Problem 82 - Chemistry The Molecular Nature of Matter

Question

How many atoms of each element are represented in each of the following expressions? (a) \(3 \mathrm{~N}_{2} \mathrm{O},\) (b) \(4\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~S},\) (c) \(2 \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

Expression (a) has 6 nitrogen atoms and 3 oxygen atoms. Expression (b) has 8 carbon atoms, 24 hydrogen atoms, and 4 sulfur atoms. Expression (c) has 2 copper atoms, 2 sulfur atoms, 13 oxygen atoms, and 10 hydrogen atoms.

Step 1: Analyze Expression (a)

The subscript number indicates the number of atoms of each element in the molecule. Coefficient in front of the chemical formula indicates the number of molecules. For expression (a), the molecule is \(N_2O\). There are two nitrogen atoms (N) and one oxygen atom (O) per molecule. The coefficient 3 means there are three molecules. Therefore, we have \(3 \times 2\) atoms of nitrogen and \(3 \times 1\) atoms of oxygen, totaling 6 nitrogen atoms and 3 oxygen atoms.

Step 2: Analyze Expression (b)

For expression (b), the molecule is \(\left(CH_3\right)_2S\), which denotes a compound with two \((CH_3)\) groups and one sulfur (S) atom. Each \((CH_3)\) group contains one carbon (C) and three hydrogen atoms (H), thus two \((CH_3)\) groups have 2 carbon atoms and 6 hydrogen atoms. Along with the 1 sulfur atom in the molecule, with the coefficient 4, we multiply each atom count by 4 to get the total number of atoms: \(4 \times 2\) carbon atoms, \(4 \times 6\) hydrogen atoms, and \(4 \times 1\) sulfur atom, totaling 8 carbon atoms, 24 hydrogen atoms, and 4 sulfur atoms.

Step 3: Analyze Expression (c)

For expression (c), the term \(2 CuSO_4 \cdot 5 H_2O\) represents a hydrate with 2 molecules of copper(II) sulfate \(CuSO_4\) and 5 molecules of water \((H_2O)\) per formula unit. Breaking it down, one \(CuSO_4\) molecule contains 1 copper (Cu), 1 sulfur (S), and 4 oxygen (O) atoms. Similarly, one water molecule \((H_2O)\) contains 2 hydrogen (H) and 1 oxygen (O) atoms. With the coefficients, we count \(2\) copper(II) sulfate molecules and \(2 \times 5\) water molecules. Therefore, we have \(2 \times 1\) copper atoms, \(2 \times 1\) sulfur atoms, \(2 \times 4 + 5 \times 1\) oxygen atoms from copper sulfate and water (totaling 1 extra for each \((H_2O)\)), and \(5 \times 2\) hydrogen atoms, totaling 2 copper atoms, 2 sulfur atoms, 13 oxygen atoms, and 10 hydrogen atoms.

Key Concepts

Molecular Composition

Understanding the molecular composition is essential when diving into the world of chemistry. It denotes the type and number of atoms that make up a molecule, which provides the molecule with its unique characteristics and properties. In simple terms, it's like knowing the ingredients and their amounts in a recipe.

For example, when we look at the molecular composition of water, H₂O, it tells us there are two hydrogen atoms and one oxygen atom in each molecule. Similarly, analyzing the molecular composition of more complex molecules, such as proteins or DNA, reveals the fascinating details of life's building blocks on a microscopic scale. To efficiently determine the molecular composition, we must be adept at interpreting chemical notations, which lead us right into the next crucial concept.

Chemical Notation

Chemical notation, or chemical formula, is the shorthand used by scientists to convey information about the types and spatial arrangement of atoms in a substance. There are a few rules to keep in mind:

• Elements are represented by one or two-letter symbols, where the first letter is always capitalized.
• Subscripts denote the number of atoms of each element in a molecule.
• A coefficient in front of a formula indicates the number of molecules or formula units.

For instance, in the expression \(4\left(CH_3\right)_2 S\), the number 4 is the coefficient, telling us we have four molecules of the compound. The letters are elemental symbols, with C for carbon, H for hydrogen, and S for sulfur. The subscript '2' outside the parentheses multiplies the number of atoms inside, indicating each molecule contains two CH₃ groups. Understanding these notations is vital as it serves as the language through which we can comprehend molecular compositions and engage with the stoichiometry involved in chemical reactions.

Mole Concept

The mole concept is a bridge that connects the microscopic world of atoms and molecules with the macroscopic quantities we can measure. One mole is defined as the amount of a substance that contains as many entities (atoms, molecules, ions, etc.) as there are atoms in 12 grams of carbon-12, which is approximately \(6.022 \times 10^{23}\) entities—a value known as Avogadro's number.

This concept is vital when we interpret chemical reactions quantitatively. For example, knowing the mole ratios of reactants helps us predict the amounts of products that will be formed. If a chemical equation states that 2 moles of hydrogen react with 1 mole of oxygen to form 2 moles of water, we can predict how many grams of water will result from a given number of grams of hydrogen. By understanding the mole concept, we are equipped to carry out precise calculations that are imperative for all sorts of chemical experimentation and industry processes.