Question

\(0.48 \mathrm{~g}\) of a sample of a compound containing boron and oxygen contains \(0.192 \mathrm{~g}\) of boron and \(0.288 \mathrm{~g}\) of oxygen. What will be the percentage composition of the compound? 9 (a) \(60 \%\) and \(40 \% \mathrm{~B}\) and \(\mathrm{O}\) respectively (b) \(40 \%\) and \(60 \% \mathrm{~B}\) and \(\mathrm{O}\) respectively (c) \(30 \%\) and \(70 \% \mathrm{~B}\) and \(\mathrm{O}\) respectively (d) \(70 \%\) and \(30 \% \mathrm{~B}\) and \(\mathrm{O}\) respectively

Short answer

The percentage composition of the compound is: Boron = 40%, Oxygen = 60% (Option b).

Step-by-step solution

Find the Percentage of Boron

To find the percentage of boron in the compound, divide the mass of boron by the total mass of the sample and then multiply by 100. Percentage of Boron = \( \frac{0.192 \mathrm{~g}}{0.48 \mathrm{~g}} \times 100 \% \)

Calculate the Percentage of Boron

Perform the calculation from Step 1. Percentage of Boron = \( \frac{0.192}{0.48} \times 100 \% = 40 \% \)

Find the Percentage of Oxygen

To find the percentage of oxygen in the compound, divide the mass of oxygen by the total mass of the sample and then multiply by 100. Percentage of Oxygen = \( \frac{0.288 \mathrm{~g}}{0.48 \mathrm{~g}} \times 100 \% \)

Calculate the Percentage of Oxygen

Perform the calculation from Step 3. Percentage of Oxygen = \( \frac{0.288}{0.48} \times 100 \% = 60 \% \)

Confirm the Percentage Composition

Verify that the sum of the percentages of boron and oxygen equals 100%, which confirms that no errors were made in the calculations and that all parts of the compound have been accounted for.

Key concepts

Chemical Compound Analysis

Understanding the chemical composition of compounds is fundamental in the field of chemistry. Chemical compound analysis involves determining the percentage of each element within a compound. This process is crucial in various applications such as material science, quality control, and pharmaceuticals, where the purity and composition of substances must be precisely known.

For example, consider the provided exercise where we analyzed a compound containing boron and oxygen. The percentage composition is calculated by dividing the mass of an individual element by the total mass of the sample, and then multiplying by 100. This allows chemists to understand the relative amounts of each element and how they contribute to the properties of the compound.

This type of analysis can be done by a variety of methods, including gravimetric analysis, and spectrometry, amongst others. With the percentage composition known, it's possible to infer the empirical formula of the compound, leading to deeper insights into its chemical characteristics and behavior.

Stoichiometry

Stoichiometry is a section of chemistry that involves the calculation of reactants and products in chemical reactions. It is based on the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. Hence, the quantity of each element must remain the same before and after a chemical reaction.

To illustrate, let's build upon our exercise involving boron and oxygen. Stoichiometry would come into play if we needed to know how much of another element or compound would react completely with a set mass of the boron-oxygen compound. It can tell us the theoretical yield of a reaction or the amounts needed to react without excess. The percentages calculated previously would assist in these stoichiometric calculations, providing the ratios of elements present which in turn influence the stoichiometry of subsequent reactions.

Mole Concept

The mole concept is a cornerstone of chemistry because it provides a bridge between the microscopic world of atoms and the macroscopic world we experience. One mole of any substance contains Avogadro's number (\( 6.022 \times 10^{23} \) entities) of particles, whether they are atoms, molecules, ions, or electrons.

In the context of our problem, if we wanted to carry out reactions using our boron-oxygen compound, we would need to convert the provided mass of the compound into moles. This is done through the formula: number of moles = mass / molar mass. By finding the molar mass of the compound from the periodic table and using the mass given, we can determine the number of moles of the compound, which would then allow us to utilize stoichiometric relationships to predict reactant and product amounts for chemical reactions.

Understanding the mole concept allows chemists to count particles by weighing, providing a practical method to use chemistry in real-world applications and advance scientific investigations.