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Percentage yield and atom economy

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Intros
Lessons
  1. Why do chemists do chemical reactions?
  2. Practical problems in chemical reactions.
  3. Atom economy and percentage yield.
  4. Worked example: Calculate atom economy.
  5. Worked example: Calculate percentage yield.
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Examples
Lessons
  1. Find the atom economy and percentage yield of chemical reactions.
    Water can be produced by reaction of hydrogen and oxygen gas according to this equation:

    2 H2+_2 + O2 _2 \, →  \, 2 H2_2O

    1. What is the atom economy of this reaction?
    2. If the reaction was performed and 150 g was the theoretical yield of water and the actual yield was only 92 g, what is the percentage yield?
  2. Find the atom economy and percentage yield of chemical reactions.
    The reaction to make iron metal by reduction uses carbon. CO2_2 is an unwanted side-product. The reaction is as follows:

    2 Fe2_2 O3+_3 + 3 C  \, →  \, 3 CO2+_2 + 4 Fe

    1. What is the atom economy of this reaction?
    2. 280 g of Fe2_2O3_3 was used in this reaction and 104 g of Fe metal was collected. Calculate the theoretical yield and then the percentage yield of this reaction.
    3. This reaction was done again and a percentage yield of 90% was achieved this time. If 250 g of Fe was collected this time, how much Fe2_2O3_3 was used up?
  3. Compare the viability of two reactions by finding the atom economy and percentage yield.
    Magnesium reacts with hydrochloric acid as shown in the following equation:

    Mg+ + 2 HCl  \, →  \, MgCl2+_2 +H2_2

    1. If this reaction was performed to make hydrogen gas, what would be the atom economy?
    2. 55 g of Mg metal was used in this reaction with HCl in excess. Only 4.21 g of H2_2 gas was produced from this reaction. What is the percentage yield of this reaction?
    3. Hydrogen gas could also be made by electrolysis of water, in the following reaction:
      2 H2_2 O→2 H2+_2 + O2_2

      Find the atom economy of this reaction. Is it a better or worse way to make hydrogen than reacting magnesium with hydrochloric acid?
Topic Notes
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Introduction to Percentage Yield and Atom Economy

Percentage yield and atom economy are crucial concepts in chemistry that help assess the efficiency of chemical reactions. Percentage yield compares the actual amount of product obtained to the theoretical maximum, indicating how well a reaction performs in practice. Atom economy, on the other hand, measures the proportion of reactant atoms that end up in the desired product, highlighting the reaction's efficiency in terms of resource utilization. The introduction video provides a comprehensive overview of these concepts, offering visual explanations and practical examples to enhance understanding. By watching this video, students and chemistry enthusiasts can grasp the significance of these measurements in real-world applications. These concepts are essential for evaluating reaction effectiveness, optimizing industrial processes, and developing sustainable chemical practices. Understanding percentage yield and atom economy is fundamental for chemists, chemical engineers, and anyone involved in the design and analysis of chemical reactions, as they provide valuable insights into reaction efficiency and environmental impact.

Understanding Percentage Yield

Definition

Percentage yield is a crucial concept in chemistry and chemical engineering that measures the efficiency of a chemical reaction. It compares the actual amount of product obtained from a reaction to the theoretical maximum amount that could be produced based on the limiting reagent. This concept is essential for evaluating the success of chemical processes and identifying areas for improvement in industrial settings.

Calculation

To calculate percentage yield, you need to know two key values: the actual yield and the theoretical yield. The formula for percentage yield is:

Percentage Yield = (Actual Yield / Theoretical Yield) × 100%

For example, if a reaction theoretically should produce 50 grams of a product, but only 40 grams are actually obtained, the percentage yield would be:

(40 g / 50 g) × 100% = 80%

This means the reaction had an 80% yield, indicating that 80% of the theoretical maximum product was obtained.

Significance

Understanding percentage yield is crucial for several reasons:

  • Efficiency Assessment: It helps chemists and engineers evaluate the efficiency of a reaction or process.
  • Cost Analysis: In industrial settings, percentage yield directly impacts production costs and profitability.
  • Process Optimization: Low yields indicate areas where improvements can be made to increase efficiency.
  • Quality Control: Consistent yields are important for maintaining product quality and meeting production targets.

What Does a High Percent Yield Mean?

A high percentage yield, typically above 90%, is generally considered good and indicates an efficient reaction. It means that most of the reactants were successfully converted into the desired product. High yields are desirable because they:

  • Minimize waste of raw materials
  • Reduce production costs
  • Indicate a well-controlled and optimized process
  • Often result in higher purity products

What Does a Low Percent Yield Mean?

A low percentage yield, typically below 50%, suggests that the reaction or process is inefficient. Low yields can be caused by various factors:

  • Side reactions producing unwanted byproducts
  • Incomplete reactions
  • Loss of product during isolation or purification steps
  • Errors in experimental technique or measurements

Low yields often indicate a need for process improvement, which might involve adjusting reaction conditions, using catalysts, or refining purification methods.

Is a High Percent Yield Always Good?

While a high percentage yield is generally desirable, it's important to consider other factors:

  • Product Purity: Sometimes a lower yield might be acceptable if it results in a higher purity product.
  • Cost-Effectiveness in Chemical Reactions: A high yield process might not be economically viable if it requires expensive reagents or complex equipment.
  • Safety and Environmental Concerns: A high-yielding process that produces hazardous waste or requires dangerous conditions may not be preferable.
  • Scale-Up Challenges: Some high-yield reactions in the lab may not scale well to industrial production.

In conclusion, percentage yield is a vital metric in chemistry and chemical engineering. It provides valuable insights into reaction efficiency, helps identify areas for improvement, and guides decision-making in both research and industrial settings. By understanding how to calculate percentage yield and interpret its significance, chemists and engineers can optimize processes, reduce costs, and improve product quality. Whether you're a student learning about chemical reactions or a professional, understanding cost-effectiveness in chemical reactions is crucial for making informed decisions.

Exploring Atom Economy

Definition

Atom economy is a fundamental concept in green chemistry that measures the efficiency of a chemical reaction. It represents the percentage of atoms from the reactants that end up in the desired product. This principle was introduced by Barry Trost in 1991 and has since become a crucial metric for evaluating the sustainability and efficiency of chemical processes. Atom economy focuses on maximizing the use of raw materials and minimizing waste production, aligning with the goals of sustainable chemistry.

Calculation

To calculate atom economy, chemists use a specific equation. The atom economy equation is as follows:

Atom Economy = (Molecular mass of desired product / Total molecular mass of all reactants) × 100%

This calculation provides a percentage that indicates how efficiently the atoms from the reactants are incorporated into the final product. A higher percentage indicates better atom economy, meaning more atoms from the reactants end up in the desired product rather than being wasted in by-products or unused reactants.

To illustrate how to calculate atom economy, let's consider a simple example:

For the reaction: 2H + O 2HO

Molecular mass of HO (product) = 18 g/mol

Total molecular mass of reactants = (2 × 2 g/mol) + (32 g/mol) = 36 g/mol

Atom Economy = (36 g/mol / 36 g/mol) × 100% = 100%

In this case, the reaction has perfect atom economy, as all atoms from the reactants end up in the product.

Importance

The concept of atom economy holds significant importance in modern chemistry for several reasons:

  1. Environmental Impact: High atom economy reactions produce less waste, reducing the environmental footprint of chemical processes. This aligns with the principles of green chemistry and sustainable development.
  2. Economic Efficiency: Reactions with high atom economy are generally more cost-effective, as they make better use of raw materials and reduce the need for waste treatment.
  3. Process Optimization: Chemists use atom economy as a metric to evaluate and improve reaction pathways, leading to more efficient synthetic routes in both research and industrial settings.
  4. Resource Conservation: By maximizing the use of reactants, high atom economy processes contribute to the conservation of valuable chemical resources.

The implications of atom economy extend beyond the laboratory. Reactions with high atom economy are preferred in industrial processes, pharmaceutical synthesis, and materials production. They often require fewer separation and purification steps, reducing energy consumption and processing time. Conversely, low atom economy reactions may be less desirable due to increased waste generation, higher costs, and greater environmental impact.

In the pharmaceutical industry, where complex molecules are synthesized, improving atom economy can lead to significant reductions in production costs and environmental impact. For example, the redesign of the synthesis pathway for the anti-inflammatory drug ibuprofen increased its atom economy from about 40% to 77%, dramatically improving the efficiency of its production.

Researchers and industrial chemists continually strive to develop reactions with higher atom economy. This effort involves exploring alternative reagents, catalysts, and reaction conditions that can improve the overall efficiency of chemical transformations. The push for better atom economy has led to innovations in catalysis, where carefully designed catalysts can facilitate reactions that proceed with minimal waste production.

It's important to note that while atom economy is a valuable metric, it should be considered alongside other factors such as reaction yield, energy requirements, and the toxicity of reagents and products. A holistic approach to green chemistry considers all these aspects to develop truly sustainable chemical processes.

In conclusion, atom economy is a crucial concept in modern chemistry that quantifies the efficiency of chemical reactions in terms of atom utilization. By understanding how to calculate atom economy and recognizing its importance, chemists can design more sustainable and efficient

Comparing Percentage Yield and Atom Economy

Percentage yield and atom economy are two crucial concepts in chemistry that help evaluate the efficiency and sustainability of chemical reactions. While both are important in assessing reaction outcomes, they focus on different aspects of the process. Understanding the similarities and differences between these concepts is essential for chemists and students alike.

Percentage yield is a measure of the actual amount of product obtained from a chemical reaction compared to the theoretical maximum amount that could be produced. It is calculated by dividing the actual yield by the theoretical yield and multiplying by 100. For example, if a reaction theoretically should produce 100 grams of a product, but only 75 grams are obtained, the percentage yield would be 75%. This concept is vital in industrial and laboratory settings as it helps assess the efficiency of a reaction and identify potential issues in the process.

On the other hand, atom economy focuses on the atomic level efficiency of a reaction. It is calculated by dividing the molecular mass of the desired product by the sum of the molecular masses of all reactants, then multiplying by 100. This concept was introduced to promote more sustainable and environmentally friendly chemical processes. A high atom economy indicates that a large proportion of the atoms from the reactants end up in the desired product, minimizing waste.

The main similarity between percentage yield and atom economy is that both aim to evaluate the efficiency of chemical reactions. However, they approach this goal from different perspectives. Percentage yield is concerned with the macroscopic quantity of the product obtained, while atom economy focuses on the atomic-level efficiency of the reaction.

One key difference is that percentage yield takes into account practical factors that may affect the reaction outcome, such as incomplete reactions, side reactions, or loss during purification. Atom economy, however, is a theoretical concept that doesn't consider these practical limitations. It assumes that all atoms from the reactants will be incorporated into the products.

Another distinction is that percentage yield can vary depending on the specific reaction conditions and the skill of the chemist performing the reaction. In contrast, atom economy is a fixed value for a given reaction, as it is based solely on the stoichiometry of the balanced equation.

Both concepts are important in chemical reactions for different reasons. Percentage yield is crucial for assessing the practical efficiency of a reaction and identifying areas for improvement in the process. It helps chemists optimize reaction conditions, improve purification techniques, and estimate the amount of starting materials needed for a desired quantity of product.

Atom economy, on the other hand, is essential for evaluating the sustainability and environmental impact of chemical processes. It encourages the development of reactions that minimize waste and make efficient use of resources. This concept is particularly important in green chemistry and the pharmaceutical industry, where reducing waste and improving efficiency can have significant economic and environmental benefits.

To illustrate the differences, consider two reactions that produce the same product but with different atom economies. Reaction A might have a high percentage yield of 90% but a low atom economy of 50%, indicating that while the reaction is efficient in terms of product formation, it generates a significant amount of waste. Reaction B could have a lower percentage yield of 70% but a higher atom economy of 80%, suggesting that although the reaction may not be as efficient in practice, it is more sustainable and generates less waste.

In conclusion, both percentage yield and atom economy are valuable tools for evaluating chemical reactions. While percentage yield provides insight into the practical efficiency of a reaction, atom economy offers a measure of its inherent sustainability. By considering both concepts, chemists can develop more efficient and environmentally friendly processes, balancing the need for high yields with the importance of minimizing waste and resource consumption.

Environmental and Economic Implications of Percentage Yield and Atom Economy

Environmental Impact

Percentage yield and atom economy are crucial concepts in chemistry that have significant environmental implications. These metrics provide valuable insights into the efficiency of chemical reactions and processes, directly impacting waste production and energy consumption. Percentage yield measures the actual amount of product obtained compared to the theoretical maximum, while atom economy calculates the efficiency of incorporating reactants into the final product.

A higher percentage yield indicates a more efficient reaction, resulting in less waste and reduced environmental impact. When reactions have low yields, more raw materials are required to produce the desired amount of product, leading to increased resource consumption and waste generation. This excess waste often requires additional treatment or disposal, further straining environmental resources and potentially contributing to pollution.

Atom economy focuses on the utilization of reactants in forming the desired product. Reactions with high atom economy incorporate a larger proportion of reactant atoms into the final product, minimizing the production of unwanted byproducts. This concept aligns closely with green chemistry principles, promoting more sustainable and environmentally friendly chemical processes. By maximizing atom economy, industries can significantly reduce waste streams and minimize the environmental footprint of their operations.

Energy efficiency is another critical aspect influenced by percentage yield and atom economy. Reactions with higher yields and better atom economy often require less energy input per unit of product. This reduction in energy consumption translates to lower greenhouse gas emissions and a decreased reliance on fossil fuels, contributing to overall environmental sustainability. Furthermore, improved efficiency can lead to smaller reactor sizes and reduced processing times, further minimizing the environmental impact of chemical manufacturing.

Economic Considerations

The economic implications of percentage yield and atom economy are equally significant. These concepts are fundamental to cost-effectiveness in chemical processes, directly impacting profitability and competitiveness in the industry. Higher percentage yields mean more product is obtained from a given amount of raw materials, reducing input costs and improving overall economic efficiency.

Reactions with low yields often require larger quantities of reactants to achieve the desired product output. This not only increases raw material costs but also necessitates larger reaction vessels, more extensive processing equipment, and higher energy inputs. All these factors contribute to increased production costs, potentially making processes economically unviable or less competitive in the market.

Atom economy plays a crucial role in resource utilization and waste management costs. Processes with high atom economy produce less waste, reducing the expenses associated with waste treatment and disposal. This aspect is particularly important in industries where byproducts may be hazardous or require specialized handling. By maximizing atom economy, companies can significantly reduce their waste management costs and potentially turn byproducts into valuable secondary streams, further enhancing economic benefits.

Energy efficiency, as influenced by these concepts, has substantial economic implications. More efficient processes require less energy input, leading to lower operational costs. In energy-intensive industries, even small improvements in efficiency can translate to significant cost savings over time. Additionally, as energy prices fluctuate and environmental regulations become more stringent, energy-efficient processes provide a competitive advantage and greater resilience to market changes.

The pursuit of higher percentage yields and better atom economy often drives innovation in chemical processes. This can lead to the development of new catalysts, reaction conditions, or process designs that not only improve efficiency but also open up new market opportunities. Such innovations can provide companies with a competitive edge, potentially leading to increased market share and profitability.

In conclusion, percentage yield and atom economy are not merely academic concepts but powerful tools for assessing and improving the environmental and economic performance of chemical processes. By focusing on these metrics, industries can simultaneously reduce their environmental impact, lower production costs, and enhance their competitive position in the global market. As sustainability becomes increasingly important, these concepts will continue to play a crucial role in shaping the future of chemical manufacturing and related industries.

Practical Applications and Examples

Percentage yield and atom economy are crucial concepts in chemistry that have significant real-world applications, particularly in industrial processes and chemical research. These principles are essential for optimizing reactions, improving efficiency, and reducing waste in various sectors.

In the pharmaceutical industry, percentage yield is a critical factor in drug manufacturing. For example, when synthesizing aspirin, chemists aim to maximize the yield to ensure cost-effectiveness. A typical industrial process might achieve a percentage yield of 80-85% for aspirin production. Researchers continuously work on improving reaction conditions, such as temperature, pressure, and catalyst selection, to increase this yield further.

Atom economy finds extensive use in green chemistry initiatives. The production of hydrogen peroxide is an excellent example of how atom economy principles are applied in industry. The traditional anthraquinone process has an atom economy of about 70%, while newer direct synthesis methods can achieve up to 100% atom economy. This improvement not only reduces waste but also lowers production costs and environmental impact.

In the polymer industry, both percentage yield and atom economy play crucial roles. For instance, in the production of polyethylene terephthalate (PET), used in plastic bottles, chemists strive to maximize yield while ensuring high atom economy. Industrial processes typically achieve yields of 90-95% with atom economies around 80-85%. Ongoing research focuses on developing catalysts and reaction conditions to push these figures even higher.

The petrochemical industry also heavily relies on these concepts. In the production of ethylene, a key building block for many chemicals, steam cracking processes are optimized for both yield and atom economy. Modern facilities can achieve ethylene yields of up to 35% from naphtha feedstock, with continuous efforts to improve efficiency and reduce byproduct formation.

In academic and industrial research settings, chemists use percentage yield and atom economy as key metrics for evaluating new synthetic routes. For example, in the development of new pharmaceuticals, researchers might compare different synthetic pathways not only based on the final yield but also on their atom economy. A reaction with a lower yield but higher atom economy might be preferred if it results in easier purification and less waste.

The fine chemicals industry, which produces specialty chemicals in smaller quantities, often faces challenges in achieving high yields due to complex synthetic routes. Here, chemists might use a combination of strategies to optimize reactions. For instance, in the synthesis of complex organic molecules, they might employ flow chemistry techniques to improve yield and atom economy simultaneously.

Biotechnology and enzyme-catalyzed reactions present another area where these concepts are crucial. Enzymatic processes often boast high atom economies, making them attractive for industrial applications. For example, the production of high-fructose corn syrup using glucose isomerase can achieve nearly 100% atom economy, showcasing the efficiency of biocatalytic processes.

In the field of materials science, the synthesis of nanomaterials often requires careful consideration of yield and atom economy. For instance, in the production of carbon nanotubes, researchers work on optimizing growth conditions to increase yield while minimizing the formation of amorphous carbon, thus improving atom economy.

Chemists use various tools and techniques to optimize reactions based on these principles. Advanced analytical methods, such as in-situ spectroscopy and real-time monitoring, allow for precise control and adjustment of reaction parameters. Computational chemistry and machine learning algorithms are increasingly employed to predict optimal conditions for maximum yield and atom economy.

In conclusion, percentage yield and atom economy are not just theoretical concepts but vital tools in modern chemistry. From large-scale industrial processes to cutting-edge research in laboratories, these principles guide chemists in developing more efficient, cost-effective, and environmentally friendly chemical processes. As the chemical industry continues to evolve, the application of these concepts will remain crucial in addressing global challenges and advancing sustainable chemistry practices.

Conclusion

In conclusion, understanding percentage yield and atom economy is crucial in chemistry. Percentage yield measures the efficiency of a chemical reaction by comparing actual to theoretical yield, while atom economy assesses reaction efficiency based on atom utilization. These concepts are vital for optimizing processes, reducing waste, and improving sustainability in chemical industries. By mastering these principles, students and professionals can make informed decisions about reaction pathways and resource allocation. The introduction video serves as an excellent foundation for grasping these fundamental ideas, providing clear explanations and practical examples. We encourage you to apply these concepts in your studies or work, as they are essential tools for analyzing and improving chemical reactions. Remember, a solid understanding of percentage yield and atom economy will enhance your ability to design more efficient and environmentally friendly chemical processes, contributing to advancements in various fields of chemistry and related industries.

Why do chemists do chemical reactions?

Practical problems in chemical reactions.

Step 1: Understanding the Basics of Chemical Reactions

To begin with, it's essential to understand what a chemical reaction is. A chemical reaction involves the transformation of reactants into products. For instance, if we consider a hypothetical reaction where one mole of A reacts with two moles of B to produce one mole of C and four moles of D, we can see that the reactants (A and B) are transformed into products (C and D). This transformation is indicated by an arrow pointing from the reactants to the products.

Step 2: The Cost of Reactants

Reactants, such as chemical A and chemical B, are not free. They cost money to purchase from suppliers or require time and resources to produce from starting reagents. This expenditure of resources is a crucial consideration for chemists. The cost of acquiring these reactants is a significant factor in why chemists perform chemical reactions.

Step 3: The Value of Products

The primary reason chemists conduct chemical reactions is the value of the products formed. The products of a chemical reaction must have some value to justify the expenditure on reactants. For example, in a chemical industry, if product D is valuable and can be sold at a high price, it makes the reaction worthwhile. Similarly, in a research setting, product D might be of significant interest for developing new medicines or other applications.

Step 4: Desirable and Side Products

In most chemical reactions, multiple products are formed. However, not all products are equally useful. The product of primary interest is referred to as the "desired product" or "useful product." For instance, if D is the product of interest, it is the desired product. On the other hand, other products like C might not be as useful or valuable and are considered "side products" or "waste products." These side products can be a burden as they may require additional resources to dispose of or manage.

Step 5: Importance of Atom Economy and Percentage Yield

Atom economy and percentage yield are critical measurements in evaluating the efficiency of a chemical reaction. Atom economy measures the proportion of reactants that become useful products, while percentage yield measures the actual amount of product obtained compared to the theoretical maximum. High atom economy and percentage yield indicate a more efficient and cost-effective reaction, with less waste and higher value products.

Step 6: Practical Problems in Chemical Reactions

Despite the best efforts, practical problems often arise in chemical reactions. These can include incomplete reactions, side reactions producing unwanted products, and difficulties in purifying the desired product. These issues can reduce the percentage yield and atom economy, making the reaction less efficient and more costly. Chemists must continually optimize reactions to minimize these problems and maximize the value of the products.

Step 7: Conclusion

In summary, chemists perform chemical reactions to produce valuable products. The efficiency of these reactions is measured by atom economy and percentage yield, which help determine the amount of waste and the value of the products. Practical problems can arise, but through careful optimization, chemists strive to make reactions as efficient and cost-effective as possible.

FAQs

Here are some frequently asked questions about percentage yield and atom economy:

  1. How do you calculate percentage yield?

    Percentage yield is calculated using the formula: (Actual Yield / Theoretical Yield) × 100%. For example, if you expect to produce 50g of a product (theoretical yield) but only obtain 40g (actual yield), the percentage yield would be (40g / 50g) × 100% = 80%.

  2. What does a 50% percent yield mean?

    A 50% percent yield means that the actual amount of product obtained from a reaction is half of the theoretical maximum amount. This could be due to factors such as incomplete reactions, side reactions, or loss during purification.

  3. How do you calculate atom economy?

    Atom economy is calculated using the formula: (Molecular mass of desired product / Total molecular mass of all reactants) × 100%. This measures the efficiency of a reaction in terms of incorporating reactant atoms into the desired product.

  4. What is a good atom economy percentage?

    Generally, an atom economy above 80% is considered good, while above 90% is excellent. Higher atom economy indicates more efficient use of reactants and less waste production. However, the specific context of the reaction should be considered when evaluating atom economy.

  5. Is a high percent yield always good?

    While a high percent yield is generally desirable, it's not always the only factor to consider. Other aspects such as product purity, cost-effectiveness, safety, and environmental impact should also be taken into account. Sometimes, a lower yield might be acceptable if it results in a purer product or uses more sustainable methods.

Prerequisite Topics

Understanding the fundamental concepts of chemistry is crucial when delving into more advanced topics like percentage yield and atom economy. Two essential prerequisite topics that lay the groundwork for this understanding are introduction to chemical reactions and balancing chemical equations.

The study of chemical reactions is fundamental to grasping the concepts of percentage yield and atom economy. When we explore chemical reactions, we learn about the transformation of substances, the rearrangement of atoms, and the formation of new compounds. This knowledge is essential because percentage yield and atom economy are directly related to the outcomes and efficiency of these reactions.

In particular, understanding stoichiometry in chemical reactions is crucial. Stoichiometry deals with the quantitative relationships between reactants and products in a chemical reaction. This concept forms the basis for calculating percentage yield, which compares the actual yield of a reaction to the theoretical yield predicted by stoichiometric calculations.

Moreover, the ability to write and interpret balanced chemical equations is indispensable when studying percentage yield and atom economy. Balanced equations provide the foundation for understanding the conservation of mass in chemical reactions, which is a key principle in calculating both percentage yield and atom economy.

When working with balanced chemical equations, students learn to account for all atoms on both sides of the equation. This skill is directly applicable to atom economy calculations, where we assess the efficiency of a reaction by determining the percentage of atoms from the reactants that end up in the desired product.

By mastering these prerequisite topics, students develop a solid foundation for understanding more complex concepts like percentage yield and atom economy. The ability to write and balance chemical equations allows for accurate predictions of reaction outcomes, while knowledge of stoichiometry enables precise calculations of theoretical yields.

Furthermore, these fundamental concepts help students appreciate the practical implications of percentage yield and atom economy in real-world applications. In industrial processes, for example, optimizing reaction conditions to improve yield and atom economy can lead to more efficient and cost-effective production methods.

In conclusion, a thorough understanding of chemical reactions and balanced equations provides the necessary context for exploring percentage yield and atom economy. These prerequisite topics not only facilitate the learning process but also enhance the overall comprehension of advanced chemical concepts, preparing students for more sophisticated studies in chemistry and its applications.

In this lesson, we will learn:
  • The meaning of atom economy, percentage yield and the difference between the terms.
  • How to calculate atom economy and percentage yield from example chemical reactions.
  • To explain the importance of atom economy as a chemist when planning and running chemical processes.

Notes:

  • In Moles, excess and limiting reagents, we learned that in chemical reactions, knowing your excess and limiting reagents is important practical information. When your limiting reagent runs out, any amounts in excess have nothing to react with, so you will stop making your products.

    • Percentage yield and atom economy are two other practical considerations when doing chemical reactions. They are both related to the amount of useful product generated in a reaction, compared to undesirable side products or unreacted starting material.

  • The atom economy of a reaction is the percentage of atomic mass of useful products in a reaction. It is calculated by:

    • Atom Economy Atom \, Economy \, (%) = Atomic mass of useful productsTotal atomic mass of produtcs ∗ \frac{Atomic \, mass \, of \, useful \, products } {Total \, atomic \, mass \, of \, produtcs } \, * \, 100

    A high atom economy means most of what the process makes is useful! In the same way, a low atom economy tells you that a reaction is mostly producing unwanted side products.
    The atom economy is used to show the efficiency of a reaction: does it make a lot of waste products that will require storage and disposal, or is most of the product valuable to us?
    • Reactions with a single product have a 100% atom economy because the only chemical being produced is the desired product.
    • Atom economy is used as an application of the conservation of mass: no atoms are created or destroyed in chemical reactions, they are only re-arranged by breaking and forming substances. We are using the amount of atomic mass as a measure of the reaction efficiency.

  • The percentage yield of a reaction is the mass of products formed as a percentage of how much could have been formed given the mass of reactants used. The equation to calculate percentage yield is:

    • Percentage yield = actual yieldtheoretical yield ∗ Percentage \, yield \, = \, \frac{actual \, yield } {theoretical \, yield} \, * \, 100

    Where:
    • Actual yield is the yield of product obtained in the experiment (in g or moles).
    • Theoretical yield is the yield of product based on the limiting reagent, i.e. the calculations done in Moles, excess and limiting reagents.

    A low percentage yield means that not much of the reactants you used has become products. A high percentage yield therefore means that a lot of the reactant chemicals you used successfully reacted to make the products.

  • Worked example: Calculate the atom economy of a reaction.
    The reaction below shows the production of iron metal by reacting iron oxide (Fe2O3) with carbon.

    • 2Fe2O3 (s) + 3C (s)   \, →  \, 4Fe (s)+ 3CO2 (g)

    This reaction is intended to produce iron metal with CO2 as an unwanted side product. What is the atom economy of this reaction?

    To begin finding atom economy, we need to know what is desirable in the products. We already know that Fe is the desired product and CO2 is undesirable side product.
    Now we need to find the atomic mass of both of these – how much of the product, in terms of atomic mass, is valuable?

    % Atom economy = \, Atom \, economy \, = \, 4 ∗ (55.8 g mol−1 Fe)(4 ∗ (55.8 g mol−1 Fe)) + (3 ∗ (44 g mol CO2)) ∗ \large \frac{4 \, * \, (55.8 \, g \, mol^{-1}\, Fe )} { (4 \, * \, (55.8 \, g \, mol^{-1} \, Fe ) ) \, + \, (3 \, * \, (44 \, g \, mol \, CO_{2})) } \, * \, 100 = 62.8 %

  • Worked example: Calculate the percentage yield of a reaction.
    The reaction below shows the production of iron metal by reacting iron oxide with carbon:

    • 2Fe2O3 (s) + 3C (s)   \, →  \, 4Fe (s) + 3CO2 (g)

    In one run of this reaction, the limiting reagent is Fe2O3. 750g of Fe2O3 was reacted in this run, and an experimental yield of 460 g of Fe metal was obtained.

    What is the theoretical and percentage yield of this run of the reaction?

    To begin, we need to find the theoretical yield. If we only have 750g of Fe2O3 and we are told this is the limiting reagent then we know this is going to run out and this amount dictates how much Fe can possibly be made.

    You can use conversion factors to find the theoretical yield of Fe metal product from the amount of Fe2O3 reactant.

    750g Fe2O3 ∗ g \, Fe_{2}O_{3} \, * \, 1 mol Fe2O3159.6g Fe2O3 ∗ 4 mol Fe2 mol Fe2O3 ∗ 55.8 g Fe1 mol Fe \large \frac{1 \, mol \, Fe_{2}O_{3} } {159.6g \, Fe_{2}O_{3} } \, * \, \frac{4\, mol \, Fe } {2 \, mol \, Fe_{2}O_{3} } \, * \, \frac{55.8 \, g \, Fe } {1 \, mol \, Fe } \, = 524.4  g Fe\, g \, Fe


    This 524.4g Fe tells us the theoretical yield of the reaction. It is the maximum possible amount of product we can get in this reaction, because we only have 750g of the Fe2O3 limiting reagent. In terms of percentage yield, this is your 100% mark.

    Now, we have the 100% mark, and we have an experimental yield of 460g of Fe. This is our actual “score”. Let’s convert 460/524.4 into a percentage.

    Percentage yield = Percentage \, yield \, = \, 460 g Fe524.4 g Fe ∗ \large \frac{460 \, g \, Fe } {524.4 \, g \, Fe} \, * \, 100 = 87.7%

    This is the percentage yield of the reaction.

  • Know the difference between yield and atom economy!
    • Atom economy is about how wasteful the reaction is. If your reaction has low atom economy, it will always be wasteful; most of the product made is simply not valuable to you. This is a chemical problem, not a practical one.
      The unwanted products are a waste of money/resources and an environmental problem because waste has to be stored or disposed of safely.
    • Yield is about how much product was successfully made. If your yield is low, this is probably a practical problem, such as not enough time to react or your conditions may need to be changed.