4.4 Extent of Reaction

Extent of reaction is a powerful tool for tracking chemical changes. It quantifies how far a reaction has progressed, helping us calculate reactant consumption and product formation. This concept is crucial for understanding reaction stoichiometry and equilibrium.

By using extent of reaction, we can determine the composition of a reaction mixture at any point. This allows us to predict yields, optimize processes, and analyze complex reaction systems. It's a fundamental concept that bridges stoichiometry and chemical equilibrium.

Understanding Extent of Reaction

Define extent of reaction and explain its significance in chemical processes

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• Extent of reaction ($\xi$) quantifies reaction progress measured in moles reacted
• Relates stoichiometric coefficients to changes in molar amounts enabling calculation of reactant consumption and product formation
• Useful for determining equilibrium compositions and reaction yield

Calculate the extent of reaction for a given chemical process

• General formula: $\xi = \frac{n_i - n_{i0}}{\nu_i}$ where $n_i$ is final moles, $n_{i0}$ is initial moles, and $\nu_i$ is stoichiometric coefficient
• Steps to calculate:

1. Write balanced chemical equation
2. Identify initial molar amounts
3. Choose reference species (usually limiting reactant)
4. Apply extent of reaction formula

• Example: For 2H₂ + O₂ → 2H₂O, if 0.5 mol H₂O formed, $\xi = \frac{0.5 - 0}{2} = 0.25$ mol

Use extent of reaction to determine the composition of a reaction mixture at any point during the reaction

• For reactants: $n_i = n_{i0} - \nu_i\xi$
• For products: $n_i = n_{i0} + \nu_i\xi$
• Calculate composition:

1. Determine extent at desired point
2. Use equations to calculate molar amounts
3. Convert to desired units (mole fractions, concentrations)

• Example: In A + 2B → C, if $\xi = 0.3$ mol and initially $n_A = 1$ mol, $n_B = 2.5$ mol, then $n_A = 1 - 0.3 = 0.7$ mol, $n_B = 2.5 - 2(0.3) = 1.9$ mol, $n_C = 0 + 0.3 = 0.3$ mol

Applications and Advanced Concepts

Apply extent of reaction to multiple reaction systems

• Independent reactions assign separate extents ($\xi_1$, $\xi_2$)
• Dependent reactions express one extent in terms of another using stoichiometric relationships
• Example: For reactions A → B and B → C, $\xi_2$ depends on $\xi_1$ as B is both product and reactant

Relate extent of reaction to reaction coordinate and degree of advancement

• Reaction coordinate equivalent to extent in homogeneous systems represents progress along reaction path
• Degree of advancement ($\alpha = \frac{\xi}{\xi_{max}}$) ranges from 0 (no reaction) to 1 (complete)
• Example: If $\xi_{max} = 0.5$ mol and current $\xi = 0.25$ mol, then $\alpha = 0.5$ or 50% complete

Analyze the limitations and assumptions when using extent of reaction

• Assumes reaction follows balanced equation without side reactions
• May not accurately represent complex networks or account for kinetics/thermodynamics
• Real systems considerations include equilibrium, reversible reactions, and multiple pathways
• Example: In A ⇌ B + C, extent alone can't predict equilibrium composition without additional thermodynamic data