Stoichiometry Guide

Stoichiometry quantifies chemical reactions using balanced equations, rooted in the conservation of mass. This MathMultiverse guide explores mole concepts, ratios, limiting reactants, and applications with visualizations.

Mole Concept

A mole is \( 6.022 \times 10^{23} \) entities (Avogadro’s number, \( N_A \)). Molar mass connects moles to grams.

\[ M_{\ce{H2O}} = 2 \times 1.008 + 15.999 = 18.015 \, \text{g/mol} \]

Moles: \( n = \frac{\text{mass}}{\text{molar mass}} \). For 36 g \( \ce{H2O} \):

\[ n = \frac{36}{18.015} \approx 2 \, \text{mol} \]

Molecules: \( 0.5 \, \text{mol} \, \ce{N2} \times N_A = 3.011 \times 10^{23} \).

Mole Ratios

For \( \ce{CH4 + 2O2 -> CO2 + 2H2O} \), ratios dictate proportions.

From 16 g \( \ce{CH4} \):

\[ n_{\ce{CH4}} = \frac{16}{16.04} \approx 1 \, \text{mol} \] \[ n_{\ce{CO2}} = 1 \times \frac{1}{1} = 44.01 \, \text{g} \]

Volume \( \ce{O2} \) for 8 g \( \ce{CH4} \):

\[ n_{\ce{O2}} = 0.5 \times \frac{2}{1} = 1 \, \text{mol} \] \[ V = 1 \times 22.414 = 22.414 \, \text{L} \]

Limiting Reactants

For \( \ce{C2H5OH + 3O2 -> 2CO2 + 3H2O} \), with 46 g \( \ce{C2H5OH} \), 80 g \( \ce{O2} \):

\[ n_{\ce{O2}} = \frac{80}{32} = 2.5 \, \text{mol} \] \[ n_{\ce{CO2}} = 2.5 \times \frac{2}{3} \approx 1.67 \, \text{mol} \]

Percent yield for 60 g \( \ce{CO2} \):

\[ \% \text{Yield} = \frac{60}{73.35} \times 100 \approx 81.8\% \]

Visualizations

Reaction Yield

Applications

  • Ammonia Synthesis: \( \ce{N2 + 3H2 -> 2NH3} \), 28 g \( \ce{N2} \) yields 34.06 g \( \ce{NH3} \).
  • Drug Synthesis: Aspirin from 138 g \( \ce{C7H6O3} \) yields 180.16 g.
  • CO2 Emissions: 114 g octane produces 352.08 g \( \ce{CO2} \).
  • Rockets: 32 g \( \ce{O2} \) needs 44.828 L \( \ce{H2} \).