Question

When barium metal is heated in chlorine gas, a binary compound forms that consists of \(65.95 \%\) Ba and \(34.05 \%\) Cl by mass. Calculate the empirical formula of the compound.

Short answer

In order to find the empirical formula of the binary compound formed by heating barium metal in chlorine gas, we first assume 100 grams of the compound, which gives us 65.95 grams of Ba and 34.05 grams of Cl. We then convert these masses into moles, resulting in 0.480 moles of Ba and 0.960 moles of Cl. Finally, we find the simplest whole number ratio by dividing each value by the smallest number of moles, which gives us a ratio of 1:2. Therefore, the empirical formula of the compound is BaCl2.

Step-by-step solution

Convert mass percentage to grams

Given the percentages of Ba and Cl by mass, let's assume we have 100 grams of the compound. So, we have 65.95 grams of Ba and 34.05 grams of Cl in the compound.

Calculate moles of each element

We will now calculate the moles of both Barium (Ba) and Chlorine (Cl), using their molar masses. The molar mass of Ba is 137.3 g/mol and that of Cl is 35.45 g/mol. Moles of Barium = \(\frac{Mass_{Ba}}{Molar\_Mass_{Ba}} = \frac{65.95 g}{137.3 \, g/mol} = 0.480\, mol\) Moles of Chlorine = \(\frac{Mass_{Cl}}{Molar\_Mass_{Cl}} = \frac{34.05\, g}{35.45 \, g/mol} = 0.960\, mol\)

Find the simplest whole number ratio

To find the simplest whole number ratio of Ba and Cl in the compound, we will divide each value by the smallest number of moles. Ratio of Ba: \(\frac{0.480}{0.480} = 1\) Ratio of Cl: \(\frac{0.960}{0.480} = 2\) Therefore, there is one mole of Ba for every two moles of Cl in the compound.

Write the empirical formula

With the whole number ratio found in Step 3, the empirical formula of the compound can be written as BaCl2.