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

45.96% barium, 54.04% silicon

Step-by-step solution

- Find the mass of silicon

The total mass of the sample is given as 73.16 grams, and it contains 33.62 grams of barium. To find the mass of silicon, subtract the mass of barium from the total mass: \[ \text{Mass of Silicon} = 73.16 \text{ g} - 33.62 \text{ g} = 39.54 \text{ g} \]

- Calculate the percent composition of barium

To find the percent composition of barium, divide the mass of barium by the total mass of the sample and then multiply by 100: \[ \text{Percent Composition of Barium} = \frac{33.62 \text{ g}}{73.16 \text{ g}} \times 100 \text{ \%} = 45.96 \text{ \%} \]

- Calculate the percent composition of silicon

To find the percent composition of silicon, divide the mass of silicon by the total mass of the sample and then multiply by 100: \[ \text{Percent Composition of Silicon} = \frac{39.54 \text{ g}}{73.16 \text{ g}} \times 100 \text{ \%} = 54.04 \text{ \%} \]

Key concepts

Mass Calculation

Mass calculation is an essential part of determining the composition of a substance. For the given problem, calculating the mass of silicon required subtracting the mass of barium from the total mass of the sample. The total mass of the sample was 73.16 grams, and it contained 33.62 grams of barium. Therefore, the mass of silicon was calculated as: \[ \text{Mass of Silicon} = 73.16 \text{ g} - 33.62 \text{ g} = 39.54 \text{ g} \] This subtraction method is a straightforward way to determine how much silicon is present after accounting for the barium.

Elemental Composition

Elemental composition refers to the amount of each element within a compound. In this example, the composition of barium and silicon needed to be determined to understand the overall makeup of the barium silicide compound. To achieve this, we calculated the percent composition of both elements. For barium: \[ \text{Percent Composition of Barium} = \frac{33.62 \text{ g}}{73.16 \text{ g}} \times 100 \text{ \%} = 45.96 \text{ \%} \] This calculation shows that 45.96% of the compound is barium. Similarly, for silicon: \[ \text{Percent Composition of Silicon} = \frac{39.54 \text{ g}}{73.16 \text{ g}} \times 100 \text{ \%} = 54.04 \text{ \%} \] We found that 54.04% of the compound consists of silicon. These percentages help in understanding the proportion of each element in the compound.

Superconducting Properties

Superconducting properties are interesting features of certain materials that, at extremely low temperatures, can conduct electricity with zero resistance. These properties make superconductors valuable for various applications, including in medical imaging (MRI machines), maglev trains, and improving the efficiency of power grids. The barium silicide sample in our problem is reported to have superconducting properties. Such materials, often involving complex compounds with metals and metalloids, exhibit superconductivity usually upon cooling to very low temperatures, often requiring liquid helium or nitrogen. Understanding these properties allows scientists to explore new ways to create efficient and powerful technological solutions.

Sample Analysis

Sample analysis involves comprehensive methods to identify and quantify the components within a material. In the context of the exercise at hand, analyzing the sample required calculating both the mass and percentage of barium and silicon. A step-by-step analysis was performed as follows:

• Determine the mass of silicon by subtracting the mass of barium from the total sample mass.
• Calculate the percent composition of barium and silicon using their respective masses and the total sample mass.

Such an analysis is vital in both academic research and various industries where the precise composition of materials must be known, such as in metallurgy, pharmaceuticals, and materials science. It enables researchers and engineers to understand and manipulate material properties for specific applications.