Chemistry chapter 9

Page 1: Introduction

• Chapter Title: Chemical Calculations and Chemical Formulas

• Author: Mark Bishop

Page 2: Chapter Map

• Key Topics Covered:

  • Isotopes (Section 2.5)

  • Conversion between names and formulas (Section 5.3)

  • Atomic mass

  • Molecular and formula mass

  • Structures of molecular and ionic compounds (Sections 3.3 & 3.5)

  • Molar mass as a conversion factor

  • Unit conversions using unit analysis (Section 8.5)

  • Rounding off answers (Section 8.2)

  • Using percentage as a conversion factor (Section 8.4)

  • Conversions between mass and moles of substance

  • Conversions between mass of element and mass of compound

  • Determining empirical formulas

  • Determining molecular formulas

Page 3: Making Phosphoric Acid

• Process Overview: Furnace process for synthesizing phosphoric acid (H3PO4) used in fertilizers, detergents, and pharmaceuticals.

• Chemical Reactions:

  1. React phosphate rock with sand and coke at 2000 ºC:

     • 2Ca3(PO4)2 + 6SiO2 + 10C → 4P + 10CO + 6CaSiO3

  2. React phosphorus with oxygen to produce tetraphosphorus decoxide:

     • 4P + 5O2 → P4O10

  3. React tetraphosphorus decoxide with water to create phosphoric acid:

     • P4O10 + 6H2O → 4H3PO4

Page 4: Sample Calculations (1)

• Calculation Goal: Maximum mass of P4O10 from 1.09 × 10^4 kg P.

• Unit Analysis Setup:

  • Use the formula of P4O10 as a conversion factor to transition from P to P4O10.

Page 5: Sample Calculations (2)

• Calculation Goal: Minimum mass of water needed to create phosphoric acid from 2.50 × 10^4 kg P4O10.

• Reaction Equation: P4O10 + 6H2O → 4H3PO4.

• Conversion Factor: Use coefficients from the balanced equation to change P4O10 amounts to H2O.

Page 6: Conversion Factors for Properties

• Goal: Develop conversion factors to link measurable property (mass) and number of particles.

  • Measurable Property 1 ⇔ Number of Particles 1 ⇔ Number of Particles 2 ⇔ Measurable Property 2.

  • Mass 1 ⇔ Number of Particles 1 ⇔ Number of Particles 2 ⇔ Mass 2.

Page 7: Counting by Weighing for Nails

• Step 1: Select an easily measurable property (mass).

• Step 2: Choose convenient mass units (pounds).

Page 8: Counting by Weighing for Nails (continued)

• Step 3: Measure mass of individual objects:

  • Sample weighing: 82 nails at 3.80 g, 14 nails at 3.70 g, 4 nails at 3.60 g.

• Step 4: Calculate weighted average mass:

  • Average = 0.82(3.80 g) + 0.14(3.70 g) + 0.04(3.60 g) = 3.78 g.

Page 9: Counting by Weighing for Nails (continued)

• Step 5: Use weighted average for conversions between mass and number of objects.

Page 10: Counting by Weighing for Nails (continued)

• Step 6: Express the number of objects in a collective unit (e.g., dozen, gross, ream).

Page 11: Counting by Weighing for Carbon Atoms

• Step 1: Choose a measurable property (mass).

• Step 2: Select a convenient measurement unit (atomic mass units).

• Atomic Mass Unit (u): 1/12 the mass of a carbon-12 atom (6 protons, 6 neutrons, 6 electrons).

Page 12: Counting by Weighing for Carbon Atoms (continued)

• Step 3: Determine mass of individual carbon measurements:

  • 98.90% are 12 u; 1.10% are 13.003355 u.

• Step 4: Calculate weighted average mass of carbon:

  • Average = 0.9890(12 u) + 0.0110(13.003355 u) = 12.011 u.

Page 13: Counting by Weighing for Carbon Atoms (continued)

• Skipping Step 5:

  • Difficulties arise with measurement in atomic mass units and very large numbers of atoms.

Page 14: Collective Units for Atoms

• Preferred Conversion Factor: Use grams instead of atomic mass units.

• Collective Unit: Mole – described tightly as a defined number of atoms.

Page 15: Mole Definition

• A mole (mol) is a substance amount containing the same particles as 12 g of carbon-12.

• Avogadro’s Number: Approximately 6.022 × 10^23 atoms in 12 g of carbon-12.

• Contextual Example: If arranged, carbon atoms from 12 g could stretch over 500 times the distance to the Sun.

Page 16: Avogadro's Number

• Fact: Arranging all carbon atoms in 12 g creates an astronomical distance, connecting Earth and the sun.

Page 17: Molar Mass Development

• Molar mass interlinks with:

  • Unified atomic mass unit definitions.

  • Relative atomic masses listed in periodic table for the elements.

• Example values:

  • 12 g C-12 = 1 mol C.

  • 15.9994 g O = 1 mol O.

  • 1.00794 g H = 1 mol H.

Page 18: Molar Mass of Elements

• Usage of Atomic Masses:

  • Taken from periodic table, used to convert grams to moles and vice versa. [ (atomic,mass), g, element \rightarrow 1, mol, element ]

Page 19: Example Calculations

• Context: Diamonds and gemstones measured in carats (5 carats per gram).

• Question: How many moles of carbon in a 0.55 carat diamond?

Page 20: Our Calculation

• Goal: Find the maximum mass of P4O10 from 1.09 × 10^4 kg P.

• Conversion Structure:

  • Mass P → moles P → moles P4O10 → mass P4O10.

Page 21: Our Calculation Steps

• Steps Overview:

  • Step 1: Mass of P to moles P.

  • Step 2: Moles P to moles P4O10.

  • Step 3: Moles P4O10 to mass P4O10.

Page 22: Conversion from Grams of P to Moles of P

• Before converting grams of P to moles, first convert kg to grams.

Page 23: Conversion from Mass P to Moles P

• Initial Step: Convert kg to grams:

  • Convert grams P to moles P using molar mass derived from atomic mass.

Page 24: Chemical Formula as Conversion Factor

• Role of the Chemical Formula: Provides vital conversion factors for moles of phosphorus to moles of tetraphosphorus decoxide (P4O10).

Page 25: Calculation Steps 1 and 2

• Focus: Completing initial calculations for maximum mass of P4O10 formed from P.

Page 26: Molecular Mass Definition

• Concept: Molecular mass is the sum of all atomic masses in a molecule.

Page 27: Molar Mass for Molecular Compounds

• Molecular Mass Formula:[ (molecular,mass), g, molecular, compound \rightarrow 1, mol, molecular, compound ]

Page 28: Definition of Formula Units

• Formula Unit: The grouping defined by a chemical formula detailing types and counts of atoms/ions.

  • Applicable to elements, molecular compounds, and ionic compounds.

Page 29: Formula Unit Examples

• Neon Gas: One Ne atom.

• Water (H2O): Contains two H and one O.

• Ammonium Chloride (NH4Cl): Contains NH4+ and Cl- ions; no separate molecules.

Page 30: Formula Mass for Ionic Compounds

• Concept: Formula mass is the sum of masses of atoms within the formula unit.

Page 31: Molar Mass for Ionic Compounds

• Formula for Determining Formula Mass:[ (formula,mass), g, ionic, compound \rightarrow 1, mol, ionic, compound ]

Page 32: Molar Mass Development

• Various methods of deriving molar masses involve:

  • Unified atomic mass definitions, relative atomic masses, and empirical data.

Page 33: General Conversions

• Framework Overview:

  1. Measurable property of substance 1 →

  2. Moles of substance 1 →

  3. Moles of substance 2 →

  4. Measurable property of substance 2.

Page 34: Unit Conversions between Substances

• Sequential Steps:

  • Start with grams of substance 1, converting through moles to grams of substance 2.

Page 35: Study Sheets

• Preparation Tips:

  • Write a description of "tip-off" for recognizing calculation types.

  • Outline the general procedure for associated problems.

  • Provide an example calculation.

Page 36: Sample Study Sheet

• Concept Focus: Convert between element mass and mass of the compound.

• Tip-off: Analyze unit types for conversions between elements and associated compound units.

Page 37: General Steps for Conversion

1. Convert the given unit to moles of the first substance.

2. Use compound formula for molar ratios to convert moles of first to moles of second substance.

3. Convert moles of second substance to required unit.

Page 38: Element and Compound Units

• Conversion Framework:

  • Grams of element ↔ moles of element ↔ moles of compound ↔ grams of compound using unit factors.

Page 39: Example Problem

• Steps Illustrated:

  1. Convert P mass to grams.

  2. Transition to molar equivalency.

  3. Calculate final compound mass in desired units.

Page 40: Empirical and Molecular Formulas

• Empirical Formula: Simplest ratio of atoms in a compound (often ionically bonded).

• Molecular Formula: Actual atom count of each element in a molecule.

Page 41: Examples of Formulas

• Hydrogen Peroxide: Molecular (H2O2), empirical (HO).

• Glucose: Molecular (C6H12O6), empirical (CH2O).

Page 42: Steps to Calculate Empirical Formulas

1. Convert given data to grams if not provided.

2. Divide grams by atomic mass to get moles.

3. Calculate simplest ratios and round to integers.

4. Adjust fractions by multiplying to whole numbers for empirical formula subscripts.

Page 43: Calculation Steps Continued

• Step 1: Obtain grams total from given percentages (assume 100 g compound).

• Step 2: Divide grams by atomic mass for moles.

Page 44: Further Calculation Steps

• Steps to Empirical Formula:

  • Round each mole value to obtain positive integers; adjust any fractions accordingly.

Page 45: Example Empirical Formula Calculation

• Ionic Compound Description:

  • Components: 35.172% K, 28.846% S, and 35.982% O.

  • Target:** Derive empirical formula from these percentages.

Page 46: Calculation Steps for Example

• Step 1: Convert percentages to gram ratio, using 100 g basis.

• Example Inputs: 35.172 g K, 28.846 g S, 35.982 g O.

Page 47: Continuing the Example Calculation

• Step 2: Conversion of grams to moles using atomic weights.

Page 48: Further Steps in Calculation

• Step 3: Divide each mole value by smallest to yield ratio.

Page 49: Finalizing the Example Calculation

• Step 4 & 5: Manage fractions from ratios to derive the proper empirical formula values (K2S2O5).

Page 50: Calculating Molecular Formulas

1. Calculate or confirm the empirical formula.

2. Divide the molecular mass by empirical formula mass for scaling factor.

3. Multiply subscripts in empirical formula by n to reach molecular formula.

Page 51: Summary of Molecular Formula Calculation Steps

1. Divide between molecular mass and empirical mass calculations.

2. Adjust empirical formula subscripts by determined factor.

Page 52: Example of a PCB Molecular Formula Calculation

• Context: Polychlorinated biphenyls (PCBs) usage and environmental impact.

• Example Composition: 39.94% C, 1.12% H, 58.94% Cl with molecular mass of 360.88.

Page 53: Continuing PCB Calculation Process

• Calculate empirical formula using percentage data from context.

Page 54: Final Steps to Determine Molecular Formula

• Follow-up Procedures: Ratio establishment from empirical data to finalize the molecular formula.