Question

Gaseous chlorine, Cl2, was combined with 0.532g of Titanium, and 2.108 g of TixCly were collected. What is the empirical formula of titanium chloride?

Answer 1

TiCl₄

Step-by-step explanation:

From the law of conservation of mass, the mass of the reactants must equal the mass of the products. In other words:

`\displaystyle \text{m Cl$_2$} + \text{ m Ti} = \text{ m Ti$_x$Cl$_y$}`

Find the mass of chlorine gas reacted:

`\displaystyle \begin{aligned} \text{ m Cl$_2$} + (0.532 \text{ g}) & = (2.108 \text{ g)} \\ \\ \text{m Cl$_2$} & = 1.576 \text{ g} \end{aligned}`

Find the number of moles of each reactant using their respective molecular weights:

`\displaystyle 1.576 \text{ g Cl$_2$} \cdot \frac{1 \text{ mol Cl$_2$}}{70.90\text{ g Cl$_2$}} \cdot \frac{2\text{ mol Cl}}{1\text{ mol Cl$_2$}} = 0.04446\text{ mol Cl}`

And:

`\displaystyle 0.532\text{ Ti} \cdot \frac{1\text{ mol Ti}}{47.87\text{ g Ti}} = 0.0111\text{ mol Ti}`

To find the empirical formula, all values by the smallest value:

`\displaystyle \begin{aligned} \frac{0.0111\text{ mol Ti}}{0.0111} & = \frac{0.04446\text{ mol Cl}}{0.0111} \\ \\ 1\text{ mol Ti} & \approx 4\text{ mol Cl}\end{aligned}`

Hence, there are four moles of chlorine for every one mole of titanium.

In conclusion, our empirical formula is TiCl₄.