Worked example 1 - Calculating atom economy for the production of methanol

Calculate the atom economy for the production of methanol (CH₃OH) from chloromethane (CH₃Cl) and potassium hydroxide (KOH). The balanced equation is:

CH₃Cl + KOH ➔ CH₃OH + KCl

Step 1: Calculate M_r_ of desired product

M_r_ of CH₃OH = 12.0 + 4(1.0) + 16.0 = 32.0

Step 2: Calculate ΣM_r_ of all reactants

M_r_ of CH_3_Cl = 12.0 + 3(1.0) + 35.5 = 50.5

M_r_ of KOH = 39.1 + 16.0 + 1.0 = 56.1

ΣM_r = 50.5 + 56.0 = 106.6

Step 3: Equation

$ \%\text{ atom economy}=\frac{\text{M}_\text{r}\text{ of desired product}}{\Sigma\text{M}_\text{r}\text{ of all reactants}}\times100 $

Step 4: Substitution and correct evaluation

$ \%\text{ atom economy}=\frac{32.0}{106.6}\times100=30.0\% $

This calculation shows that only 30.0% of the reactant atoms are incorporated into the desired product, indicating a low atom economy for this substitution reaction.

Worked example 2 - Calculating atom economy for the fermentation of glucose

Calculate the atom economy for the production of ethanol (C₂H₅OH) from the fermentation of glucose (C₆H₁₂O₆). The balanced chemical equation is:

C₆H₁₂O₆ ➔ 2C₂H₅OH + 2CO₂

Step 1: Calculate M_r of desired product

M_r_ of C₂H₅OH = 2(12.0) + 6(1.0) + 16.0 = 46.0

Step 2: Multiply by reaction stoichiometry

Since the equation produces 2 moles of C₂H₅OH the total M_r_ for C₂H₅OH = 2 × 46.0 = 92.0

Step 2: Calculate ΣM_r of all reactants

M_r_ of C₆H₁₂O₆ = 6(12.0) + 12(1.0) + 6(16.0) = 180.0

Step 4: Equation

$ \%\text{ atom economy}=\frac{\text{M}_\text{r}\text{ of desired product}}{\Sigma\text{M}_\text{r}\text{ of all reactants}}\times100 $

Step 5: Substitution and correct evaluation

$ \%\text{ atom economy}=\frac{92.0}{180.0}\times100=51.1\% $

This calculation shows that 51.1% of the reactant atoms are incorporated into the desired product, indicating a moderate atom economy for this reaction.

Atom economy in different reaction types

Addition reactions

In an addition reaction, two reactants combine to form a single product. For example, ethene and hydrogen undergo an addition reaction:

C₂H₄ + H₂ ➔ C₂H₆

Since all reactant atoms end up in the desired product ethane, addition reactions always have 100% atom economy.

Substitution reactions

In a substitution reaction, some atoms are substituted between reactants, generating at least two products - the desired product and an unavoidable by-product. For example, chloromethane reacts with potassium hydroxide in a substitution reaction:

CH₃Cl + KOH ➔ CH₃OH + KCl

Here the desired product is methanol, but potassium chloride is also produced as waste. The atom economy will be less than 100%.

Green chemistry takes a holistic approach

Green chemistry considers the environmental impact of the entire manufacturing process, not just the yield and cost of the desired product.

It encourages scientists to:

• Minimise the use and generation of hazardous chemicals.
• Design sustainable industrial reactions and processes.
• Reduce waste, pollution and energy consumption.

Some common green chemistry practices include:

1. Using water or solvent-free reactions.
2. Choosing renewable starting materials.
3. Employing mild reaction conditions.
4. Using efficient catalysts.
5. Finding uses for any by-products formed.

By taking this holistic view, green chemistry aims to make the chemical industry safer and more environmentally friendly.

Atom economy measures reaction efficiency

Atom economy is a key concept in green chemistry that quantifies how efficiently the atoms from the starting materials are incorporated into the desired product.

It is calculated using the following equation:

$\%\text{ atom economy}=\frac{\text{M}_\text{r}\text{ of desired product}}{\Sigma\text{M}_\text{r}\text{ of all reactants}}\times100$

Some key points about atom economy:

• It is based on the balanced chemical equation, so make sure to use the correct mole ratios.
• Atom economy gives no indication of the percentage yield or losses during processing.

Interpreting atom economy:

• An ideal reaction would have 100% atom economy, meaning all the atoms end up in the target product.
• Reactions that produce unwanted by-products always have <100% atom economy.

Therefore, atom economy is inversely related to the amount of waste generated. Higher atom economy means a more efficient and sustainable process.