Questions: How many kilograms of TiO2 can be prepared from 5.80 kg of TiCl4?

Solution Steps

The chemical reaction for the preparation of $\mathrm{TiO}_2$ from $\mathrm{TiCl}_4$ is: \[ \mathrm{TiCl}_4 + 2 \mathrm{H_2O} \rightarrow \mathrm{TiO}_2 + 4 \mathrm{HCl} \]

Calculate the molar masses of $\mathrm{TiCl}_4$ and $\mathrm{TiO}_2$:

• Molar mass of $\mathrm{TiCl}_4$: \[ \mathrm{TiCl}_4 = 47.867 + 4 \times 35.453 = 189.678 \, \mathrm{g/mol} \]
• Molar mass of $\mathrm{TiO}_2$: \[ \mathrm{TiO}_2 = 47.867 + 2 \times 15.999 = 79.865 \, \mathrm{g/mol} \]

Convert the given mass of $\mathrm{TiCl}_4$ to moles: \[ \text{Moles of } \mathrm{TiCl}_4 = \frac{5.80 \, \mathrm{kg}}{189.678 \, \mathrm{g/mol}} = \frac{5800 \, \mathrm{g}}{189.678 \, \mathrm{g/mol}} = 30.58 \, \text{moles} \]

From the balanced equation, 1 mole of $\mathrm{TiCl}_4$ produces 1 mole of $\mathrm{TiO}_2$. Therefore, the moles of $\mathrm{TiO}_2$ produced are: \[ \text{Moles of } \mathrm{TiO}_2 = 30.58 \, \text{moles} \]

Convert the moles of $\mathrm{TiO}_2$ to mass: \[ \text{Mass of } \mathrm{TiO}_2 = 30.58 \, \text{moles} \times 79.865 \, \mathrm{g/mol} = 2442 \, \mathrm{g} = 2.442 \, \mathrm{kg} \]

Final Answer