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

The empirical formula of the compound formed when barium metal is heated in chlorine gas is BaCl2.

Step-by-step solution

List the Given Information

We are given the following mass percentages for the compound: - Barium (Ba): \(65.95 \% \) - Chlorine (Cl): \(34.05 \% \) We will now assume we have 100 grams of the compound, which allows us to use the percentages as grams.

Convert Mass Percentages to Moles

To calculate the empirical formula, we need to convert the mass percentages into moles. We will use the molar mass of each element to do so. Molar Masses: - Barium (Ba): 137.33 g/mol - Chlorine (Cl): 35.45 g/mol Calculate the number of moles for each element: - Barium (Ba): \(\frac{65.95\,\text{g}}{137.33\,\text{g/mol}} = 0.480\,\text{mol}\) - Chlorine (Cl): \(\frac{34.05\,\text{g}}{35.45\,\text{g/mol}} = 0.960\,\text{mol}\)

Find the Mole Ratio

Now, we will determine the smallest whole number ratios for each element. First, divide both molar values by the smallest value: - Barium (Ba): \(\frac{0.480\,\text{mol}}{0.480\,\text{mol}} = 1\) - Chlorine (Cl): \(\frac{0.960\,\text{mol}}{0.480\,\text{mol}} = 2\) The mole ratio is 1:2 for Barium and Chlorine.

Write the Empirical Formula

The whole number ratio of Barium and Chlorine is 1:2, so the empirical formula of the compound formed is BaCl2.

Key concepts

Binary Compound

In chemistry, a binary compound is composed of two different elements. These elements can be metals, non-metals, or one of each, but they must only consist of two types of atoms. For example, the binary compound formed when barium reacts with chlorine contains only barium (Ba) and chlorine (Cl) atoms.
This simplicity makes binary compounds an excellent starting point for learning to calculate empirical formulas. Understanding the basic nature of binary compounds is crucial because it helps in identifying the elements involved and simplifies the process of determining the formula based on mass percentages.

Molar Mass

Molar mass is the mass of one mole of a substance, measured in grams per mole (g/mol). It serves as a bridge between the mass of a substance and the amount in terms of moles, which is essential for chemical calculations. For any element, the molar mass is numerically equal to the atomic mass from the periodic table.
In our exercise, we used the molar masses of barium and chlorine to convert mass percentages into moles.

• Barium has a molar mass of 137.33 g/mol.
• Chlorine has a molar mass of 35.45 g/mol.

By converting from grams to moles, we better understand the proportion of each element in a compound, which is a crucial step in determining empirical formulas.

Mole Ratio

The mole ratio is the ratio of the amounts in moles of any two substances involved in a chemical reaction. It is essential in determining the simplest form of chemical formulas.
In the empirical formula calculation, we determine the mole ratio by dividing the number of moles of each element by the smallest number of moles calculated.
For instance, in our barium chloride compound, we calculated:

• 0.480 mol of Barium (Ba)
• 0.960 mol of Chlorine (Cl)

Dividing each by the smallest value (0.480 mol), we received a ratio of 1:2 between barium and chlorine, indicating that the empirical formula contains one atom of barium for every two atoms of chlorine.

Empirical Formula Step-by-Step

Calculating the empirical formula is a methodical process. Here's how it works step-by-step:
1. **List Given Mass Percentages:** Start by noting the mass percentages of each element, as if you had 100 grams of the compound. This allows translating the percentages straight to grams.
2. **Convert to Moles:** Use the molar mass of each element to convert mass (grams) to moles. This is crucial because chemical formulas are based on moles, not mass.
3. **Determine Mole Ratio:** Identify the simplest whole number ratio of moles by dividing each element’s amount by the smallest mole value obtained.
4. **Formulate the Empirical Formula:** Use the mole ratios to write down the simplest formula. In our example, the process resulted in BaCl₂, indicating one barium atom for every two chlorine atoms.
Understanding each step deeply and sequentially makes the concept clear, ensuring accuracy when working with any binary compound or beyond.