Problem 49 - Chemistry: The Central Science in SI Units, Global Edition

Question

Write the empirical formula corresponding to each of the following molecular formulas: (a) \(\mathrm{Al}_{2} \mathrm{Br}_{6}\), (b) \(\mathrm{C}_{8} \mathrm{H}_{10}\) (c) \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2}\) (d) \(\mathrm{P}_{4} \mathrm{O}_{10}\) (e) \(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{2}\) (f) \(\mathrm{B}_{3} \mathrm{~N}_{3} \mathrm{H}_{6}\)

Step-by-Step Solution

Answer

Empirical formulas: (a) \(AlBr_{3}\), (b) \(C_{4}H_{5}\), (c) \(C_{2}H_{4}O\), (d) \(P_{2}O_{5}\), (e) \(C_{3}H_{2}Cl\), (f) \(BNH_{2}\)

Step 1: (a) Determine empirical formula for Al₂Br₆

To find the simplest whole number ratio of Al and Br, let's find the greatest common divisor (GCD) for the subscripts 2 and 6. The GCD of 2 and 6 is 2. Divide the subscripts by the GCD: Al: 2 / 2 = 1 Br: 6 / 2 = 3 Empirical formula: \(AlBr_{3}\)

Step 2: (b) Determine empirical formula for C₈H₁₀

To find the simplest whole number ratio of C and H, let's find the GCD for the subscripts 8 and 10. The GCD of 8 and 10 is 2. Divide the subscripts by the GCD: C: 8 / 2 = 4 H: 10 / 2 = 5 Empirical formula: \(C_{4}H_{5}\)

Step 3: (c) Determine empirical formula for C₄H₈O₂

To find the simplest whole number ratio of C, H, and O, let's find the GCD for the subscripts 4, 8, and 2. The GCD of 4, 8, and 2 is 2. Divide the subscripts by the GCD: C: 4 / 2 = 2 H: 8 / 2 = 4 O: 2 / 2 = 1 Empirical formula: \(C_{2}H_{4}O\)

Step 4: (d) Determine empirical formula for P₄O₁₀

To find the simplest whole number ratio of P and O, let's find the GCD for the subscripts 4 and 10. The GCD of 4 and 10 is 2. Divide the subscripts by the GCD: P: 4 / 2 = 2 O: 10 / 2 = 5 Empirical formula: \(P_{2}O_{5}\)

Step 5: (e) Determine empirical formula for C₆H₄Cl₂

To find the simplest whole number ratio of C, H, and Cl, let's find the GCD for the subscripts 6, 4, and 2. The GCD of 6, 4, and 2 is 2. Divide the subscripts by the GCD: C: 6 / 2 = 3 H: 4 / 2 = 2 Cl: 2 / 2 = 1 Empirical formula: \(C_{3}H_{2}Cl\)

Step 6: (f) Determine empirical formula for B₃N₃H₆

To find the simplest whole number ratio of B, N, and H, let's find the GCD for the subscripts 3, 3, and 6. The GCD of 3, 3, and 6 is 3. Divide the subscripts by the GCD: B: 3 / 3 = 1 N: 3 / 3 = 1 H: 6 / 3 = 2 Empirical formula: \(BNH_{2}\)

Key Concepts

Molecular Formulas

Molecular formulas represent the actual number of atoms of each element in a molecule. This information is crucial because it tells you exactly how a molecule is composed. For example, the molecular formula for water is \(H_2O\), indicating that each water molecule consists of two hydrogen atoms and one oxygen atom.

These formulas can be expanded upon or reduced to show the smallest ratio of the atoms within the molecule, which then leads to what we call empirical formulas. Molecular formulas are often used in chemical equations, allowing chemists to keep track of what occurs during a chemical reaction. By knowing the molecular makeup, chemists can predict the behavior and interaction of substances during chemical reactions.

The task of finding molecular formulas involves understanding a compound's molecular structure and determining the exact count of different atoms within that molecule.

Chemical Ratios

Chemical ratios help us understand the proportion of elements within a compound. When converting molecular formulas to empirical formulas, it involves calculating these ratios. To do this, finding the greatest common divisor (GCD) of the subscripts of the elements in the molecular formula is necessary. This simplifies the formula to its most basic ratio.

For instance, if given a formula like \(C_8H_{10}\), the process would involve determining the GCD of 8 and 10, which is 2. By dividing the number of carbon and hydrogen atoms by this GCD, we achieve a simpler, more fundamental ratio, resulting in the empirical formula \(C_4H_5\).

Understanding chemical ratios is vital in the study of chemistry as it forms the basis of comparing different compounds and predicting the outcomes of chemical reactions. It helps in comprehending the relative amounts of each substance that react and the products that are formed.

Stoichiometry Calculations

Stoichiometry calculations involve quantitative relationships in chemical reactions based on balanced chemical equations. By using stoichiometry, we can calculate the relative amounts of reactants and products involved in a chemical reaction, ensuring the conservation of mass.

This concept works closely with both molecular and empirical formulas. For instance, once you have determined the empirical formula, you can then use stoichiometry to calculate how much of a certain substance is needed or how much will be produced. This involves molar ratios, a crucial aspect of stoichiometry, derived from balanced equations.

In practice, stoichiometry calculations enable chemists and students to predict the amounts of substances consumed and created in reactions. It's a fundamental skill in chemistry that supports a wide range of analyses, from laboratory work to industrial chemical processes.