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Boron and hydrogen form a number of compounds called boranes (see Interchapter I). A certain borane is found to contain \(85.63 \%\) boron by mass, the rest being hydrogen. What is the empirical formula of the borane?

Short Answer

Expert verified
The empirical formula of the borane is \(B_5H_9\).

Step by step solution

01

Determine Mass Percent of Hydrogen

Since the compound consists only of boron and hydrogen, the percentage of hydrogen can be calculated by subtracting the percentage of boron from 100%. Thus, the mass percentage of hydrogen is: \(100\% - 85.63\% = 14.37\%\).
02

Convert to Grams

Assume you have 100 grams of the compound. This means you have 85.63 grams of boron and 14.37 grams of hydrogen.
03

Convert Mass to Moles

To find the number of moles, use the molar mass of each element. The molar mass of boron is approximately 10.81 g/mol, and for hydrogen, it is approximately 1.01 g/mol. Calculate moles of boron: \[\text{Moles of B} = \frac{85.63 \text{ g}}{10.81 \text{ g/mol}} \approx 7.92 \text{ mol}\]Calculate moles of hydrogen: \[\text{Moles of H} = \frac{14.37 \text{ g}}{1.01 \text{ g/mol}} \approx 14.23 \text{ mol}\]
04

Determine the Simplest Whole Number Ratio

Divide by the smallest number of moles to get the simplest whole number ratio.For boron: \[\frac{7.92}{7.92} = 1\]For hydrogen:\[\frac{14.23}{7.92} \approx 1.8\]Since we want whole numbers, it is usually more accurate to multiply these ratios by a common factor to get integers, if they are not reasonably close already. Here multiplying both ratios by 5 helps achieve whole numbers. After multiplying: \[B_5H_9\]
05

Write the Empirical Formula

Given the whole number ratio calculated, the empirical formula of the borane is \(B_5H_9\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Boron Compounds
Boron compounds, which are primarily composed of boron and other elements, are fascinating due to their unique properties and structures. These compounds are immensely important in various fields, from industrial manufacturing to chemical research.
Boranes, a subset of boron compounds, are compounds of boron and hydrogen. Boranes illustrate a vast array of structural diversity and complexity, which stems from the ability of boron to form unusual bonding arrangements. Unlike carbon, boron can engage in three-center two-electron bonds, leading to structures called cages or clusters.
Some essential qualities of boron compounds include:
  • High melting and boiling points, often resulting from strong covalent bonding.
  • Chemical reactivity that varies widely, dependent on the other elements present alongside boron.
  • Excellent thermal and chemical stability, making them valuable in extreme applications.
Understanding these compounds starts with empirical formulas like that of a specific borane, aiding chemists in predicting and manipulating compound behavior.
Borane Chemistry
Borane chemistry delves into the structure, synthesis, and reactivity of compounds formed between boron and hydrogen. In this form of chemistry, one finds a world different from traditional organic chemistry, primarily due to boron’s ability to engage in non-classical bonding.
Boranes exhibit a fascinating range of polyhedral shapes due to boron’s electron-deficient character. The electron-pair sharing across three atoms instead of two creates deltahedral and polyhedral clusters, allowing for complex geometries beyond simple diatomic or triatomic molecules.
These unique characteristics include:
  • Versatile bonding schemes that permit various geometries.
  • Tendency to form clusters, which are not often seen with other elements.
  • Potential as precursors in high-temperature ceramics or other high-tech materials.
Exploring borane chemistry enhances our understanding of molecular geometry and bonding, crucial for advanced material science and catalysis.
Mole Concept
The mole concept is a foundational principle in chemistry, acting as the bridge between the microscopic world of atoms and the macroscopic quantities we observe in laboratories and nature. One mole contains Avogadro's number ( 6.022 × 10^{23} ) of entities, which can be atoms, molecules, ions, or other particles.
Using the mole concept allows scientists to convert measurable mass into numbers of atoms or molecules—a key step in chemical analysis and reactions.
Here's how it applies:
  • Moles turn abstract atomic weights into tangible masses that can be measured.
  • Stoichiometric calculations often pivot on converting between mass, moles, and number of particles.
  • Molar mass provides a shortcut— the mass of one mole of a substance—linking the theoretical calculations to experimental data.
Understanding and mastering the mole concept is essential for solving all quantitative chemical problems and helps in determining the empirical formulas, like with borane.
Chemical Composition Analysis
Chemical composition analysis is the process of determining the distribution of different elements within a chemical substance. This information is crucial for identifying unknown compounds, verifying material properties, and ensuring quality control.
The analysis often starts with empirical formula determination. To find an empirical formula, one begins by calculating the percentage composition of each element in the compound, as demonstrated in the borane example.
The systematic approach is:
  • Determine the mass percentage of all elements present.
  • Convert the percentages to masses, assuming a convenient sample like 100 grams.
  • Convert these masses to moles using atomic weights.
  • Simplify the mole ratio to acquire the simplest whole-number ratio, yielding the empirical formula.
Such analyses are essential for chemists in research and development, as well as applied industries, enabling precise control over product composition and properties.

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Most popular questions from this chapter

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