Question

A compound has the following percentages by mass: barium, 58.84\%; sulfur, 13.74\%; oxygen, 27.43\%. Determine the empirical formula of the compound.

Short answer

The empirical formula of the compound is BaSO_4.

Step-by-step solution

Convert percentages to grams

Assume that we have a 100-gram sample of the compound. This assumption is helpful because it doesn't affect the mole ratio and simplifies calculations. Using the given mass percentages for each element, we can find the mass of each element in the 100-gram sample: - Barium: \(58.84\% \times 100g = 58.84g\) - Sulfur: \(13.74\% \times 100g = 13.74g\) - Oxygen: \(27.43\% \times 100g = 27.43g\)

Determine the number of moles of each element

Using the molar mass of each element, we can find the number of moles for each element in our sample: - Barium: \(\frac{58.84g}{137.33g/mol} = 0.4284 mol\) - Sulfur: \(\frac{13.74g}{32.07g/mol} = 0.4284 mol\) - Oxygen: \(\frac{27.43g}{16.00g/mol} = 1.714 mol\)

Find the ratio of moles of each element

To find the mole ratio, we will divide the moles of each element by the smallest number of moles among the elements. In our case, the smallest number of moles is 0.4284 (for Barium and Sulfur). Therefore, the mole ratios are: - Barium: \(\frac{0.4284}{0.4284} = 1\) - Sulfur: \(\frac{0.4284}{0.4284} = 1\) - Oxygen: \(\frac{1.714}{0.4284} ≈ 4\)

Write the empirical formula

Now that we have the ratio of moles for each element, we can write the empirical formula of the compound using these mole ratios: BaSO_4 Therefore, the empirical formula of the compound is BaSO_4.

Key concepts

Percent Composition

Understanding the percent composition of a compound is a vital part of determining its empirical formula. It tells us the percentage by mass of each element in the compound. This information is crucial because it forms the basis to find out the simplest ratio of atoms in the compound, known as the empirical formula. The given problem provides the percent composition of a compound consisting of Barium, Sulfur, and Oxygen. For instance, Barium has a percentage of 58.84%. This means that in every 100 grams of the compound, 58.84 grams are Barium. Similarly, Sulfur and Oxygen have percentages of 13.74% and 27.43%, respectively. Using percent composition helps us convert these percentages into masses, thereby simplifying the process of calculating the number of moles and determining the empirical formula.

Mole Ratio

The mole ratio is an essential step in finding the empirical formula of a compound. Once we have converted the mass of each element from the percent composition into grams, the next step is to calculate the moles of each element using their molar masses. In our exercise, the moles are calculated for Barium, Sulfur, and Oxygen. After calculating, we have:

• Barium: 0.4284 moles
• Sulfur: 0.4284 moles
• Oxygen: 1.714 moles

The mole ratio is derived by dividing each element's mole quantity by the smallest mole value among them. This normalizes the ratios so we can easily find the simplest whole number ratio, which represents the proportions of the atoms in the compound's empirical formula. For this exercise, the smallest mole count is 0.4284. After dividing, we find that the mole ratio is approximately 1:1:4 for Barium, Sulfur, and Oxygen respectively.

Elemental Analysis

Elemental analysis involves examining a chemical compound to determine its elemental composition, typically expressed as a percentage. This technique is foundational in empirical formula determination as it provides the data needed to calculate the mole ratio. For our current exercise, the elemental analysis indicates that the sample contains Barium, Sulfur, and Oxygen with specific mass percentages. This data is used to convert these percentages into grams, which can subsequently be transformed into moles for further calculation. Chemical analysis thus gives us not just the framework but the precise values needed to decode any unknown compound's empirical formula, making it a powerful tool in chemistry.

Step-by-step Calculations

Step-by-step calculations are pivotal for solving complex chemical problems like determining an empirical formula. Breaking down the problem into smaller, manageable tasks allows for a clearer understanding and easier processing of information. Here's how it unfolds in this exercise:

• Convert the percentage of each element into grams based on a 100g sample. For our compound, that means 58.84g of Barium, 13.74g of Sulfur, and 27.43g of Oxygen.
• Use the periodic table values to convert these masses into moles. This involves dividing the mass of each element by its atomic weight.
• Normalize the mole quantities by dividing each by the smallest number of moles calculated. This gives a simplified ratio of the elements.
• Translate this ratio into an empirical formula; in this example, BaSO₄.

Using step-by-step calculations ensures accuracy and makes this often challenging topic approachable for students.