(1.01) + 12.01 + 16.00 = 60.07 g/mol

Additional Examples of Molar Calculations

  • Example: Calculate the mass in grams of 0.25 mol of (NH2)2CO:

    • Solution:
    • Mass = $0.25 ext{ mol} imes 60.07 ext{ g} / 1 ext{ mol} = 15.02 ext{ g}$

  • Example: Calculate the moles in 50.0 g of (NH2)2CO:

    • Solution:
    • Moles = $50.0 ext{ g} imes rac{1 ext{ mol}}{60.07 ext{ g}} = 0.832 ext{ mol}$

  • Example: Determine the number of (NH2)2CO molecules in 50.0 g of the compound:

    • Calculation Steps:
    • Determine moles: $0.832 ext{ mol} = 50.0 ext{ g} imes rac{1 ext{ mol}}{60.07 ext{ g}}$
    • Calculate molecules: $0.832 ext{ mol} imes rac{6.022 imes 10^{23} ext{ molecules}}{1 ext{ mol}} = 5.01 imes 10^{23} ext{ molecules}$

Assignments for Understanding

  • Task: For each compound (CH4, C2H6, C3H8, C8H18):
    • Calculate the molar mass.
    • Calculate the moles in 1.00 g of the compound.