Question

Formula Mass and the Mole Concept for Compounds Calculate the number of moles in each sample. $$ \begin{array}{llll}{\text { a. } 72.5 \mathrm{gCCl}_{4}} & {\text { b. } 12.4 \mathrm{g} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}} \\ {\text { c. } 25.2 \mathrm{kg} \mathrm{C}_{2} \mathrm{H}_{2}} & {\text { d. } 12.3 \mathrm{g} \text { of dinitrogen monoxid }}\end{array} $$

Short answer

a. 0.472 moles of CCl4, b. 0.0355 moles of C12H22O11, c. 902.07 moles of C2H2, d. 0.276 moles of N2O. Use the formula mass for each compound and convert the mass of the sample to moles.

Step-by-step solution

Calculate the formula mass of each compound

Find the atomic masses of each element in the compound and multiply it by the number of atoms of that element in the compound. Then, add the masses of all elements together to get the formula mass of the compound. For example, carbon tetrachloride (CCl4) has one carbon atom (12.01 amu) and four chlorine atoms (35.45 amu each). Formula mass of CCl4 = (12.01 amu for C) + 4 * (35.45 amu for Cl) = 153.81 amu.

Convert grams to moles

Use the formula mass to convert grams to moles. The number of moles is equal to the mass of the sample in grams divided by the formula mass of the compound. mole = mass (g) / formula mass (amu). For example, for CCl4: moles of CCl4 = 72.5 g / 153.81 g/mol.

Calculate moles for all compounds

Repeat steps 1 and 2 for each compound given in the exercise. Convert kg to grams if necessary by multiplying by 1000. For example, for C2H2, first convert 25.2 kg to grams: 25.2 kg * 1000 = 25200 g.

Key concepts

Calculating Formula Mass

Understanding the formula mass of a compound is crucial in chemistry, as it represents the sum of the atomic masses of all the atoms in its molecular formula. To calculate it, simply identify each element present in the molecule, refer to the periodic table for the atomic mass of each element, and multiply this by the number of times the element occurs in the molecule.

For instance, in our exercise with carbon tetrachloride (CCl4), there's one carbon atom and four chlorine atoms in the molecular formula. Using the atomic mass unit (amu) as the standard unit of measurement, carbon has an atomic mass of approximately 12.01 amu, and chlorine has an atomic mass of about 35.45 amu. Thus, the formula mass for CCl4 is calculated as \( 12.01 \text{ amu (for } C) + 4 \times 35.45 \text{ amu (for } Cl) = 153.81 \text{ amu} \).

It's crucial to sum these accurately to ensure the subsequent calculations in chemistry, such as stoichiometry, are correct.

Conversion of Grams to Moles

Once the formula mass is known, the conversion of grams to moles becomes a straightforward step. The mole is a fundamental unit in chemistry that measures the amount of substance. One mole of any substance contains Avogadro's number (\(6.022 \times 10^{23}\)) of particles (atoms, molecules, ions, etc.).

To convert the mass of a compound from grams to moles, you divide the mass in grams by the formula mass in amu, which gives you the result in moles. In the example with carbon tetrachloride (CCl4), the calculation would be \(72.5 \text{ g} / 153.81 \text{ g/mol}\), which yields the number of moles of CCl4. This step is imperative for understanding chemical reactions and quantities involved.

Atomic Mass Unit (amu)

The atomic mass unit (amu) is a standard unit of mass that quantifies mass on an atomic or molecular scale. It's defined as one twelfth (\(1/12\)) of the mass of a carbon-12 atom, which is approximately \(1.66 \times 10^{-24}\) grams.

Every element's atomic mass, often noted on the periodic table, is its average mass in amu, taking into account the different isotopes and their abundances. When you're calculating formula mass, you're adding up these atomic masses. It's this precision that allows chemists to make accurate measurements and predictions in their work.

Stoichiometry

Stoichiometry is the section of chemistry that pertains to the measurement of the quantities of reactants and products in chemical reactions. It's based on the laws of conservation of mass and fixed proportions, often represented by balanced chemical equations.

In practice, stoichiometry involves using the mole concept to calculate how much of a reactant is needed to produce a certain amount of product, or vice versa. Each step in our exercise—calculating formula mass and converting grams to moles—is a fundamental stoichiometric technique. By mastering these, one can deduce how different compounds react in defined proportions, ultimately allowing chemists to scale reactions and create new materials.