Question

A 73.16-g sample of an interesting barium silicide reported to have superconducting properties was found to contain \(33.62 \mathrm{~g}\) barium and the remainder silicon. Calculate the percent composition of the compound.

Short answer

Barium: 45.96%, Silicon: 54.04%

Step-by-step solution

- Calculate the mass of silicon

First, determine the mass of silicon in the sample by subtracting the mass of barium from the total mass of the compound. Mass of silicon = Total mass - Mass of barium Mass of silicon = 73.16 g - 33.62 g Mass of silicon = 39.54 g

- Calculate the percent composition of barium

Next, calculate the percent composition of barium in the compound. Use the formula: Percent composition of barium = \[ \frac{ \text{Mass of barium} }{ \text{Total mass} } \times 100 \] Substituting the values: Percent composition of barium = \[ \frac{ 33.62 \text{ g} }{ 73.16 \text{ g} } \times 100 \] Percent composition of barium ≈ 45.96%

- Calculate the percent composition of silicon

Finally, calculate the percent composition of silicon in the compound. Use the formula: Percent composition of silicon = \[ \frac{ \text{Mass of silicon} }{ \text{Total mass} } \times 100 \] Substituting the values: Percent composition of silicon = \[ \frac{ 39.54 \text{ g} }{ 73.16 \text{ g} } \times 100 \] Percent composition of silicon ≈ 54.04%

Key concepts

percent composition

Percent composition is an important concept in chemistry that helps to understand the relative amounts of each element in a compound. It tells you the percentage by mass of each element in the sample. Therefore, knowing the percent composition helps chemists to determine the formula of a compound and to verify its purity.

The process to calculate the percent composition follows these general steps:

• Calculate the mass of each element in the compound.
• Divide the mass of the element by the total mass of the compound.
• Multiply the result by 100.

For example, in the provided exercise, the mass of barium was 33.62 g in a 73.16 g sample. To find the percent composition of barium, we divided the 33.62 g by 73.16 g and then multiplied by 100, which resulted in approximately 45.96%.

mass calculation

Mass calculation is crucial for determining the composition of a substance. It involves straightforward arithmetic, but accuracy is key. In the exercise provided, the first step was to calculate the mass of silicon in the sample. This was done by subtracting the mass of barium from the total mass:

Mass of silicon = Total mass - Mass of barium ewline Mass of silicon = 73.16 g - 33.62 g ewline Mass of silicon = 39.54 g

It's important to ensure all measurements are in the same units and that subtraction is performed correctly to avoid errors. Having accurate mass calculations allows for precise determination of percent compositions, which is essential for further chemical analysis.

barium silicide

Barium silicide is an intriguing compound with potential superconducting properties, which means it could conduct electricity without resistance at certain temperatures. Understanding the percent composition of barium silicide not only helps in confirming the identity and purity of the compound but also provides insights into its empirical formula.

For the compound in the exercise with a total mass of 73.16 g, the mass of barium was found to be 33.62 g, and the mass of silicon was 39.54 g. By calculating the percent compositions, it was determined that barium makes up approximately 45.96% and silicon about 54.04% of the compound. These calculations are essential for chemists working on developing and studying new materials with unique properties.