Problem 28 - Chemistry: Principles and Reactions

Question

Convert the following to moles. (a) \(35.00 \mathrm{~g}\) of \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\), a chlorofluorocarbon that destroys the ozone layer in the atmosphere (b) \(100.0 \mathrm{mg}\) of iron(II) sulfate, an iron supplement prescribed for anemia (c) \(2.00 \mathrm{~g}\) of Valium \(\left(\mathrm{C}_{15} \mathrm{H}_{13} \mathrm{ClN}_{2} \mathrm{O}-\right.\) diazepam \()\)

Step-by-Step Solution

Answer

Question: Calculate the number of moles for each of the following substances: (a) 35.00 g of CF2Cl2, (b) 32.00 mg of iron(II) sulfate (FeSO4), and (c) 2.00 g of diazepam (C15H13ClN2O).

Step 1: Find the molar mass of CF2Cl2

Find the molar mass of each element in the formula using the periodic table: C = 12.01 g/mol, F = 19.00 g/mol, and Cl = 35.45 g/mol. Then calculate the molar mass of CF2Cl2 using the formula: Molar mass = (1 x C) + (2 x F) + (2 x Cl)

Step 2: Calculate the moles of CF2Cl2

Use the molar mass and the given mass of CF2Cl2 to calculate the number of moles: Number of moles = (35.00 g) / (Molar mass of CF2Cl2) #(b):#

Step 1: Find the molar mass of FeSO4

Find the molar mass of each element in the formula using the periodic table: Fe = 55.85 g/mol, S = 32.07 g/mol, and O = 16.00 g/mol. Then calculate the molar mass of FeSO4 using the formula: Molar mass = (1 x Fe) + (1 x S) + (4 x O)

Step 2: Convert mg to g

We need to convert the mass of iron(II) sulfate from mg to g. We can do this using the conversion factor: 1 g = 1000 mg

Step 3: Calculate the moles of FeSO4

Use the molar mass and the given mass of FeSO4 to calculate the number of moles: Number of moles = (mass in g) / (Molar mass of FeSO4) #(c):#

Step 1: Find the molar mass of C15H13ClN2O

Find the molar mass of each element in the formula using the periodic table: C = 12.01 g/mol, H = 1.01 g/mol, Cl = 35.45 g/mol, N = 14.01 g/mol, and O = 16.00 g/mol. Then calculate the molar mass of C15H13ClN2O using the formula: Molar mass = (15 x C) + (13 x H) + (1 x Cl) + (2 x N) + (1 x O)

Step 2: Calculate the moles of C15H13ClN2O

Use the molar mass and the given mass of diazepam to calculate the number of moles: Number of moles = (2.00 g) / (Molar mass of C15H13ClN2O)

Key Concepts

Molar Mass Calculation

The concept of molar mass is central to chemistry and is particularly important when it comes to mole conversion exercises. Molar mass, expressed in grams per mole (g/mol), represents the weight of one mole of a substance. To calculate the molar mass of a compound, you need to know the chemical formula of the substance and the atomic mass of each element that composes it.

To illustrate this concept, let's consider the first exercise where the molar mass of chlorofluorocarbon \textbf{CF}\(_2\)\textbf{Cl}\(_2\) is determined. The process involves multiplying the atomic mass of each element by the number of atoms of that element in the formula and adding these values together. For example,

\textbf{Molar mass} = (1 x 12.01 g/mol) + (2 x 19.00 g/mol) + (2 x 35.45 g/mol)

With this calculation, we derive the molar mass of the compound, which is then used to convert a given mass of the substance into moles, providing a bridge between the mass of a substance and the number of particles contained in that mass.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the calculation of the reactants and products in chemical reactions. It is grounded on the law of conservation of mass where the total mass of the reactants equals the total mass of the products. The stoichiometric calculations often involve mole conversions, which take into account the molar mass of the substances involved.

Understanding stoichiometry is essential for solving problems like the ones given in the exercise, where you have to convert the mass of a substance to moles. Here's how the process follows:

• Use the molar mass of the substance, derived from its chemical formula, to determine the number of moles contained in a given mass.
• Apply this concept along with stoichiometric coefficients from a balanced chemical equation to relate amounts of one substance to another.

In the case of exercise (b), once the molar mass of iron(II) sulfate is known, the mass given in milligrams is first converted to grams, adhering to stoichiometric principles, and then to moles using the molar mass.

Chemical Formula

A chemical formula is a symbolic representation of a substance that indicates the elements present and their relative proportions. It is critical for determining the molar mass of a compound, which in turn is essential for conversions between mass and moles. The chemical formula provides the necessary information to understand the composition of a molecule and thus play a pivotal role in stoichiometry and mole conversions.

When examining a chemical formula, such as \textbf{C}\(_{15}\)\textbf{H}\(_{13}\)\textbf{ClN}\(_2\)\textbf{O} for Valium, the subscripts tell us the number of atoms of each element in one molecule of the compound. Knowing this, we can calculate its molar mass by summing the atomic masses of its constituent atoms, just as shown in the solution for exercise (c). It's fundamental to grasp the concept of a chemical formula to seamlessly transition from the symbolic to the quantitative analysis of substances in chemistry.