Question

Determine the molecular and empirical formulas of the following: (a) the organic solvent benzene, which has six carbon atoms and six hydrogen atoms; \((\mathbf{b})\) the compound silicon tetrachloride, which has a silicon atom and four chlorine atoms and is used in the manufacture of computer chips; \((\mathbf{c})\) the reactive substance diborane, which has two boron atoms and six hydrogen atoms; (d) the sugar called glucose, which has six carbon atoms, twelve hydrogen atoms, and six oxygen atoms.

Short answer

Benzene: \( C_6H_6 \) and \( CH \); Silicon tetrachloride: \( SiCl_4 \) and \( SiCl_4 \); Diborane: \( B_2H_6 \) and \( BH_3 \); Glucose: \( C_6H_{12}O_6 \) and \( CH_2O \).

Step-by-step solution

Identify the Elements and Count Atoms

For each compound mentioned, begin by noting the elements present and the number of atoms of each element in the molecules.

Determine Molecular Formula for Benzene

Benzene is composed of 6 carbon atoms and 6 hydrogen atoms. Thus, the molecular formula for benzene is \(C_6H_6\).

Determine Empirical Formula for Benzene

The empirical formula is the simplest whole-number ratio of the elements. For benzene, both carbon and hydrogen have 6 atoms, so the ratio is 1:1, making the empirical formula \(CH\).

Determine Molecular Formula for Silicon Tetrachloride

Silicon tetrachloride has one silicon atom and four chlorine atoms. Therefore, the molecular formula is \(SiCl_4\).

Determine Empirical Formula for Silicon Tetrachloride

Since the molecular formula shows a 1:4 ratio and cannot be simplified further, the empirical formula for silicon tetrachloride is also \(SiCl_4\).

Determine Molecular Formula for Diborane

Diborane consists of 2 boron atoms and 6 hydrogen atoms, so the molecular formula is \(B_2H_6\).

Determine Empirical Formula for Diborane

The ratio of boron to hydrogen is 2:6, which simplifies to a 1:3 ratio. Thus, the empirical formula for diborane is \(BH_3\).

Determine Molecular Formula for Glucose

Glucose is made up of 6 carbon, 12 hydrogen, and 6 oxygen atoms. This results in the molecular formula \(C_6H_{12}O_6\).

Determine Empirical Formula for Glucose

The formula \(C_6H_{12}O_6\) simplifies to a 1:2:1 ratio, giving the empirical formula \(CH_2O\).

Key concepts

Organic Chemistry

Organic chemistry is a fascinating branch of chemistry that focuses on the study of carbon-based compounds. Since carbon atoms can form strong bonds with many elements, including themselves, a vast array of complex structures can be created—from simple hydrocarbons to large biomolecules.
One of the most intriguing classes of organic compounds is aromatic compounds, such as benzene. Benzene consists solely of carbon and hydrogen, with its atoms arranged in a hexagonal ring structure. This ring stability makes benzene essential in various chemical applications.

• Why Carbon? Carbon's ability to form four covalent bonds makes it uniquely capable of forming long chains and complex structures essential for life.
• Aromaticity: The concept of aromaticity, exemplified by benzene, involves electron delocalization within a ring structure, conferring stability and distinct chemical properties.

In organic chemistry, understanding the structure and formula of compounds like benzene allows chemists to predict reactivity and behaviors in larger, more complex molecules found in nature and industry.

Chemical Compounds

Chemical compounds are substances composed of two or more different types of atoms bonded together. The nature of these bonds and the arrangement of the atoms determine the compound's characteristics. In chemistry, compounds like silicon tetrachloride and diborane highlight the diversity in compound formation.
Silicon tetrachloride (SiCl₄) is a simple compound made from one silicon atom bonded to four chlorine atoms. Despite its simplicity, it plays a crucial role in the semiconductor industry, particularly in the manufacture of computer chips. This shows how even simple compounds can have significant technological applications.

• Covalent Bonds: Both silicon tetrachloride and diborane are held together by covalent bonds. These bonds involve the sharing of electron pairs between atoms, leading to strong and stable compounds.
• Industrial Relevance: Many chemical compounds, despite being simple in their chemical formulas, are integral to industrial processes—demonstrating the importance of chemical synthesis and understanding.

Recognizing the formation and use of chemical compounds enables us to harness their properties for technological and practical applications.

Chemical Formulas

In chemistry, chemical formulas are crucial for conveying information about the substances involved. They tell us which elements are present in a compound and how many atoms of each element exist. Understanding both molecular and empirical formulas allows chemists to describe compounds with precision.
The molecular formula represents the actual number of atoms of each element in a molecule, while the empirical formula shows the simplest whole-number ratio of these atoms. For instance, for glucose, the molecular formula is \(C_6H_{12}O_6\), reflecting the exact number of carbon, hydrogen, and oxygen atoms. The empirical formula simplifies this to \(CH_2O\), which conveys the basic ratio.

• Molecular vs. Empirical: While molecular formulas give a detailed picture of a compound's composition, empirical formulas offer a simplified version, often used when the actual molecule structure isn't easy to identify.
• Simplification: Sometimes simplification is beneficial, such as in comparing different compounds or studying reaction stoichiometry where ratios are more relevant than actual counts.

Ultimately, chemical formulas are indispensable tools, providing foundational knowledge for deeper exploration and manipulation of chemical substances.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It’s essential for understanding how chemical reactions occur and how to manipulate them to achieve desired outcomes.
This concept is illustrated when determining empirical and molecular formulas. For instance, knowing that diborane has a molecular formula of \(B_2H_6\) and an empirical formula of \(BH_3\) informs us about the stoichiometric proportions of boron and hydrogen during chemical reactions.

• Mole Concept: Central to stoichiometry is the mole, a unit used to measure chemical substances. It allows chemists to count atoms, molecules, or ions by weighing them.
• Reaction Ratios: Stoichiometry calculations help predict the amounts of reactants needed and products formed, vital for chemical manufacturing and laboratory experiments.

By grasping stoichiometry, students can accurately calculate yields, understand reaction mechanisms, and improve efficiencies in chemical processes.