Problem 81 - Chemistry: An Atoms-Focused Approach

Question

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

Step-by-Step Solution

Answer

Answer: The molar masses of the gases are: (a) SO2 = 64.07 g/mol, (b) O3 = 48.00 g/mol, (c) CO2 = 44.01 g/mol, and (d) N2O5 = 108.02 g/mol.

Step 1: Calculate the molar mass of SO2

To do this, multiply the molar mass of each element by the number of atoms in the compound and add the results. M(SO2) = M(S) + 2 * M(O) = 32.07 g/mol + 2 * 16.00 g/mol = 32.07 g/mol + 32.00 g/mol = 64.07 g/mol The molar mass of SO2 is 64.07 g/mol.

Step 2: Calculate the molar mass of O3

There are three atoms of oxygen in O3. M(O3) = 3 * M(O) = 3 * 16.00 g/mol = 48.00 g/mol The molar mass of O3 is 48.00 g/mol.

Step 3: Calculate the molar mass of CO2

M(CO2) = M(C) + 2 * M(O) = 12.01 g/mol + 2 * 16.00 g/mol = 12.01 g/mol + 32.00 g/mol = 44.01 g/mol The molar mass of CO2 is 44.01 g/mol.

Step 4: Calculate the molar mass of N2O5

M(N2O5) = 2 * M(N) + 5 * M(O) = 2 * 14.01 g/mol + 5 * 16.00 g/mol = 28.02 g/mol + 80.00 g/mol = 108.02 g/mol The molar mass of N2O5 is 108.02 g/mol. In conclusion: (a) M(SO2) = 64.07 g/mol (b) M(O3) = 48.00 g/mol (c) M(CO2) = 44.01 g/mol (d) M(N2O5) = 108.02 g/mol

Key Concepts

Chemical Formulas

Chemical formulas are representations of molecules using element symbols and numbers to show the types and numbers of atoms present. Understanding chemical formulas is key to calculating molar masses, as it informs us how many atoms of each element make up a compound.

For example, in the chemical formula for sulfur dioxide, \( \mathrm{SO}_{2} \), the \( \mathrm{S} \) represents sulfur, and the \( \mathrm{O}_{2} \) indicates that there are two oxygen atoms bonded to one sulfur atom. Learning to interpret these formulas helps in determining molecular compositions and is foundational to stoichiometry calculations.

Some tips for understanding chemical formulas include:

• Recognizing element symbols: Each element on the periodic table has a unique symbol, like \( \mathrm{C} \) for carbon.
• Interpreting subscripts: Numbers written as subscripts indicate the count of atoms of that element in the compound, like the '2' in \( \mathrm{CO}_{2} \).
• Knowing common groups: Familiarize yourself with common molecular structures and formulas, such as \( \mathrm{H}_{2} \mathrm{O} \) for water.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It uses the balanced chemical equation to relate quantities of molecules to each other. Understanding stoichiometry is critical when you need to know how much of a substance is needed or produced in a reaction.

For instance, when calculating molar masses as seen in the exercise, stoichiometry helps in understanding the proportional relationship.

When sulfur dioxide (\( \mathrm{SO}_{2} \)) is formed, stoichiometry lets us accurately calculate the molar mass as each sulfur atom and two oxygen atoms contribute to the overall grams per mole, as stated in the chemical formula:

• Calculate individual atomic contributions: Use the molar mass of each element, as done in steps outlined in the solution.
• Add up these contributions: The stoichiometric coefficients (subscripts) guide how these are combined, leading to the total compound mass.

By outlining clear steps using stoichiometry, we ensure correct and efficient chemical calculations.

Atomic Mass

Atomic mass is the mass of a single atom, typically expressed in atomic mass units (amu) or grams per mole (g/mol) when considering a mole of atoms. It's an essential concept when calculating the molar mass of chemical compounds. For example, the atomic mass of oxygen is approximately 16.00 g/mol. This value is used to calculate the molar mass of compounds containing oxygen, as seen in the solution. Key points about atomic mass:

• Atomic mass affects molar mass: Since molar mass is the sum of individual atomic masses in a molecule, understanding atomic masses helps determine overall mass.
• Variability due to isotopes: Elements can have isotopes, which affect the average atomic mass listed on the periodic table.
• Periodic table reference: Always refer to the periodic table for the most accurate atomic mass information for each element.

With these insights, you can confidently approach calculating and comprehending molecular masses effectively.