Question

How many atoms of each element are represented in each of the following expressions? (a) \(7 \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\), (b) \(2\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\) (c) \(5 \mathrm{C}_{3} \mathrm{H}_{5}(\mathrm{OH})_{3}\)

Short answer

(a) 14 C atoms, 28 H atoms, 14 O atoms; (b) 4 N atoms, 8 H atoms, 2 C atoms, 2 O atoms; (c) 15 C atoms, 70 H atoms, 15 O atoms.

Step-by-step solution

Identify the elements in each compound

First, determine the different elements that make up each compound. For (a) the elements are Carbon (C), Hydrogen (H), and Oxygen (O). For (b), the elements are Nitrogen (N), Hydrogen (H), Carbon (C), and Oxygen (O). For (c), the elements are Carbon (C), Hydrogen (H), and Oxygen (O).

Calculate the number of atoms of each element in compound (a)

Distribute the coefficient 7 across each element in the chemical formula to find the total number of atoms for each element in compound (a). For C: there are two carbons (one in CH3 and one in CO2), so 2 * 7 = 14. For H: there are four hydrogens (three in CH3 and one in CO2H), so 4 * 7 = 28. For O: there are two oxygens in CO2H, so 2 * 7 = 14.

Calculate the number of atoms of each element in compound (b)

Distribute the coefficient 2 across the subgroups and elements within the parenthesis and formula for compound (b). In the (NH2)2 group, there are two N and four H, so for N: 2 * 2 = 4, and for H: 4 * 2 = 8. There is one C and one O in CO, so for C: 1 * 2 = 2 and for O: 1 * 2 = 2.

Calculate the number of atoms of each element in compound (c)

Multiply the coefficient 5 by the subscript of each element within the compound. For C: there are 3 carbons, so 3 * 5 = 15. For H: there are 5 hydrogens in C3H5, and 3 hydrogens in each OH group, in total 5 + 3*3 = 5 + 9, and multiplied by the coefficient, (5 + 9) * 5 = 14 * 5 = 70. For O: there are three hydrogens in (OH)3, so 3 * 5 = 15.

Key concepts

Chemical Formula Interpretation

Understanding a chemical formula is essential in analyzing the composition of a compound. The formula provides a wealth of information, detailing the types and quantities of atoms present. In a formula like \(7 \mathrm{CH}_{3}\mathrm{CO}_{2}\mathrm{H}\), the letters represent the elements: C for Carbon, H for Hydrogen, and O for Oxygen. Subscripts indicate the quantity of each atom in a single molecule or formula unit. For instance, \(CH_{3}\) means one Carbon atom is bonded to three Hydrogen atoms.

The coefficient at the beginning, such as '7' in the example, multiplies the entire molecule, scaling up the amount by that number. Therefore, interpreting \(7 \mathrm{CH}_{3}\mathrm{CO}_{2}\mathrm{H}\) involves counting the elements and then multiplying each by seven. This coefficient is important when calculating the total number of atoms in a given mass or volume of a substance. Learning to correctly interpret these notations allows for a deeper understanding of molecular composition and is crucial for stoichiometric calculations.

Stoichiometric Calculations

Stoichiometry involves quantitative relationships between reactants and products in chemical reactions, often relying on the balanced chemical equations. When given an expression like \(2(\mathrm{NH}_{2})_{2}\mathrm{CO}\), our task is to calculate the number of atoms of each element.

Methodology

Begin by identifying the groups within the compounds – for instance, \((\mathrm{NH}_{2})_{2}\) indicates two \(\mathrm{NH}_{2}\) groups. Then, apply the provided coefficients to determine the total count of atoms, making sure to distribute these numbers across each atom in the compound. The process entails multiplying the subscript numbers of the atoms by the coefficient, taking into account every group and element within the compound. The outcome of these calculations allows for predictions concerning reactants needed or products formed in a chemical reaction, all rooted in the principle of conservation of mass.

Molecular Composition

The molecular composition refers to the types and numbers of atoms that constitute a molecule. In an expression such as \(5 \mathrm{C}_{3}\mathrm{H}_{5}(\mathrm{OH})_{3}\), not only can we see that the molecule consists of Carbon (C), Hydrogen (H), and Oxygen (O) atoms, but we also understand their respective ratios within the molecule.

Each subscript tells us how many of those atoms are present in one unit of the compound, and the coefficients show how many units we have in total. This information is key when considering the properties of the molecule, such as molecular weight and how it will interact with other substances. For example, the \(\mathrm{OH}\) group signifies a hydroxyl group which impacts the molecule's behavior, including its solubility in water and its boiling point. By grasping the molecular composition, one can infer not only the structure and physical properties of the compound but also the potential chemical reactions it may undergo.