Problem 33 - Chemistry The Science in Context

Question

Calculate the molar masses of the following atmospheric molecules: \((\mathrm{a}) \mathrm{SO}_{2} ;(\mathrm{b}) \mathrm{O}_{3} ;(\mathrm{c}) \mathrm{CO}_{2} ;(\mathrm{d}) \mathrm{N}_{2} \mathrm{O}_{5}\).

Step-by-Step Solution

Answer

Question: Calculate the molar masses of the following atmospheric molecules: SO2, O3, CO2, and N2O5. Answer: The molar masses of the given atmospheric molecules are: a) SO2: 64.07 g/mol b) O3: 48.00 g/mol c) CO2: 44.01 g/mol d) N2O5: 108.02 g/mol

Step 1: Identify the elements present in each molecule

For each molecule, we need to identify the elements present and their respective quantities. Based on the given molecular formulas, we have: a) SO2: 1 Sulfur atom (S) and 2 Oxygen atoms (O) b) O3: 3 Oxygen atoms (O) c) CO2: 1 Carbon atom (C) and 2 Oxygen atoms (O) d) N2O5: 2 Nitrogen atoms (N) and 5 Oxygen atoms (O)

Step 2: Find the molar mass of each element

Using the periodic table, we can find the molar mass of each element present in the molecules as follows: Sulfur (S): 32.07 g/mol Oxygen (O): 16.00 g/mol Carbon (C): 12.01 g/mol Nitrogen (N): 14.01 g/mol

Step 3: Calculate the molar mass of each molecule

We will multiply the molar mass of each element by the number of atoms of that element in the molecule and then sum up the molar masses of all elements in each molecule to obtain the total molar mass. a) SO2: (1 × 32.07) + (2 × 16.00) = 32.07 + 32.00 = 64.07 g/mol b) O3: (3 × 16.00) = 48.00 g/mol c) CO2: (1 × 12.01) + (2 × 16.00) = 12.01 + 32.00 = 44.01 g/mol d) N2O5: (2 × 14.01) + (5 × 16.00) = 28.02 + 80.00 = 108.02 g/mol So the molar masses of the given atmospheric molecules are: a) SO2: 64.07 g/mol b) O3: 48.00 g/mol c) CO2: 44.01 g/mol d) N2O5: 108.02 g/mol

Key Concepts

Molecular Formula

When studying chemistry, the molecular formula is a crucial piece of information that represents the number and types of atoms that constitute a single molecule of a substance. It provides an exact count of how many atoms of each element are included within that compound. For instance, the molecular formula for water is H₂O, which tells us that there are two hydrogen (H) atoms and one oxygen (O) atom in each water molecule.

Understanding the molecular formula is key to performing chemical calculations, such as determining the molar mass. The precision of the formula allows for accurate and consistent computations across various chemical contexts.

Periodic Table

The periodic table is a chemist's roadmap, offering a wealth of information arranged in a manageable and systematic way. Each box in the table represents a different element, displaying its atomic number, symbol, average atomic mass, and sometimes additional data such as electron configurations. The arrangement of the elements based on increasing atomic number and chemical properties allows for predictable patterns to emerge.

Understanding the organization of the periodic table supports the identification of elements and the gathering of data, such as atomic mass, which is vital for the calculation of molar masses of compounds as outlined in the original exercise.

Atomic Mass

The atomic mass, commonly expressed in atomic mass units (amu) or grams per mole (g/mol), reflects the average mass of an atom of an element, taking into account the distribution of its isotopes. One mole of a substance contains Avogadro's number of entities (approximately 6.022 x 10²³), and thus the atomic mass also represents the mass of one mole of an element's atoms.

When calculating molar masses for molecules, the atomic mass of each element is required. To calculate the molar masses of the atmospheric molecules SO₂, O₃, CO₂, and N₂O₅, we used the atomic masses for Sulfur, Oxygen, Carbon, and Nitrogen obtained from the periodic table.

Stoichiometry

Stoichiometry is the section of chemistry concerned with the relative quantities of reactants and products in chemical reactions. At the heart of stoichiometry lies the balanced chemical equation, from which the proportions of each substance involved can be deduced. Stoichiometric calculations can involve aspects like calculating the amounts of reactants needed or products produced, or as illustrated in our original exercise, determining the molar mass of a compound from its molecular formula.

By using the stoichiometry principles, we can accurately calculate how many moles of each element are present in a given molecular formula and then use that information to find the total molar mass of the compound. This is done by adding up the atomic masses (in g/mol) of all the atoms contained within the molecule.