Chemistry: Stoichiometry Conversions (Moles, Grams, Liters) Cheat Sheet

Introduction to Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in chemical reactions. It forms the mathematical foundation of chemistry, enabling scientists to predict reaction yields, determine limiting reactants, and calculate the precise amounts of substances needed for reactions. Mastering stoichiometry conversions is essential for success in chemistry courses, laboratory work, and industrial chemical processes. This cheat sheet provides a comprehensive guide to converting between moles, grams, liters, and more in chemical calculations.

Core Concepts and Definitions

Fundamental Units and Constants

• Mole (mol): The SI unit representing 6.022 × 10²³ particles (Avogadro’s number)
• Molar mass (g/mol): Mass of one mole of a substance in grams
• Molar volume: Volume occupied by one mole of gas at STP (22.4 L at 0°C and 1 atm)
• Avogadro’s number (NA): 6.022 × 10²³ particles/mol
• Standard Temperature and Pressure (STP): 0°C (273.15 K) and 1 atm (101.325 kPa)
• Standard Ambient Temperature and Pressure (SATP): 25°C (298.15 K) and 1 atm

Key Relationships

Basic Conversion Pathways

Comprehensive Conversion Map

                        ┌─── Particles (atoms/molecules) ───┐
                        │           × NA or ÷ NA            │
                        ▼                                   │
      ┌────── Moles ◄──────┐                               │
      │     × MM   ÷ MM    │        × NA                   │
      ▼                    ▼                               │
   Mass ───────────────► Particles ◄───────────────────────┘
   (g)        ÷ MM    (atoms/molecules)
      │                    ▲
      │      × ρ   ÷ ρ    │
      ▼                    │
   Volume ──────────────► Mass
    (L)         × ρ        (g)
      │
      │      PV = nRT
      ▼
  Gas Volume
     (L)

Step-by-Step Conversion Processes

1. Grams to Moles: Divide mass by molar mass

   • n (mol) = mass (g) ÷ molar mass (g/mol)

2. Moles to Grams: Multiply moles by molar mass

   • mass (g) = moles (mol) × molar mass (g/mol)

3. Moles to Particles: Multiply moles by Avogadro’s number

   • particles = moles (mol) × 6.022 × 10²³ particles/mol

4. Particles to Moles: Divide number of particles by Avogadro’s number

   • moles (mol) = particles ÷ 6.022 × 10²³ particles/mol

5. Moles to Gas Volume (at STP): Multiply moles by molar volume

   • volume (L) = moles (mol) × 22.4 L/mol (at STP)

6. Gas Volume to Moles (at STP): Divide volume by molar volume

   • moles (mol) = volume (L) ÷ 22.4 L/mol (at STP)

Molar Mass Calculations

Calculating Molar Mass

1. Identify all elements in the compound
2. Multiply atomic mass of each element by its subscript
3. Sum all values to get total molar mass

Example Calculations

Reaction Stoichiometry Conversions

Mass-to-Mass Conversions

1. Convert mass of given substance to moles
2. Use mole ratio from balanced equation
3. Convert moles of desired substance to mass

Step-by-Step Process:

Mass A → Moles A → Moles B → Mass B
   ÷ MM_A    × ratio    × MM_B

Example: 2H₂ + O₂ → 2H₂O

To convert 4.0 g H₂ to g H₂O:

• 4.0 g H₂ ÷ 2.016 g/mol = 1.98 mol H₂
• 1.98 mol H₂ × (2 mol H₂O ÷ 2 mol H₂) = 1.98 mol H₂O
• 1.98 mol H₂O × 18.02 g/mol = 35.7 g H₂O

Gas Volume Conversions

1. Convert volume to moles using gas laws
2. Use mole ratio from balanced equation
3. Convert moles to desired quantity

Example: CH₄ + 2O₂ → CO₂ + 2H₂O

To convert 5.0 L CH₄ at STP to L CO₂:

• 5.0 L CH₄ ÷ 22.4 L/mol = 0.223 mol CH₄
• 0.223 mol CH₄ × (1 mol CO₂ ÷ 1 mol CH₄) = 0.223 mol CO₂
• 0.223 mol CO₂ × 22.4 L/mol = 5.0 L CO₂

Solution Stoichiometry

Concentration Conversions

• Molarity (M): moles of solute per liter of solution

  • M = moles of solute ÷ volume of solution (L)
  • moles = M × volume (L)
  • mass (g) = M × volume (L) × molar mass (g/mol)

• Molality (m): moles of solute per kg of solvent

  • m = moles of solute ÷ mass of solvent (kg)
  • moles = m × mass of solvent (kg)

• Mass Percent (% w/w): (mass of solute ÷ mass of solution) × 100%

  • mass of solute = (% w/w ÷ 100) × mass of solution

• Volume Percent (% v/v): (volume of solute ÷ volume of solution) × 100%

• Parts per Million (ppm): (mass of solute ÷ mass of solution) × 10⁶

Dilution Calculations

• Dilution formula: M₁V₁ = M₂V₂
  • M₁ = initial concentration (mol/L)
  • V₁ = initial volume (L)
  • M₂ = final concentration (mol/L)
  • V₂ = final volume (L)

Solution Stoichiometry Steps

1. Calculate moles of reactant from solution concentration
   • Moles = molarity (mol/L) × volume (L)
2. Use mole ratio from balanced equation
3. Calculate required volume or concentration of other reactants/products

Gas Law Stoichiometry

The Ideal Gas Law

• Formula: PV = nRT
  • P = pressure (atm or kPa)
  • V = volume (L)
  • n = moles (mol)
  • R = gas constant (0.0821 L·atm/mol·K or 8.314 L·kPa/mol·K)
  • T = temperature (K)

Mole-Volume-Mass Conversions at Non-STP Conditions

1. Use ideal gas law to find moles: n = PV ÷ RT
2. Convert moles to mass: mass = moles × molar mass
3. For reactions, apply stoichiometric ratios

Gas Density Calculations

• Gas density: d = MM × P ÷ RT
  • d = density (g/L)
  • MM = molar mass (g/mol)
  • P = pressure (atm)
  • R = 0.0821 L·atm/mol·K
  • T = temperature (K)

Reaction Yield Calculations

Theoretical Yield

1. Identify limiting reactant (if necessary)
2. Calculate moles of limiting reactant
3. Use stoichiometric ratio to determine theoretical moles of product
4. Convert to mass: theoretical yield = moles × molar mass

Percent Yield

• Formula: % yield = (actual yield ÷ theoretical yield) × 100%
• Actual yield: Measured mass of product obtained experimentally
• Theoretical yield: Maximum possible mass based on stoichiometry

Limiting Reactant Determination

1. Calculate moles of each reactant
2. Divide by respective stoichiometric coefficients
3. Lowest resulting value identifies the limiting reactant
4. Base all yield calculations on the limiting reactant

Advanced Conversions and Applications

Empirical and Molecular Formula Determination

1. Convert mass percent to mass in 100g sample
2. Convert mass to moles for each element
3. Divide by smallest mole value to get mole ratios
4. Multiply by small integer if necessary to get whole numbers
5. Determine molecular formula if molar mass is known:
   • (Molecular formula) = (Empirical formula) × n
   • n = (Molecular mass) ÷ (Empirical formula mass)

Combustion Analysis

1. Calculate moles of CO₂ and H₂O from combustion data
2. Determine moles of C and H in sample
3. Calculate mass percent or empirical formula

Titration Calculations

1. Calculate moles of titrant: moles = molarity × volume (L)
2. Use reaction stoichiometry to determine moles of analyte
3. Calculate concentration or mass of analyte

Common Challenges and Solutions

Quick Reference Tables

Common Molar Masses

Common Unit Conversion Factors

Gas Conversion Factors at STP (0°C, 1 atm)

Gas Conversion Factors at SATP (25°C, 1 atm)

Practical Tips and Best Practices

Problem-Solving Strategy

1. Identify given and unknown quantities

   • Write down all values with units
   • Identify the target unit/quantity

2. Map a conversion pathway

   • Identify the sequence of conversions needed
   • Use the conversion map as a guide

3. Set up the calculation

   • Use dimensional analysis (factor-label method)
   • Check that units cancel properly

4. Perform calculations and verify

   • Check significant figures
   • Ensure answer is reasonable (magnitude check)

Common Pitfalls to Avoid

• Forgetting to balance chemical equations before stoichiometry
• Mixing up molar mass (g/mol) and molecular weight (amu)
• Using incorrect gas constants or forgetting temperature conversions
• Neglecting to identify the limiting reactant
• Confusing molarity (mol/L) with molality (mol/kg)
• Using atomic masses instead of molecular masses
• Not accounting for waters of hydration in hydrated compounds

Resources for Further Learning

Recommended Textbooks

• “Chemistry: The Central Science” by Brown, LeMay, et al.
• “Chemical Principles” by Zumdahl & Zumdahl
• “Quantitative Chemical Analysis” by Harris

Online Resources

• Khan Academy: Chemistry Stoichiometry Course
• ChemCollective: Virtual Lab Simulations
• American Chemical Society Education Resources
• NIST Chemistry WebBook (for reliable data)

Practice Problem Sources

• Textbook end-of-chapter problems
• ACS Chemistry Olympiad past exams
• AP Chemistry free-response questions
• University chemistry department practice worksheets

Remember that stoichiometry proficiency comes with practice. Start with simple conversions and gradually move to more complex problems. The key is to develop a systematic approach and be consistent with units throughout your calculations.