Problem 38 - Chemistry: The Central Science

Question

(a) What is the mass, in grams, of \(1.223\) mol of iron (III) sulfate? (b) How many moles of ammonium ions are in \(6.955 \mathrm{~g}\) of ammonium carbonate? (c) What is the mass, in grams, of \(1.50 \times 10^{21}\) molecules of aspirin, \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\) ? (d) What is the molar mass of diazepam (Valium \()\) if \(0.05570 \mathrm{~mol}\) has a mass of \(15.86 \mathrm{~g}\) ?

Step-by-Step Solution

Answer

(a) The mass of 1.223 mol of Iron (III) sulfate is 489.00 g. (b) There are 0.1447 moles of ammonium ions in 6.955 g of ammonium carbonate. (c) The mass of \(1.50 \times 10^{21}\) molecules of aspirin is 4.486 g. (d) The molar mass of Diazepam (Valium) is 284.6 g/mol.

Step 1: (a) Finding the mass of Iron (III) sulfate

First, we need to find the molar mass of Iron (III) Sulfate. The molar mass is calculated as follows: Iron (III) sulfate: Fe₂(SO₄)₃ Molar mass = 2 × M(Fe) + 3 × (M(S) + 4 × M(O)), where M(Fe), M(S), and M(O) are the molar masses of Iron, Sulfur, and Oxygen respectively. Molar mass of Fe₂(SO₄)₃ = 2 × (55.85 g/mol) + 3 × (32.07 g/mol + 4 × 16.00 g/mol) = 399.88 g/mol Now, we want to find the mass of 1.223 mol of Fe₂(SO₄)₃. Mass = Moles × Molar mass Mass of Iron (III) sulfate = 1.223 mol × 399.88 g/mol = 489.00 g

Step 2: (b) Finding the moles of ammonium ions in ammonium carbonate

First, we need to find the molar mass of Ammonium carbonate: (NH₄)₂CO₃ Molar mass = 2 × (M(N) + 4 × M(H)) + M(C) + 3 × M(O) where M(N), M(H), M(C), and M(O) are the molar masses of Nitrogen, Hydrogen, Carbon, and Oxygen respectively. Molar mass of (NH₄)₂CO₃ = 2 × (14.01 g/mol + 4 × 1.01 g/mol) + 12.01 g/mol + 3 × 16.00 g/mol = 96.11 g/mol Now, we want to find the moles of ammonium carbonate in 6.955 g. Moles = Mass ÷ Molar mass Moles of (NH₄)₂CO₃ = 6.955 g ÷ 96.11 g/mol = 0.07234 mol Since there are 2 moles of ammonium ions (NH₄⁺) in 1 mole of ammonium carbonate, Moles of ammonium ions = 2 × 0.07234 mol = 0.1447 mol

Step 3: (c) Finding the mass of aspirin

First, we need to find the molar mass of aspirin (C₉H₈O₄) Molar mass = 9 × M(C) + 8 × M(H) + 4 × M(O), where M(C), M(H), and M(O) are the molar masses of Carbon, Hydrogen, and Oxygen respectively. Molar mass of C₉H₈O₄ = 9 × 12.01 g/mol + 8 × 1.01 g/mol + 4 × 16.00 g/mol = 180.17 g/mol Now, we have 1.50 × 10²¹ molecules of aspirin. We first convert molecules to moles using Avogadro's constant (6.022 × 10²³/mol): Moles of aspirin = (1.50 × 10²¹) ÷ (6.022 × 10²³/mol) = 0.02492 mol Finally, find the mass of 0.02492 mol of aspirin: Mass = Moles × Molar mass Aspirin mass = 0.02492 mol × 180.17 g/mol = 4.486 g

Step 4: (d) Finding the molar mass of Diazepam (Valium)

We are given the mass (15.86 g) and the moles (0.05570 mol) of Diazepam (Valium). We can find the molar mass directly: Molar mass = Mass ÷ Moles Molar mass of Diazepam (Valium) = 15.86 g ÷ 0.05570 mol = 284.6 g/mol

Key Concepts

Molar Mass

Molar mass is a fundamental concept in stoichiometry. It is the mass of one mole of a given substance, expressed in grams per mole (g/mol). To determine the molar mass of a compound, you need to sum the atomic masses of all the elements present according to their proportions in the compound's chemical formula.
For example, consider the compound Iron (III) sulfate, expressed as Feₓ(SO₄)ᵧ. To find its molar mass, you multiply the atomic mass of iron (Fe) by the number of iron atoms, add to that the sum of the atomic masses of sulfur (S) and oxygen (O) multiplied by their respective counts in the sulfate ion.
Knowing the molar mass is crucial when you need to perform calculations, like converting between mass and moles or determining what mass a certain number of moles corresponds to.

Moles Calculation

Calculating moles involves converting between the mass of a substance and the number of moles it contains. The basic formula used is \( \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \).
Let's apply this formula: if you have a mass amount of a compound, divide this by its molar mass to obtain the number of moles. This is essential for figuring out how much of a substance is present in a specific sample amount.
For compound conversions, once you determine the number of moles, you can further analyze the number of individual elements or ions in the compound using stoichiometry rules, such as multiplying by a ratio based on the chemical formula.

Chemical Formulas

Chemical formulas serve as the shorthand representation of the composition of molecules and compounds. They display the types and quantity of atoms involved. For example, (NH₄)₂CO₃ reflects ammonium carbonate, illustrating that two ammonium ions and one carbonate ion make up the compound.
Understanding the chemical formula allows you to grasp how molecules are built and balanced. A correct interpretation of these formulas is crucial for tasks such as calculating molar masses, interpreting reaction equations, and performing chemical synthesis.
Each part of the formula gives important insight into the compound's chemical and physical properties, helping predict how substances behave in chemical reactions.

Avogadro's Number

Avogadro's number, \( 6.022 \times 10^{23} \), is a constant used to relate the number of particles in a substance to the amount of substance in moles. It tells you how many entities (atoms, molecules, ions) are in one mole of a substance.
This conversion is particularly useful when switching from a number of molecules or atoms to moles and vice versa. For example, to convert molecules of aspirin to moles, you divide the number of molecules by Avogadro's number.
Avogadro's number is a cornerstone of mole calculations. Whether working with atoms or large biomolecules, it allows for consistent and accurate transformations between microscopic countable particles and macroscopic measurable quantities.