Question

Which from following formulae is a correct formula to determine percent atom economy?

• A. $\% \text{ Atom economy} = \text{Formula weight of product} \times 100$
• B. $\% \text{ Atom economy} = \text{Sum of formula weight of all reactants} \times 100$
• C. $\% \text{ Atom economy} = \frac{\text{Formula weight of desired product}}{\text{Sum of formula weight of all reactants}} \times 100$
• D. $\% \text{ Atom economy} = \frac{\text{Sum of formula weight of all reactants}}{\text{Formula weight of desired product}} \times 100$

Hint:

Think of atom economy just like a typical exam score percentage: (What you want) (Total available) $\times$ 100. The "Desired Product" goes on top as the numerator, and the "Sum of All Reactants" serves as the denominator.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question requires us to identify the mathematically correct formula used to calculate the percent atom economy of a chemical process under green chemistry principles.

Step 2: Key Formula or Approach:
Atom economy is a metric used in green chemistry to measure the efficiency of a chemical reaction by calculating what percentage of the total mass of starting materials ends up in the final useful product. It is defined as: $$\% \text{ Atom Economy} = \frac{\text{Mass of Desired Product}}{\text{Total Mass of All Reactants}} \times 100$$

Step 3: Detailed Explanation:
Let's analyze the concepts behind the choices: A chemical reaction can generate both a desired target product and unwanted structural byproducts. To maximize sustainability, a reaction should incorporate as many reactant atoms as possible into the target structure. Therefore, the efficiency is evaluated by dividing the formula weight (or molecular mass) of the single desired product by the combined sum of the formula weights of all reactants scaled into a standard percentage format ($\times 100$). This aligns exactly with the relationship shown in option (C).

Step 4: Final Answer:
The correct mathematical formula is represented by option (C).