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Chapter 3: Problem 39

The element \(X\) forms the chloride \(X C l_{4}\) containing \(75.0 \% \mathrm{Cl},\) by mass. What is element \(\mathrm{X} ?\)

Short Answer

Expert verified
The unknown element X is Titanium (Ti).

Step by step solution

01

Calculate mass of chlorine

The mass percent of chlorine is given as 75.0%. This means that in a 100 g sample of the compound, 75 g will be chlorine and the remainder will be element X. So, calculate the mass of the unknown element X: \(mass_X = total mass - mass_{Cl} = 100 g - 75 g = 25 g\).
02

Translate mass to mole

In the next step, convert the mass of both element X and chlorine to moles using their respective molar masses. The molar mass of chlorine (Cl) is 35.45 g/mol: \(\text{Moles}_{\text{Cl}} = \frac{\text{mass}_{\text{Cl}}}{\text{molar mass}_{\text{Cl}}} = \frac{75 g}{35.45 g/mol} = 2.12 mol\). Since the formula of the compound is XCl4, meaning for every 1 mole of X there are 4 moles of Cl. Therefore, the mole of X is: \(\text{Moles}_{\text{X}} = \frac{\text{moles}_{\text{Cl}}}{4} = \frac{2.12 mol}{4} = 0.53 mol\).
03

Identify the unknown element

Finally, calculate the molar mass of X, and the element X can be identified by it: \(\text{Molar mass}_{\text{X}} = \frac{\text{mass}_{\text{X}}}{\text{moles}_{\text{X}}} = \frac{25 g}{0.53 mol} = 47.17 g/mol\). The molar mass closest to 47.17 g/mol in the periodic table of elements is Titanium (Ti) with a molar mass of 47.88 g/mol.

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