Calculate The Atom Economy of The Following Reaction

The atom economy of a chemical reaction measures the efficiency of the reaction by calculating the percentage of atoms in the desired product relative to the total atoms in all reactants. This metric helps chemists evaluate and optimize reaction processes.

What is atom economy?

Atom economy is a concept in chemistry that quantifies the efficiency of a chemical reaction. It represents the percentage of the total mass of the reactants that ends up in the desired product. A higher atom economy indicates a more efficient reaction with less waste.

The concept was introduced by Sir Robert Robinson in 1951 as a way to evaluate the sustainability and economic viability of chemical processes. It's particularly important in industrial chemistry where minimizing waste and maximizing product yield are critical.

Atom economy is different from atom utilization, which measures the percentage of atoms in the desired product relative to the atoms in the limiting reactant.

How to calculate atom economy

The atom economy is calculated using the following formula:

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

To calculate atom economy:

Determine the molecular weights of all reactants and the desired product
Calculate the total mass of all reactants
Calculate the mass of the desired product
Divide the mass of the desired product by the total mass of reactants
Multiply by 100 to get the percentage

For reactions involving multiple steps, you can calculate the atom economy for each step and then determine the overall atom economy of the entire process.

Example calculation

Let's calculate the atom economy for the following reaction:

C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O

1. Calculate molecular weights:

Glucose (C₆H₁₂O₆): 180.16 g/mol
Oxygen (O₂): 32.00 g/mol
Carbon dioxide (CO₂): 44.01 g/mol
Water (H₂O): 18.02 g/mol

2. Total mass of reactants (1 mole of glucose + 6 moles of oxygen):

(1 × 180.16) + (6 × 32.00) = 180.16 + 192.00 = 372.16 g

3. Mass of desired products (6 moles of CO₂ + 6 moles of H₂O):

(6 × 44.01) + (6 × 18.02) = 264.06 + 108.12 = 372.18 g

4. Atom economy calculation:

(372.18 / 372.16) × 100% ≈ 100%

This reaction has a perfect atom economy of 100%, meaning all atoms from the reactants end up in the desired products with no waste.

Interpretation of results

Interpreting atom economy results requires understanding several factors:

100% atom economy: Indicates a perfect reaction where all atoms from reactants end up in the desired products. This is rare in practice.
High atom economy (70-90%): Generally considered good, indicating efficient use of reactants.
Moderate atom economy (40-60%): May indicate some waste or byproducts, but still acceptable for many applications.
Low atom economy (<40%): Suggests significant waste or inefficient use of reactants, which may require process optimization.

Atom economy should be considered alongside other factors like reaction yield, cost of reactants, and environmental impact when evaluating a chemical process.

Remember that atom economy is a theoretical maximum - actual yields in industrial processes are often lower due to practical limitations.

FAQ

What is the difference between atom economy and atom utilization?

Atom economy measures the percentage of atoms in the desired product relative to the total atoms in all reactants, while atom utilization measures the percentage of atoms in the desired product relative to the atoms in the limiting reactant. Atom economy provides a more comprehensive view of reaction efficiency.

How can I improve the atom economy of a reaction?

To improve atom economy, consider: using more efficient catalysts, optimizing reaction conditions, designing reactions to minimize byproducts, and selecting reactants that produce less waste. Sometimes, changing the target product can also improve atom economy.

Is atom economy always a good thing to maximize?

While higher atom economy is generally desirable, it's not always the only factor to consider. Other important factors include reaction yield, cost of reactants, safety considerations, and environmental impact. A balance between these factors is often needed in industrial applications.

Can atom economy be calculated for multi-step reactions?

Yes, atom economy can be calculated for each step of a multi-step reaction. The overall atom economy of the entire process can then be determined by considering the atom economy of each step and the yields between steps.