Problem 23 - Chemistry for Allied Health

Question

How many atoms of each element are represented by the following combinations of coefficients and chemical formulas? a. \(5 \mathrm{Br}_{2}\) b. \(2 \mathrm{NH}_{3}\) c. \(4\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) d. \(2 \mathrm{CH}_{3} \mathrm{COOH}\) e. \(3 \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\) f. \(2 \mathrm{~K}_{3} \mathrm{PO}_{4}\)

Step-by-Step Solution

Answer

a) 10 Br, b) 2 N, 6 H, c) 8 N, 32 H, 4 S, 16 O, d) 4 C, 8 H, 4 O, e) 3 Fe, 9 N, 27 O, f) 6 K, 2 P, 8 O

Step 1: Analyze Compound a

For the compound \(5 \mathrm{Br}_{2}\), there are 2 bromine atoms per molecule. Since there are 5 molecules, the total number of bromine atoms is \(5 \times 2 = 10\).

Step 2: Analyze Compound b

For the compound \(2 \mathrm{NH}_{3}\), each molecule contains 1 nitrogen and 3 hydrogen atoms. For 2 molecules, total nitrogen atoms are \(2 \times 1 = 2\) and total hydrogen atoms are \(2 \times 3 = 6\).

Step 3: Analyze Compound c

For the compound \(4\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\), each unit contains 2 nitrogen, 8 hydrogen, 1 sulfur, and 4 oxygen atoms. For 4 units, calculate:- Nitrogen: \(4 \times 2 = 8\)- Hydrogen: \(4 \times 8 = 32\)- Sulfur: \(4 \times 1 = 4\)- Oxygen: \(4 \times 4 = 16\)

Step 4: Analyze Compound d

For the compound \(2 \mathrm{CH}_3 \mathrm{COOH}\), each molecule contains 2 carbon, 4 hydrogen, and 2 oxygen atoms. For 2 molecules, calculate:- Carbon: \(2 \times 2 = 4\)- Hydrogen: \(2 \times 4 = 8\)- Oxygen: \(2 \times 2 = 4\)

Step 5: Analyze Compound e

For the compound \(3 \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\), each unit contains 1 iron, 3 nitrogen, and 9 oxygen atoms. For 3 units, calculate:- Iron: \(3 \times 1 = 3\)- Nitrogen: \(3 \times 3 = 9\)- Oxygen: \(3 \times 9 = 27\)

Step 6: Analyze Compound f

For the compound \(2 \mathrm{K}_3 \mathrm{PO}_4\), each unit contains 3 potassium, 1 phosphorus, and 4 oxygen atoms. For 2 units, calculate:- Potassium: \(2 \times 3 = 6\)- Phosphorus: \(2 \times 1 = 2\)- Oxygen: \(2 \times 4 = 8\)

Key Concepts

Stoichiometry

Stoichiometry is a branch of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It is essential because it helps us understand how to balance chemical equations and determine the exact amount of substances needed for reactions to occur. In the context of chemical formula analysis, stoichiometry allows us to predict how different elements will react based on their chemical formulas and coefficients. By understanding stoichiometry, students can determine the number of atoms in a molecule, translate between moles and atoms, and comprehend the relationships between compounds in a chemical equation.

Molecular Composition

Molecular composition refers to the specific atoms and their ratios in a chemical compound. Each molecule is made up of atoms of different elements, and these atoms are bonded together in definite ratios to form the compound. The chemical formula gives us a glimpse of this arrangement. For example, in the compound \( \mathrm{NH}_3 \), one nitrogen atom is bonded with three hydrogen atoms. By studying the molecular composition, we can understand the structure of the compound and predict its properties and behavior in chemical reactions.

Element Counting

Element counting involves determining the number of each type of atom present in a given chemical formula. It is crucial for understanding the composition of a compound and for performing stoichiometric calculations. To count elements, you need to consider the subscript numbers in chemical formulas and the coefficients in front of them. For example, in \( 2 \mathrm{NH}_3 \), there are two sets of ammonia molecules, each containing one nitrogen and three hydrogen atoms. This results in a total of two nitrogen atoms and six hydrogen atoms. This skill helps in analyzing the molecular composition of compounds.

Chemical Formulas in Reactions

Chemical formulas represent the composition of substances involved in chemical reactions. They indicate not only which elements are present, but also in what proportion. This is vital for predicting how substances will interact. For example, in a reaction where \( \mathrm{H}_2 \) reacts with \( \mathrm{O}_2 \) to form water, the chemical formulas tell us that hydrogen and oxygen will combine in a 2:1 ratio to produce \( \mathrm{H}_2\mathrm{O} \). Understanding chemical formulas is key to balancing chemical equations, which ensures the conservation of mass during a reaction. This balance reflects the stoichiometric relationships established by the formulas of the reactants and products.