Question

Calculate the number of molecules present in each of the following samples. a. 3.54 moles of sulfur dioxide, \(\mathrm{SO}_{2}\) b. 3.54 g of sulfur dioxide, \(\mathrm{SO}_{2}\) c. \(4.46 \times 10^{-5} \mathrm{~g}\) of ammonia, \(\mathrm{NH}_{3}\) d. \(4.46 \times 10^{-5}\) moles of ammonia, \(\mathrm{NH}_{3}\) e. \(1.96 \mathrm{mg}\) of ethane, \(\mathrm{C}_{2} \mathrm{H}_{6}\)

Short answer

The number of molecules present in each sample is as follows: a. \(2.13 \times 10^{24}\) molecules of sulfur dioxide b. \(3.32 \times 10^{22}\) molecules of sulfur dioxide c. \(1.58 \times 10^{18}\) molecules of ammonia d. \(2.68 \times 10^{19}\) molecules of ammonia e. \(3.93 \times 10^{19}\) molecules of ethane

Step-by-step solution

Identify the given values and find molar masses

For all cases, we have the given values. We also need to find the molar mass for each substance (sulfur dioxide, ammonia, and ethane) using the periodic table: 1. Sulfur dioxide, \(\mathrm{SO}_{2}\): Molar mass = 32.1 g/mol (for S) + 2 * 16.0 g/mol (for O) = 64.1 g/mol 2. Ammonia, \(\mathrm{NH}_{3}\): Molar mass = 14.0 g/mol (for N) + 3 * 1.0 g/mol (for H) = 17.0 g/mol 3. Ethane, \(\mathrm{C}_{2} \mathrm{H}_{6}\): Molar mass = 2 * 12.0 g/mol (for C) + 6 * 1.0 g/mol (for H) = 30.0 g/mol

Calculate the number of molecules for each substance

Use the given values, molar masses, and Avogadro's number to calculate the number of molecules present in each sample. a. 3.54 moles of sulfur dioxide, \(\mathrm{SO}_{2}\): This value is already in moles, so we just need to convert it to molecules using Avogadro's number: Molecules = 3.54 moles * Avogadro's number Molecules = 3.54 moles * \(6.022 \times 10^{23}\) molecules/mol Molecules = \(2.13 \times 10^{24}\) molecules of sulfur dioxide b. 3.54 g of sulfur dioxide, \(\mathrm{SO}_{2}\): First, convert grams to moles using the molar mass, and then convert moles to molecules using Avogadro's number: Moles = 3.54 g / 64.1 g/mol = 0.0552 moles Molecules = 0.0552 moles * \(6.022 \times 10^{23}\) molecules/mol Molecules = \(3.32 \times 10^{22}\) molecules of sulfur dioxide c. \(4.46 \times 10^{-5} \mathrm{~g}\) of ammonia, \(\mathrm{NH}_{3}\): Moles = \(4.46 \times 10^{-5} \mathrm{~g}\) / 17.0 g/mol = \(2.62 \times 10^{-6}\) moles Molecules = \(2.62 \times 10^{-6}\) moles * \(6.022 \times 10^{23}\) molecules/mol Molecules = \(1.58 \times 10^{18}\) molecules of ammonia d. \(4.46 \times 10^{-5}\) moles of ammonia, \(\mathrm{NH}_{3}\): Molecules = \(4.46 \times 10^{-5}\) moles * \(6.022 \times 10^{23}\) molecules/mol Molecules = \(2.68 \times 10^{19}\) molecules of ammonia e. \(1.96 \mathrm{mg}\) of ethane, \(\mathrm{C}_{2} \mathrm{H}_{6}\): First, convert mg to g and then proceed with the same steps as before. Mass in grams = 1.96 mg * (1 g / 1000 mg) = 0.00196 g Moles = 0.00196 g / 30.0 g/mol = \(6.53 \times 10^{-5}\) moles Molecules = \(6.53 \times 10^{-5}\) moles * \(6.022 \times 10^{23}\) molecules/mol Molecules = \(3.93 \times 10^{19}\) molecules of ethane

Key concepts

Avogadro's Number

When studying chemistry, one of the foundational concepts is that of Avogadro's number. This number, named after the Italian scientist Amedeo Avogadro, is used to represent the number of units in one mole of any substance. To be precise, Avogadro's number is equal to exactly 6.02214076 ×10^23. This could be atoms, ions, or in this context, molecules.

Understanding Avogadro's number is crucial for bridging the gap between the microscopic world, where things are too small to count, and the macroscopic world, where we measure substances in grams or moles. This large number provides a way to discuss a practical quantity of particles. Whether you are calculating the number of molecules in a certain amount of moles of a gas, or trying to understand the number of atoms that make up a crystal lattice, Avogadro's number is your key to the molecular scale.

Moles to Molecules Conversion

Converting moles to molecules is a central skill in chemistry that makes use of Avogadro's number. As seen in the solved exercises, this conversion relies on the straightforward principle that one mole of any substance contains Avogadro's number of molecules or atoms.

To execute this conversion, simply multiply the number of moles by Avogadro's number, which is the numerical value we discussed earlier. This simple multiplication translates moles, a convenient measurement of chemical amounts at the human scale, into molecules, the actual number of particles present at the atomic scale.

Here's the formula:
\[\text{{Number of molecules}} = \text{{Moles}} \times \text{{Avogadro's number}}\]
Using the exercises from the problem provided, when provided with the amount in moles, one can directly apply this conversion to determine how many individual molecules are present in the given sample. This step is an essential component in analyzing chemical reactions and calculating yields of products as well.

Chemical Molar Mass

The molar mass of a chemical compound is another crucial concept and it's the bridge between the mass of a substance we can measure and the number of moles which chemists use for calculations. This value represents the mass of one mole of a substance and is measured in grams per mole (g/mol).

To find the molar mass of a compound, we add up the atomic masses of all the atoms in the molecular formula, which are conveniently listed in the periodic table. For example, for sulfur dioxide (SO2), we take the atomic masses of sulfur and oxygen and calculate the molar mass by adding one sulfur atom's mass to that of two oxygen atoms.

Here's the calculation for sulfur dioxide:
\[\text{{Sulfur dioxide molar mass}} = (1 \times 32.1) \text{{g/mol}} + (2 \times 16.0) \text{{g/mol}} = 64.1 \text{{g/mol}}\]
A correct molar mass is essential to convert between grams and moles—a step that is often necessary when preparing chemical solutions or reacting substances in stoichiometric calculations. In the given exercises, correct molar mass calculations enabled the accurate conversion from grams to moles before applying Avogadro's number to reach the final answer.