Question

Formula Mass and the Mole Concept for Compounds Determine the number of moles (of molecules or formula units) in each sample. $$\begin{array}{ll}{\text { a. } 55.98 \mathrm{g} \mathrm{CF}_{2} \mathrm{Cl}_{2}} & {\text { b. } 23.6 \mathrm{kg} \mathrm{Fe}\left(\mathrm{NO}_{3}\right)} \\ {\text { c. } 0.1187 \mathrm{g} \mathrm{C}_{8} \mathrm{H}_{18}} & {\text { d. } 195 \mathrm{kg} \mathrm{CaO}}\end{array}$$

Short answer

a. 0.463 moles of CF2Cl2, b. 97.58 moles of Fe(NO3)3, c. 0.00104 moles of C8H18, d. 3477.23 moles of CaO

Step-by-step solution

Calculate Molar Mass of CF2Cl2

First, calculate the molar mass of CF2Cl2 by adding the atomic masses of carbon (C), fluorine (F), and chlorine (Cl). The atomic masses are approximately C (12.01 g/mol), F (19.00 g/mol), Cl (35.45 g/mol). Therefore, the molar mass of CF2Cl2 is: \(1 \times 12.01 + 2 \times 19.00 + 2 \times 35.45 = 120.91 \text{ g/mol}\).

Convert Grams to Moles for CF2Cl2

Use the molar mass calculated in step 1 to convert grams to moles: \(55.98 \text{ g CF2Cl2} \times \frac{1 \text{ mol}}{120.91 \text{ g}} = 0.463 \text{ moles of CF2Cl2}\).

Calculate Molar Mass of Fe(NO3)3

Calculate the molar mass of Fe(NO3)3 by adding the atomic masses of iron (Fe), nitrogen (N), and oxygen (O). The atomic masses are approximately Fe (55.85 g/mol), N (14.01 g/mol), O (16.00 g/mol). Molar mass of Fe(NO3)3 is: \(1 \times 55.85 + 3 \times (14.01 + 3 \times 16.00) = 241.86 \text{ g/mol}\).

Convert Kilograms to Moles for Fe(NO3)3

First, convert kilograms to grams: \(23.6 \text{ kg} = 23600 \text{ g}\). Then, use the molar mass from step 3 to find moles: \(23600 \text{ g Fe(NO3)3} \times \frac{1 \text{ mol}}{241.86 \text{ g}} = 97.58 \text{ moles of Fe(NO3)3}\).

Calculate Molar Mass of C8H18

Calculate the molar mass of C8H18 (octane) by adding the atomic masses of carbon (C) and hydrogen (H). The atomic masses are approximately C (12.01 g/mol), H (1.008 g/mol). Molar mass of C8H18 is: \(8 \times 12.01 + 18 \times 1.008 = 114.23 \text{ g/mol}\).

Convert Grams to Moles for C8H18

Now, convert grams to moles for C8H18: \(0.1187 \text{ g C8H18} \times \frac{1 \text{ mol}}{114.23 \text{ g}} = 0.00104 \text{ moles of C8H18}\).

Calculate Molar Mass of CaO

Calculate the molar mass of calcium oxide (CaO) by adding the atomic masses of calcium (Ca) and oxygen (O). The atomic masses are approximately Ca (40.08 g/mol), O (16.00 g/mol). Molar mass of CaO is: \(1 \times 40.08 + 1 \times 16.00 = 56.08 \text{ g/mol}\).

Convert Kilograms to Moles for CaO

Convert kilograms to grams and then to moles for CaO: \(195 \text{ kg} = 195000 \text{ g}\). Then use the molar mass to find moles: \(195000 \text{ g CaO} \times \frac{1 \text{ mol}}{56.08 \text{ g}} = 3477.23 \text{ moles of CaO}\).

Key concepts

Molar Mass Calculation

Understanding the molar mass of a substance is crucial for chemists. It represents the mass of one mole of a given substance and is usually expressed in grams per mole (g/mol). To calculate the molar mass, you look at the chemical formula and sum up the atomic masses of all the atoms present. For example, for a compound like CF₂Cl₂, we simply identify each element's atomic mass, multiply it by the number of times the element occurs in the molecule, and add everything together.

Once we have the molar mass, it becomes a powerful tool for converting between grams and moles, a fundamental concept in stoichiometry. Getting the molar mass correct is vital, as errors can compound in later calculations. When introducing this topic, always stress the importance of precise measurement and knowledge of the periodic table.

Converting Grams to Moles

When faced with the task of converting grams to moles, the molar mass serves as our conversion factor. The following formula is the bridge that connects mass to moles: umber of moles = \( \frac{mass of the sample (g)}{molar mass (g/mol)} \).For instance, with CF₂Cl₂, 55.98 grams is equivalent to 0.463 moles using the previously calculated molar mass of 120.91 g/mol. It's a simple ratio, yet it forms the backbone of much of quantitative chemistry. Emphasize the idea that grams measure the amount of matter we have, while moles count the number of molecules, and this calculation bridges the two.

Atomic Mass

At its core, atomic mass is the weight of a single atom, usually expressed in atomic mass units (amu) or the more practical unit for chemistry applications, grams per mole when referring to a mole of atoms. Atomic mass is found on the periodic table for each element, like carbon with an atomic mass of approximately 12.01 g/mol. In the exercises, we utilize these masses as building blocks to determine the molar mass of compounds. Teach students to view the periodic table not just as a list of elements, but as a resource filled with data crucial for their calculations in chemistry.

Stoichiometry

Stoichiometry is where all these concepts intersect. It deals with the quantitative relationships of the substances as they participate in chemical reactions.

When working out problems involving stoichiometry, we use balanced chemical equations to determine the proportions in which reactants combine and products form. The calculations depend on the mole ratio, derived from the coefficients in the balanced equation. Understanding mole concept, molar mass, and how to convert grams to moles is tantamount to mastering stoichiometry. A solid grasp of stoichiometry is essential for any budding chemist as it’s applied in tasks ranging from laboratory experiments to industrial chemical production.