Answer to Question #275157 in General Chemistry for maxxxx

Question

Titanium is a strong, lightweight, corrosion-resistant metal that is used in the construction of rockets, aircrafts, and jet engines. It is prepared by the reduction of titanium (IV) chloride with molten magnesium between 950 oC and 1150 oC:

TiCl4(g) + 2Mg(l) → Ti(s) + 2MgCl2(l)

In a certain operation 3.54 x 104 kg of TiCl4 is reacted with 1.13 x 104 kg of Mg.

Answer 1

NB: Kindly note some information is missing in the question. Adjusting the conditions of the question.

If $3.54×10^4kg$ of $TiCl_4$ are reacted with $1.13×10^4kg$ of Mg.

Yielding $7.91×10^3kg$ of Titanium.

Part A (Theoretical yield of Ti)

Molar mass of TiCl$_4=189.679g/mol$

Molar mass of Ti $=47.867$

Molar mass of Mg $=24.305$

Moles of TiCl$_4$ reacted

$=\frac{3.54×10^{4}×10^{3}}{189.679}$ $=1.866×10^5$

Moles of Mg

$=\frac{1.13×10^4×10^3}{24.305}=4.649×10^5$

Which is greater than twice moles of TiCl$_4$

$\implies$ Mg is in excess

Reacting mole ratio TiCl$_4:$ Ti $=1:1$

Mass of Ti expected $=1.866×10^5×47.867$

$=8.933×10^6g$

Part B

$\%$ yield $=\frac{7.91×10^3×10^3}{8.933×10^6}=88.55\%$