TiCl₄ + 2Mg → 2MgCl₂ + Ti The atom economy for the production of titanium in the above equation is equal to: A) $\frac{47}{9} \times 100$ B) $\frac{47}{189 + 2 \times 243} \times 100$ C) $\frac{95.3 + 47}{189 + 243} \times 100$ D) $\frac{(2 \times 47)}{189 + 243} \times 100$ - Scottish Highers Chemistry - Question 14 - 2017

To calculate the atom economy, we first need to identify the relevant components from the balanced equation:

1. Calculate the molar mass of products and reactants:

   • Molar mass of titanium (Ti): 47 g/mol
   • Molar mass of TiCl₄: 189 g/mol
   • Molar mass of 2Mg: 48 g (2 x 24 g/mol)
   • Molar mass of 2MgCl₂: 2 x 243 g/mol = 486 g/mol

2. Calculate the total mass of the reactants:

   $ext{Total mass of reactants} = 189 + 48 = 237 ext{ g}$

3. Calculate the total mass of the desired product (Ti):

   $ext{Total mass of product (Ti)} = 47 ext{ g}$

4. Use the formula for atom economy:

   $ext{Atom economy} = \left( \frac{\text{mass of desired product}}{\text{total mass of reactants}} \right) \times 100$

   $\text{Atom economy} = \left( \frac{47}{189 + 243} \right) \times 100$

   Thus, the correct answer is B: $\frac{47}{189 + 2 \times 243} \times 100$.