Question

Give the total number of atoms of each element in each of these molecules. (a) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOC}_{2} \mathrm{H}_{5}\) (b) \(\mathrm{HOOCCH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\) (c) \(\mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\) (d) \(\mathrm{C}_{10} \mathrm{H}_{9} \mathrm{NH}_{2} \mathrm{Fe}\) (e) \(\mathrm{C}_{6} \mathrm{H}_{2} \mathrm{CH}_{3}\left(\mathrm{NO}_{2}\right)_{3}\)

Short answer

(a) C: 9, H: 10, O: 2; (b) C: 4, H: 6, O: 4; (c) N: 1, C: 3, H: 7, O: 2; (d) C: 10, H: 11, N: 1, Fe: 1; (e) C: 7, H: 5, N: 3, O: 6.

Step-by-step solution

Analyze Molecular Formula (a)

For the molecule \( \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOC}_{2} \mathrm{H}_{5} \), break down the formula to find the total number of atoms for each element. Count each section of the formula:- \( \mathrm{C}_{6} \): 6 Carbon atoms- \( \mathrm{H}_{5} \): 5 Hydrogen atoms- \( \mathrm{COO} \): 1 Carbon, 2 Oxygen atoms- \( \mathrm{C}_{2} \): 2 Carbon atoms - \( \mathrm{H}_{5} \): 5 Hydrogen atomsSumming these, the molecule has:- Carbon: \(6 + 1 + 2 = 9 \) atoms- Hydrogen: \(5 + 5 = 10 \) atoms- Oxygen: \(2 \) atoms.

Analyze Molecular Formula (b)

For the molecule \( \mathrm{HOOCCH}_{2} \mathrm{CH}_{2} \mathrm{COOH} \), break it down:- \( \mathrm{HOOC} \): 1 Hydrogen, 1 Carbon, 2 Oxygen atoms- \( \mathrm{CH}_{2} \): 1 Carbon, 2 Hydrogen atoms- \( \mathrm{CH}_{2} \): 1 Carbon, 2 Hydrogen atoms- \( \mathrm{COOH} \): 1 Carbon, 2 Oxygen, 1 Hydrogen atomsAdding these together, the molecule has:- Carbon: \(1 + 1 + 1 + 1 = 4 \) atoms- Hydrogen: \(1 + 2 + 2 + 1 = 6 \) atoms- Oxygen: \(2 + 2 = 4 \) atoms.

Analyze Molecular Formula (c)

For the molecule \( \mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH} \), count each section:- \( \mathrm{NH}_{2} \): 1 Nitrogen, 2 Hydrogen atoms- \( \mathrm{CH}_{2} \): 1 Carbon, 2 Hydrogen atoms- \( \mathrm{CH}_{2} \): 1 Carbon, 2 Hydrogen atoms- \( \mathrm{COOH} \): 1 Carbon, 2 Oxygen, 1 Hydrogen atomsThe number of atoms are:- Nitrogen: \(1 \) atom- Carbon: \(1 + 1 + 1 = 3 \) atoms- Hydrogen: \(2 + 2 + 2 + 1 = 7 \) atoms- Oxygen: \(2 \) atoms.

Analyze Molecular Formula (d)

For \( \mathrm{C}_{10} \mathrm{H}_{9} \mathrm{NH}_{2} \mathrm{Fe} \), decompose the formula:- \( \mathrm{C}_{10} \): 10 Carbon atoms- \( \mathrm{H}_{9} \): 9 Hydrogen atoms- \( \mathrm{NH}_{2} \): 1 Nitrogen, 2 Hydrogen atoms- \( \mathrm{Fe} \): 1 Iron atomAdding these, it has:- Carbon: \(10 \) atoms- Hydrogen: \(9 + 2 = 11 \) atoms- Nitrogen: \(1 \) atom- Iron: \(1 \) atom.

Analyze Molecular Formula (e)

For \( \mathrm{C}_{6} \mathrm{H}_{2}\mathrm{CH}_{3}\left(\mathrm{NO}_{2}\right)_{3} \), analyze each component:- \( \mathrm{C}_{6} \): 6 Carbon atoms- \( \mathrm{H}_{2} \): 2 Hydrogen atoms- \( \mathrm{CH}_{3} \): 1 Carbon, 3 Hydrogen atoms- \( \left(\mathrm{NO}_{2}\right)_{3} \): 3 Nitrogen, \(3 \times 2 = 6\) Oxygen atomsThe atom totals are:- Carbon: \(6 + 1 = 7 \) atoms- Hydrogen: \(2 + 3 = 5 \) atoms- Nitrogen: \(3 \) atoms- Oxygen: \(6 \) atoms.

Key concepts

Elemental Composition

Understanding the elemental composition of a molecule is crucial for comprehending its chemical properties and behavior. Elemental composition refers to the elements that make up a compound and the proportion of each element within that compound. In a molecular formula, each element is represented by its chemical symbol, such as C for carbon, H for hydrogen, and O for oxygen. These symbols are followed by subscripts indicating the number of atoms of each element present. For instance, in the molecule \( \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOC}_{2} \mathrm{H}_{5} \), the elemental composition includes three types of atoms: carbon, hydrogen, and oxygen. Each segment of the molecular formula contributes to the overall elemental composition. Recognizing these segments helps in understanding the quantity of individual atoms present and provides insight into the compound's stoichiometry. This knowledge is essential for applications in chemistry such as balancing chemical reactions and determining empirical formulas.

Atom Counting

Atom counting is the process of determining the number of each type of atom within a molecule based on its chemical formula. The molecular formula provides a roadmap for this by listing the types of atoms and their counts. Take for example \( \mathrm{HOOCCH}_{2} \mathrm{CH}_{2} \mathrm{COOH} \). To count atoms, separate each part of the formula. In \( \mathrm{HOOC} \), you find 1 hydrogen, 1 carbon, and 2 oxygen atoms. Repeating this process for each segment ensures that no atom is left uncounted. Using this method helps you arrive at totals such as 4 carbons, 6 hydrogens, and 4 oxygens in this case. Such counting is vital for precise chemical measurement and is instrumental when synthesizing compounds, analyzing reactions, or even deducing the structure of an unknown substance.

Chemical Notation

Chemical notation is a standardized system used to describe chemical compounds and reactions. It employs symbols to represent elements and subscripts to denote the number of atoms. This concise language is powerful, allowing chemists to convey complex information succinctly. Consider the molecule \( \mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH} \). The chemical notation reveals 1 nitrogen (N), denoted as \( \mathrm{NH}_{2} \), where the subscript 2 indicates two hydrogen atoms bonded to nitrogen. This notation continues similarly for the rest of the molecule, helping understand the arrangement and number of each atom type. Such notation is crucial for clarity in communication among scientists, enabling them to exchange information with precision and accuracy. Whether it’s for performing calculations, predicting chemical reactions, or elucidating molecular structures, chemical notation is an essential tool in the chemist's toolkit.