Sure, let's solve this problem step-by-step:
1. Identify the given quantity and molar masses:
- We are given 761.8 grams of [tex]\( \text{TiCl}_4 \)[/tex].
- The molar mass of [tex]\( \text{TiCl}_4 \)[/tex] is 189.68 g/mol.
- The molar mass of [tex]\( \text{MgCl}_2 \)[/tex] is 95.21 g/mol.
2. Calculate the moles of [tex]\( \text{TiCl}_4 \)[/tex]:
To find the moles of [tex]\( \text{TiCl}_4 \)[/tex], we'll divide the given mass by its molar mass:
[tex]\[
\text{Moles of } \text{TiCl}_4 = \frac{\text{mass of TiCl}_4}{\text{molar mass of TiCl}_4} = \frac{761.8 \text{ g}}{189.68 \text{ g/mol}} \approx 4.01624 \text{ moles}
\][/tex]
3. Determine the moles of [tex]\( \text{MgCl}_2 \)[/tex] produced:
According to the balanced chemical equation, 1 mole of [tex]\( \text{TiCl}_4 \)[/tex] produces 2 moles of [tex]\( \text{MgCl}_2 \)[/tex].
Therefore, the moles of [tex]\( \text{MgCl}_2 \)[/tex] produced can be calculated as:
[tex]\[
\text{Moles of } \text{MgCl}_2 = 2 \times \text{Moles of } \text{TiCl}_4 = 2 \times 4.01624 \approx 8.03248 \text{ moles}
\][/tex]
4. Calculate the mass of [tex]\( \text{MgCl}_2 \)[/tex] produced:
To find the mass of [tex]\( \text{MgCl}_2 \)[/tex], we multiply the moles of [tex]\( \text{MgCl}_2 \)[/tex] by its molar mass:
[tex]\[
\text{Mass of } \text{MgCl}_2 = \text{moles of } \text{MgCl}_2 \times \text{molar mass of } \text{MgCl}_2 = 8.03248 \text{ moles} \times 95.21 \text{ g/mol} \approx 764.772 \text{ g}
\][/tex]
5. Convert the mass of [tex]\( \text{MgCl}_2 \)[/tex] to kilograms:
Since 1 kilogram equals 1000 grams, we convert the mass of [tex]\( \text{MgCl}_2 \)[/tex] produced to kilograms by dividing by 1000:
[tex]\[
\text{Mass of } \text{MgCl}_2 \text{ in kilograms} = \frac{764.772 \text{ g}}{1000} \approx 0.764772 \text{ kg}
\][/tex]
So, from 761.8 grams of [tex]\( \text{TiCl}_4 \)[/tex], approximately 0.764772 kilograms of [tex]\( \text{MgCl}_2 \)[/tex] would be produced.
