Chapter 6: Chemical Reactions: Mole and Mass Relationships

Chapter 6: Chemical Reactions: Mole and Mass Relationships

6.1 The Mole and Avogadro’s Number

• Definition of a Mole:

  • A mole is the amount of a substance whose mass in grams is numerically equal to its molecular or formula weight.

  • One mole of any substance contains $6.022 \times 10^{23}$ formula units, known as Avogadro's number.

• Molecular and Atomic Weights:

  • Atomic Weight: Average mass of an element's atoms, measured in atomic mass units (amu).

  • Molecular Weight (MW): Average mass of a substance's molecules, calculated by summing atomic weights of all atoms in the formula unit.

• Relationship Between Mass and Mole:

  • Molecular weights can be used to provide mass ratios for reactants in chemical reactions.

  • Samples with the same mass ratio have the same number of molecules/formula units when their individual weights match.

6.2 Gram–Mole Conversions

• Molar Mass as Conversion Factor:

  • Molar mass is the mass in grams of 1 mol of a substance, equivalent to its molecular weight.

  • Enables conversion between moles and mass.

6.3 Mole Relationships and Chemical Equations

• Chemical Stoichiometry:

  • The coefficients in balanced chemical equations indicate the number of moles of each reactant and product involved.

  • Mole ratios can serve as conversion factors in chemical calculations.

• Example:

  • For the reaction $3 H<em>2 + N</em>2 \rightarrow 2 NH_3$:

  • From this, 3 moles of hydrogen produce 2 moles of ammonia.

6.4 Mass Relationships and Chemical Equations

• Conversions:

  • Mole-to-mole conversions utilize mole ratios from a balanced equation.

  • Mole-to-mass and mass-to-mole conversions utilize molar mass as conversion factors.

• Four Steps for Mass Relationships:

  1. Write the balanced chemical equation.

  2. Choose molar masses and mole ratios to convert known information into needed information.

  3. Set up the factor-label expression and calculate the answer.

  4. Check the answer against an estimated ballpark value.

6.5 Limiting Reagent and Percent Yield

• Limiting Reagent:

  • It is the reactant that runs out first during the reaction, limiting the amount of product formed.

• Theoretical vs. Actual Yield:

  • Theoretical Yield: Maximum amount of product that could be formed from given quantities of reactants under ideal conditions.

  • Actual Yield: Amount of product actually obtained from a chemical reaction.

  • Percent Yield: Calculated as:

  $\text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100$

• Example Calculation:

  • For the combustion of acetylene:
    $2 C<em>2H</em>2 + 5 O<em>2 \rightarrow 4 CO</em>2 + 2 H_2O$

  • Theoretical yield of $CO_2$ is 88.0 g; actual yield is 72.4 g, leading to:

  • $\text{Percent Yield} = \left( \frac{72.4}{88.0} \right) \times 100 = 82.73\%$

6.6 Empirical and Molecular Formulas

• Empirical Formula:

  • Represents the simplest whole-number ratio of atoms in a compound.

  • Determined by converting mass percentages to moles and simplifying.

• Molecular Formula:

  • May be the same as the empirical formula or an integer multiple of it.

  • Requires experimental molar mass for accurate determination.

• Example for Molecular Formula Determination:

  • For a compound with 30.46% nitrogen and 69.54% oxygen (molar mass between 90-95 g), empirical formula is $NO_2$ (resulting from simplification). If the empirical molar mass is 46 g, and actual molar mass is approximately 92 g:

  • The molecular formula is $N<em>2O</em>4$.

Conclusion

• Understanding the relationship between moles, mass, and chemical reactions is crucial for stoichiometry in chemistry. Mastery of these concepts enables effective calculation and prediction of yields and compositions in chemical processes.