R2.1.5 Atom economy Notes

Atom Economy: A Measure of Reaction Efficiency

What is Atom Economy?

1. The formula for atom economy is: $$
   \text{Atom Economy} = \frac{\text{Molar Mass of Desired Product}}{\text{Sum of Molar Masses of All Products}} \times 100
   $$
2. This calculation considers the stoichiometry of the reaction and the masses of all products, not just the reactants.
3. Unlike percentage yield, which measures how much of the desired product is obtained experimentally, atom economy is a theoretical measure based on the balanced chemical equation.

Calculating Atom Economy: A Step-by-Step Process

Let’s break down how to calculate atom economy using an example.

The Synthesis of Ethanol

Consider the hydration of ethene to produce ethanol:

$$
\text{C}_2\text{H}_4(g) + \text{H}_2\text{O}(g) \rightarrow \text{C}_2\text{H}_5\text{OH}(l)
$$

1. Identify the desired product:
   1. In this reaction, ethanol ($\text{C}_2\text{H}_5\text{OH}$) is the desired product.
2. Calculate the molar mass of the desired product:
   1. Molar mass of $\text{C}_2\text{H}_5\text{OH}$ = $2(12.01) + 6(1.01) + 16.00 = 46.08 \, \text{g mol}^{-1}$.
3. Sum the molar masses of all products:
   1. Since ethanol is the only product, the sum of molar masses of all products = $46.08 \, \text{g mol}^{-1}$.
4. Apply the formula: $$
   \text{Atom Economy} = \frac{\text{46.08}}{\text{46.08}} \times 100 = 100\%
   $$

Atom Economy and Green Chemistry

Why Does Atom Economy Matter?

1. In the context of green chemistry, atom economy is a critical metric for designing sustainable chemical processes.
2. High atom economy reduces waste, minimizes the need for disposal, and conserves resources.
3. This makes it an essential consideration for industries aiming to reduce their environmental footprint.

Trade-Offs in Reaction Design

While high atom economy is desirable, other factors must also be considered:

1. Energy Requirements: A reaction with high atom economy might require high temperatures or pressures, increasing energy consumption.
2. Reaction Feasibility: Some reactions with low atom economy are easier to carry out or have higher yields, making them more practical.
3. Toxicity and Safety: The choice of reactants and solvents can affect the environmental and health impacts of the process.

Comparing Reactions: Atom Economy in Practice

Let’s compare two reactions for producing hydrogen gas:

Reaction 1: Methane Steam Reforming $$
\text{CH}_4(g) + 2\text{H}_2\text{O}(g) \rightarrow \text{CO}_2(g) + 4\text{H}_2(g)
$$

1. Desired product: $\text{H}_2$
2. Molar mass of desired product: $4 \times 2.02 = 8.08 \, \text{g mol}^{-1}$
3. Total molar mass of products: $44.01 + 8.08 = 52.09 \, \text{g mol}^{-1}$
4. Atom economy:
   $$
   \text{Atom Economy} = \frac{8.08}{52.09} \times 100 \approx 15.5\%
   $$

Reaction 2: Electrolysis of Water$$
2\text{H}_2\text{O}(l) \rightarrow 2\text{H}_2(g) + \text{O}_2(g)
$$

1. Desired product: $\text{H}_2$
2. Molar mass of desired product: $2 \times 2.02 = 4.04 \, \text{g mol}^{-1}$
3. Total molar mass of products: $4.04 + 32.00 = 36.04 \, \text{g mol}^{-1}$
4. Atom economy:
   $$
   \text{Atom Economy} = \frac{4.04}{36.04} \times 100 \approx 11.2\%
   $$

Challenges and Limitations

While atom economy is a valuable tool, it has limitations:

1. Does Not Consider Energy Use: A reaction with high atom economy may still be energy-intensive.
2. Ignores Toxicity: Atom economy does not account for the environmental or health hazards of reactants and by-products.
3. Assumes 100% Yield: In practice, reactions rarely achieve complete conversion of reactants to products.