B Calculate The Percent Atom Economy for The Following Reactions

What is atom economy?

Atom economy is a measure of the efficiency of a chemical process, specifically how well the atoms in the reactants are directed into the desired product. It's calculated as the percentage of the total mass of the reactants that ends up in the product, with the remainder being lost as waste.

High atom economy indicates a more efficient reaction, where fewer atoms are wasted. This is particularly important in industrial chemistry where minimizing waste and maximizing product yield are critical for sustainability and cost-effectiveness.

How to calculate atom economy

Calculating atom economy involves determining the molecular weights of the reactants and products, then comparing the mass of the desired product to the total mass of all reactants. Here's the step-by-step process:

1. Identify the balanced chemical equation for the reaction
2. Calculate the molar mass of each reactant and product
3. Determine the mass of the desired product formed
4. Calculate the total mass of all reactants used
5. Apply the atom economy formula

Formula

The formula shows that atom economy is simply the ratio of the mass of the desired product to the total mass of all reactants, expressed as a percentage. This provides a straightforward measure of how efficiently atoms are being utilized in the reaction.

Example calculation

Let's consider the following reaction:

2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O

We want to calculate the atom economy for the production of CO₂.

1. Calculate molar masses:
   • C₂H₆: 2×12 + 6×1 = 30 g/mol
   • O₂: 2×16 = 32 g/mol
   • CO₂: 12 + 2×16 = 44 g/mol
   • H₂O: 2×1 + 16 = 18 g/mol
2. Assume we use 60 g of C₂H₆ (2 moles) and 224 g of O₂ (7 moles)
3. Total mass of reactants = 60 + 224 = 284 g
4. Mass of CO₂ produced = 4 × 44 = 176 g
5. Atom economy = (176 / 284) × 100 = 62.01%

In this example, the atom economy is 62.01%, indicating that 62.01% of the reactant mass ends up in the desired CO₂ product.

Interpreting results

Interpreting atom economy results requires understanding what the percentage represents and how it relates to the reaction's efficiency. Here are some key points to consider:

• Higher percentages indicate more efficient reactions with less waste
• Typical values range from 20% to 90%, with 50-70% being considered good
• Low atom economy may indicate the need for reaction optimization
• Consider the context - some reactions inherently have lower atom economies

While atom economy provides valuable insights, it should be considered alongside other metrics like yield and selectivity when evaluating reaction performance.