Answer : The mass of [tex]TiO_2[/tex] prepared can be 176.48 grams.
Explanation :
First we have to calculate the mass of [tex]FeTiO_3[/tex].
As we are given that the 88.3 % [tex]FeTiO_3[/tex] by mass. That means, 88.3 grams of [tex]FeTiO_3[/tex] present in 100 grams of solution.
[tex]\text{Mass of }FeTiO_3=\frac{88.3}{100}\times 379=334.657g[/tex]
Now we have to calculate the moles of [tex]FeTiO_3[/tex].
Molar mass of [tex]FeTiO_3[/tex] = 151.7 g/mole
[tex]\text{Moles of }FeTiO_3=\frac{\text{Mass of }FeTiO_3}{\text{Molar mass of }FeTiO_3}=\frac{334.657g}{151.7g/mole}=2.206moles[/tex]
Now we have to calculate the moles of [tex]TiO_2[/tex].
The balanced chemical reaction is,
[tex]2FeTiO_3+4HCl+Cl+2\rightarrow 2FeCl_3+2TiO_2+2H_2O[/tex]
From the balanced reaction, we conclude that
As, 2 moles of [tex]FeTiO_3[/tex] react to give 2 moles of [tex]TiO_2[/tex]
So, 2.206 moles of [tex]FeTiO_3[/tex] react to give 2.206 moles of [tex]TiO_2[/tex]
Now we have to calculate the mass of [tex]TiO_2[/tex].
[tex]\text{Mass of }TiO_2=\text{Moles of }TiO_2\times \text{Molar mass of }TiO_2[/tex]
Molar mass of [tex]TiO_2[/tex] = 80 g/mole
[tex]\text{Mass of }TiO_2=(2.206mole)\times (80g/mole)=176.48g[/tex]
Therefore, the mass of [tex]TiO_2[/tex] prepared can be 176.48 grams.
