Percentage Yield and Atom Economy

Percentage Yield

Definition

Percentage Yield is the ratio of the actual yield (the amount of product obtained in a reaction) to the theoretical yield (the amount of product predicted by stoichiometry), expressed as a percentage.

Formula

• Actual Yield: The mass (in grams or moles) of the product actually obtained from the experiment.
• Theoretical Yield: The maximum amount of product (in grams or moles) that can be produced from the given amount of reactants, assuming complete conversion and no loss.

Calculating Theoretical Yield

1. Balance the Chemical Equation: Ensure the equation is balanced to establish the correct stoichiometric ratios.
2. Determine the Limiting Reactant: Identify the reactant that will be completely consumed first, thus limiting the amount of product formed.
3. Calculate Moles of Limiting Reactant: Use the formula:
   \$\$ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \$\$
4. Use Stoichiometry: Use the stoichiometric ratio from the balanced equation to determine the moles of product that can be formed from the limiting reactant.
5. Calculate Theoretical Yield (Mass): Convert the moles of product to mass using the formula:
   \$\$ \text{Mass} = \text{Moles} \times \text{Molar Mass} \$\$

Factors Affecting Percentage Yield

• Incomplete Reactions: Not all reactants may convert to products.
• Side Reactions: Unwanted reactions may occur, consuming reactants and forming by-products.
• Loss During Transfer: Some product may be lost during transfer between containers or during purification.
• Experimental Error: Errors in measurement can affect the accuracy of the yield.

Example Calculation

Consider the reaction:
\(C_6H_{12}O_6 \rightarrow 2C_2H_5OH + 2CO_2\)

If 180 g of glucose (\(C_6H_{12}O_6\)) yields 80 g of ethanol (\(C_2H_5OH\)), calculate the percentage yield.

1. Theoretical Yield:
   • Moles of glucose = \(\frac{180 \text{ g}}{180 \text{ g/mol}} = 1 \text{ mol}\)
   • From the balanced equation, 1 mol of glucose produces 2 mol of ethanol.
   • Moles of ethanol (theoretical) = \(2 \text{ mol}\)
   • Molar mass of ethanol = \(46 \text{ g/mol}\)
   • Theoretical yield of ethanol = \(2 \text{ mol} \times 46 \text{ g/mol} = 92 \text{ g}\)
2. Percentage Yield:
   • Percentage yield = \(\frac{80 \text{ g}}{92 \text{ g}} \times 100\% = 86.96\%\)

KEY TAKEAWAY: Percentage yield reflects the efficiency of a chemical reaction, influenced by factors such as incomplete reactions and loss of product during handling.

Atom Economy

Definition

Atom Economy is a measure of the proportion of reactant atoms that become incorporated into the desired product in the balanced chemical equation. It reflects the efficiency of a reaction in terms of waste generation.

Formula

• Only consider the reactants in the calculation.
• If there are coefficients in front of reactants or products in the balanced equation, they must be accounted for in the molar mass calculation.
• A higher atom economy indicates a more efficient and sustainable process.

Example Calculation

Consider the reaction:
\(C_2H_4 + H_2 \rightarrow C_2H_6\)

Calculate the atom economy for the production of ethane (\(C_2H_6\)).

1. Molar Mass of Desired Product (Ethane): \(30 \text{ g/mol}\)
2. Molar Mass of All Reactants (Ethene + Hydrogen): \((28 \text{ g/mol} + 2 \text{ g/mol}) = 30 \text{ g/mol}\)
3. Atom Economy:
   • Atom Economy = \(\frac{30 \text{ g/mol}}{30 \text{ g/mol}} \times 100\% = 100\%\)

Importance of Atom Economy

• Sustainability: High atom economy minimizes waste and reduces the environmental impact of chemical processes.
• Cost-Effectiveness: Reduces the need for waste disposal and purification, lowering production costs.
• Green Chemistry: Atom economy is a key principle of green chemistry, promoting the development of more sustainable chemical processes.

Comparison of Percentage Yield and Atom Economy

Multi-Step Reaction Pathways

Overall Percentage Yield

For a multi-step reaction, the overall percentage yield is the product of the percentage yields of each individual step.

Where \(\text{Yield}_1\), \(\text{Yield}_2\), \(\text{Yield}_3\) are the percentage yields of step 1, step 2, step 3, respectively, expressed as decimals (e.g. 80% = 0.80).

Overall Atom Economy

For a multi-step reaction, the overall atom economy is calculated based on the initial reactants and the final desired product. Intermediate compounds are not considered.

Advantages of High Atom Economy

• Reduced waste disposal costs
• Less pollution
• More efficient use of resources
• Increased sustainability

EXAM TIP: When calculating atom economy, make sure to only consider the reactants. The coefficients in the balanced equation are crucial for accurate calculations.

Green Chemistry Principles

Renewable Feedstocks

Using renewable resources (e.g., plant-based materials) as starting materials for chemical processes helps reduce dependence on finite resources like fossil fuels.

Catalysis

Using catalysts to speed up reactions can lower energy requirements and reduce waste. Catalysts are not consumed in the reaction, so they can be used repeatedly.

Designing Safer Chemicals

Designing chemicals that are less toxic and hazardous reduces the risk of accidents and environmental damage.

Other Green Chemistry Principles

• Prevention: It is better to prevent waste than to treat or clean up waste after it has been created.
• Maximize Atom Economy: Design syntheses so that the final product contains the maximum proportion of the starting materials.
• Less Hazardous Chemical Syntheses: Design syntheses to use and generate substances with little or no toxicity to human health and the environment.
• Safer Solvents and Auxiliaries: Avoid using auxiliary substances (e.g., solvents, separation agents) wherever possible, and make such substances innocuous when they are used.
• Design for Energy Efficiency: Minimize energy requirements for chemical processes and conduct reactions at ambient temperature and pressure whenever possible.
• Use of Renewable Feedstocks: Use renewable raw materials or feedstocks rather than depletable resources whenever technically and economically practicable.
• Reduce Derivatives: Minimize or avoid unnecessary derivatization (use of blocking groups, protection/ deprotection, temporary modification of physical/chemical processes) because such steps require additional reagents and can generate waste.
• Catalysis: Use catalytic reagents (as selective as possible) rather than stoichiometric reagents.
• Design for Degradation: Design chemical products so that at the end of their function they break down into innocuous degradation products and do not persist in the environment.
• Real-time Analysis for Pollution Prevention: Develop analytical methodologies needed to allow for real-time, in-process monitoring and control prior to the formation of hazardous substances.
• Inherently Safer Chemistry for Accident Prevention: Choose substances and the form of a substance used in a chemical process to minimize the risk of chemical accidents, including releases, explosions, and fires.

COMMON MISTAKE: Students often confuse percentage yield and atom economy. Percentage yield is an experimental measure, while atom economy is a theoretical calculation based on the balanced equation.

Examples of Sustainable Organic Reactions

Transesterification of Plant Triglycerides to Produce Biodiesel

• Reaction: Plant triglycerides react with an alcohol (e.g., methanol or ethanol) in the presence of a catalyst (e.g., sodium hydroxide) to produce biodiesel (fatty acid methyl esters) and glycerol.
• Sustainability: Uses renewable feedstocks (plant oils) and produces a valuable by-product (glycerol).

Addition Reactions

• Reaction: Ethene reacting with steam in the presence of an acid catalyst to produce ethanol.
• Sustainability: This reaction has a 100% atom economy, as all of the reactants are incorporated into the product.

STUDY HINT: Practice calculating percentage yield and atom economy with various chemical reactions to gain proficiency. Pay close attention to the stoichiometry of the reactions.

Advantages for Society and Industry

Society

• Reduced Environmental Impact: Sustainable chemical processes minimize pollution and waste, leading to a cleaner environment.
• Resource Conservation: Efficient use of resources ensures their availability for future generations.
• Safer Products: Green chemistry principles promote the design of safer chemicals, reducing risks to human health.

Industry

• Cost Savings: Reduced waste disposal costs, lower energy consumption, and efficient use of raw materials can lead to significant cost savings.
• Improved Public Image: Companies that adopt sustainable practices can enhance their reputation and attract environmentally conscious consumers.
• Innovation: The pursuit of green chemistry drives innovation and the development of new technologies.

VCAA FOCUS: VCAA exams often require students to apply their knowledge of percentage yield and atom economy to evaluate the sustainability of different chemical processes. Be prepared to discuss the advantages of high atom economy and green chemistry principles.