Unit 7B Classification of Chemical Reactions: Mole and Mass Relationships

Unit 7B: Classification of Chemical Reactions: Mole and Mass Relationships

Learning Objectives

• Review the definition of the mole and convert between the number of moles and the number of particles of a substance.

• Use molar mass to convert between the mass and the number of particles of a substance.

• Convert between mass, moles, and the number of particles (ions, atoms, formula units) of a substance.

• Determine molar ratios of reactants and products using balanced chemical equations.

• Calculate the number of moles of products or reactants required for a chemical reaction to occur using balanced chemical equations.

• Using mole ratios, calculate the mass of product that can be formed from a given mass of reactant and vice versa.

• Calculate the theoretical yield and percent yield for a reaction.

Concepts to Review

• Problem Solving: Unit Conversions and Estimating Answers – Unit 1

• Molecular Formulas and Formula Units – Unit 4 Pts 1&2

• Balancing Chemical Equations – Unit 7 Pt1

The Mole and Avogadro’s Number

• The mole: A counting unit used for very small particles such as atoms, ions, molecules, and formula units.

• Learning Objective: Review the definition of the mole and convert between the number of moles and the number of particles of a substance.

Definition of Mole

• A counting term used to state a specific number of items. For example, terms like dozen, case, gross, and ream serve similar purposes in counting.

Avogadro's Number

• The mole, defined as Avogadro's number, contains $6.02 imes 10^{23}$ items.

  • Used for counting small particles such as atoms, molecules, and ions.

  • 1 mole = $6.02 imes 10^{23}$ items

  • Avogadro's number is named after Amedeo Avogadro (1776–1856), an Italian physicist.

Mole Content

• 1 mole of an element = $6.02 imes 10^{23}$ atoms of that element.

  • Example: 1 mole of carbon = $6.02 imes 10^{23}$ atoms of carbon.

  • Example: 1 mole of sulfur = $6.02 imes 10^{23}$ atoms of sulfur.

Conversion Factor - Avogadro's Number

• Used to convert moles of a substance to particles.

• Equality: 1 mole = $6.02 imes 10^{23}$ particles.

Study Check: Guide to Calculating Atoms or Molecules

1. How many $CO_2$ molecules are in 0.500 mole of $CO_2$?

2. The number of atoms in 2.0 moles of Al is: ____.

3. The number of moles of S in $1.8 imes 10^{24}$ atoms of S is: ____.

Gram-Mole Conversions

• Molar mass: The mass of 1 mole of substance = Mass of $6.022 imes 10^{23}$ molecules = Molecular weight in grams.

• Learning Objective: Use molar mass to convert between the mass and the number of particles of a substance.

  • Convert between mass, moles, and the number of particles (ions, atoms, formula units).

Molar Mass Units

• Measured in g/mol.

• Examples:

  • The molar mass of ethylene (C2H4) is 28.0 g/mol.

  • The molar mass of lithium sulfide (Li2S) is 45.95 g/mol.

  • Atomic weight of 2 Li: $2 imes 6.941 ext{ amu} = 13.882 ext{ amu}$

  • Atomic weight of 1 S: 32.07 amu.

  • Formula Weight (FW) of Li2S = 45.95 amu.

  • Molar mass of a compound: Numerically equal to molecular or formula weight, expressed as g/mol.

Calculations Using Molar Mass with Avogadro’s Number

• Converting between grams and moles:

  • Molar mass Equality: 1 mole = g of pure substance.

  • Conversion Factors: For converting to number of particles, use Avogadro's number.

Practice Problem: Guide to Calculating Particles from Mass or Mass from Particles

• A tiny pencil mark visible to the naked eye contains about $3 imes 10^{17}$ atoms of carbon. What is the mass of this pencil mark in grams?

• Pseudoephedrine hydrochloride ($C_{10}H_{16}ClNO$): How many molecules are in a tablet that contains a dose of 30.0 mg?

In-Class Question

• What is the mass in grams of $3.2 imes 10^{22}$ molecules of water?
  a. 0.0029 g
  b. 339 g
  c. 0.90 g
  d. 0.96 g

Moles of Elements in a Formula

• Example: Aspirin, $C_9H_8O_4$, has the following:

  • 9 atoms of Carbon (C) = 9 moles of C.

  • 8 atoms of Hydrogen (H) = 8 moles of H.

  • 4 atoms of Oxygen (O) = 4 moles of O.

• Subscripts: Directly relate the number of atoms in one molecule and can be used to write conversion factors for moles of each element in 1 mole of a compound.

Study Check: Guide to Calculating Atoms of Element in a Compound

• How many atoms of O are in 0.150 mole of aspirin, $C_9H_8O_4$?

Practice Problem

• Maximum dose of sodium hydrogen phosphate ($Na_2HPO_4$, MW = 142.0 amu) for use as a laxative is 3.8 g. How many moles of $Na^+$ ions and total moles of ions are in this dose?

In-Class Question

• For $Ca_5(PO_4)_3OH$ (hydroxyapatite), how many moles of $Ca^{2+}$ ions are present in 1 mol of hydroxyapatite?
  a) 5 moles of $Ca^{2+}$ ions
  b) 1 mole of $Ca^{2+}$ ions
  c) $1.39 imes 10^{24}$ $Ca^{2+}$ ions
  d) $6.00 imes 10^{23}$ $Ca^{2+}$ ions

Mole Relationships and Chemical Equations

• In chemical reactions, the unit specifying the relationship between reactants and products is the mole.

• Learning Objective: Determine molar ratios of reactants and products using balanced chemical equations.

Law of Conservation of Mass

• Indicates that in an ordinary chemical reaction:

  • Matter cannot be created or destroyed.

  • No change in total mass occurs.

  • Mass of products equals mass of reactants.

Coefficients in a Chemical Equation

• Tell how many molecules (or formula units), thus how many moles, of each reactant are needed, and how many of each product are formed.

Information from a Balanced Equation

• Example: In the equation $2Ag(s) + S(s) ightarrow Ag_2S(s)$:

  • 2 moles of Ag = $2(6.02 imes 10^{23})$ Ag atoms
    defining particle counts, molar relationships, and corresponding grams.

Mole–Mole Factors from an Equation

• In the equation $2Fe(s) + 3S(s) ightarrow Fe_2S_3(s)$:

  • Interpret as: 2 moles of Fe react with 3 moles of S to yield 1 mole of $Fe_2S_3$.

Molar Ratios Example

• Example equation: $N_2 + 3H_2 <br>ightarrow 2NH_3$ can be interpreted as 1 mole of N2 reacts with 3 moles of H2.