Question

A \(3.455-\mathrm{g}\) sample of a mixture was analyzed for barium ion by adding a small excess of sulfuric acid to an aqueous solution of the sample. The resultant reaction produced a precipitate of barium sulfate, which was collected by filtration, washed, dried, and weighed. If \(0.2815 \mathrm{~g}\) of barium sulfate was obtained, what was the mass percentage of barium in the sample?

Short answer

The mass percentage of barium in the sample is approximately 4.8%. This is calculated by first finding the moles of barium sulfate obtained and then the mass of barium in the sample. Finally, the mass percentage is determined using the given mass of the mixture.

Step-by-step solution

Identify the molar mass of Barium (Ba) and Barium Sulfate (BaSO4)

To calculate the mass of barium, we need to know the molar mass of barium and barium sulfate. Using the periodic table, we can find the molar mass of each element. Barium (Ba): 137.33 g/mol Sulfur (S): 32.07 g/mol Oxygen (O): 16.00 g/mol Now, let's calculate the molar mass of Barium Sulfate (BaSO4): BaSO4 = 137.33 + (32.07) + 4(16.00) = 137.33 + 32.07 + 64.00 = 233.40 g/mol

Find the moles of Barium Sulfate (BaSO4)

Next, we need to find the moles of barium sulfate obtained, using the mass of precipitate and its molar mass. moles of BaSO4 = mass of BaSO4 / molar mass of BaSO4 moles of BaSO4 = 0.2815 g / 233.40 g/mol ≈ 0.00121 mol

Find the mass of Barium (Ba) in the sample

Since there is one mole of barium per mole of barium sulfate, the moles of barium will be equal to the moles of barium sulfate. moles of Ba = 0.00121 mol Now we can find the mass of barium from its moles using its molar mass. mass of Ba = moles of Ba × molar mass of Ba mass of Ba = 0.00121 mol × 137.33 g/mol ≈ 0.166 g

Calculate the mass percentage of Barium (Ba) in the sample

Now that we have the mass of barium in the sample, we can calculate its mass percentage using the given mass of the mixture. mass percentage of Ba = (mass of Ba / mass of the mixture) × 100 mass percentage of Ba = (0.166 g / 3.455 g) × 100 ≈ 4.8% The mass percentage of barium in the sample is approximately 4.8%.

Key concepts

Barium Sulfate

Barium Sulfate, with the chemical formula \( \text{BaSO}_4 \), is a white crystalline solid that is insoluble in water, making it ideal for various industrial and medical applications. In laboratory settings, barium sulfate is often used in precipitation reactions to determine the presence and quantity of barium ions. When sulfuric acid is added to a barium-containing solution, barium sulfate precipitates out of solution due to its low solubility. This property makes it particularly useful for quantitative analysis in chemistry.
In the context of our problem, barium ions were precipitated as barium sulfate to facilitate their measurement. This technique relies on the stoichiometry of the reaction and the known properties of barium sulfate to accurately determine the amount of barium present in a sample. Understanding the formation and characteristics of barium sulfate allows chemists to perform accurate and reliable analyses.

Molar Mass Calculation

Calculating the molar mass of a compound is a fundamental step in solving stoichiometry problems. The molar mass is defined as the mass of one mole of a given substance, expressed in grams per mole (g/mol). It is obtained by summing the atomic masses of all atoms in the compound's chemical formula.
In our example, we calculated the molar mass of barium sulfate \( \text{BaSO}_4 \). Using the periodic table, we found that barium (Ba) has a molar mass of 137.33 g/mol, sulfur (S) has a molar mass of 32.07 g/mol, and oxygen (O) has a molar mass of 16.00 g/mol. For barium sulfate, the molar mass calculation is as follows:

• Barium: 137.33 g/mol
• Sulfur: 32.07 g/mol
• Oxygen: 4 \times 16.00 g/mol = 64.00 g/mol

Adding these together gives a molar mass of \( 233.40 \) g/mol for \( \text{BaSO}_4 \). Accurate molar mass calculations are crucial for converting between moles and grams in chemical reactions.

Mass Percentage Calculation

Mass percentage is a way to express the concentration of a component in a mixture. It tells us what fraction of the total mass of the mixture is composed of a specific substance, expressed as a percentage. This is a useful concept in chemistry for understanding the composition of complex mixtures.
To calculate the mass percentage, you divide the mass of the component by the total mass of the mixture and then multiply by 100. In our exercise, we calculated the mass percentage of barium in the mixture using the formula:
\[\text{Mass Percentage of Ba} = \left(\frac{\text{Mass of Ba}}{\text{Mass of Mixture}}\right) \times 100\]
The mass of barium was found to be approximately 0.166 g, and the total mass of the mixture was 3.455 g. Plugging these values into the formula yields:
\[\left( \frac{0.166}{3.455} \right) \times 100 \approx 4.8\%\]
This means that barium constitutes 4.8% of the original mixture. Understanding mass percentage calculations enables chemists to quantitatively describe the compositions of mixtures.