Question

Determine the mass of each sample. (a) 1.32 mol carbon tetrafluoride (b) 0.555 mol magnesium fluoride (c) 1.29 mmol carbon disulfide (d) 1.89 kmol sulfur trioxide

Short answer

Mass of each sample: (a) 116.17 g CF4, (b) 34.58 g MgF2, (c) 98.22 mg CS2, (d) 151.3323 kg SO3.

Step-by-step solution

Calculate the Molar Mass of Carbon Tetrafluoride (CF4)

Find the atomic weights of carbon (C) and fluorine (F) from the periodic table. Carbon has an atomic weight of approximately 12.01 g/mol and fluorine has an atomic weight of approximately 19.00 g/mol. The molar mass of CF4 = (1 x 12.01 g/mol) + (4 x 19.00 g/mol) = 12.01 g/mol + 76.00 g/mol = 88.01 g/mol.

Calculate the Mass of the Carbon Tetrafluoride Sample

Use the formula mass (in grams) = number of moles x molar mass. For carbon tetrafluoride, mass = 1.32 mol x 88.01 g/mol = 116.17 g.

Calculate the Molar Mass of Magnesium Fluoride (MgF2)

The atomic weight of magnesium (Mg) is approximately 24.31 g/mol. Using the atomic weights from the periodic table: Molar mass of MgF2 = (1 x 24.31 g/mol) + (2 x 19.00 g/mol) = 24.31 g/mol + 38.00 g/mol = 62.31 g/mol.

Calculate the Mass of the Magnesium Fluoride Sample

Using the formula from Step 2, for magnesium fluoride, mass = 0.555 mol x 62.31 g/mol = 34.58 g.

Calculate the Molar Mass of Carbon Disulfide (CS2)

The atomic weights of carbon (C) and sulfur (S) are approximately 12.01 g/mol and 32.07 g/mol, respectively. The molar mass of CS2 = (1 x 12.01 g/mol) + (2 x 32.07 g/mol) = 12.01 g/mol + 64.14 g/mol = 76.15 g/mol.

Calculate the Mass of the Carbon Disulfide Sample in g

Remember to convert millimoles to moles (1 mmol = 0.001 mol). Therefore, 1.29 mmol = 1.29 x 0.001 mol = 0.00129 mol. The mass of carbon disulfide is then 0.00129 mol x 76.15 g/mol = 0.09822 g.

Calculate the Molar Mass of Sulfur Trioxide (SO3)

The atomic weight of sulfur (S) is approximately 32.07 g/mol and oxygen (O) is 16.00 g/mol. The molar mass of SO3 = (1 x 32.07 g/mol) + (3 x 16.00 g/mol) = 32.07 g/mol + 48.00 g/mol = 80.07 g/mol.

Calculate the Mass of the Sulfur Trioxide Sample in kg

Remember to convert kilometers to moles (1 kmol = 10^3 mol). Therefore, 1.89 kmol = 1.89 x 10^3 mol. The mass of sulfur trioxide is then 1.89 x 10^3 mol x 80.07 g/mol = 151,332.3 g or 151.3323 kg.

Key concepts

Mole-to-Mass Conversion

The concept of mole-to-mass conversion is fundamental in chemistry and provides a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure. It's akin to translating a language, where each atom or molecule's language of 'moles' gets translated to the more familiar 'grams'.

In practice, the process hinges on a simple formula: \(\text{mass} = \text{number of moles} \times \text{molar mass}\). To illustrate, let's consider the example of carbon tetrafluoride (CF₄). Given a certain number of moles, we multiply this by the substance's molar mass, which is the combined atomic weight of all atoms in a molecule, to find the mass in grams.

Understanding this concept allows students to precisely calculate how much material they will need in a reaction or how much they have produced, which is the essence of stoichiometry.

Stoichiometry

Stoichiometry might remind one of a balancing act in mathematics, but instead of numbers, we are juggling atoms and molecules. It involves the calculations of the quantities of reactants and products in a chemical reaction. It's actually the heart of chemistry because everything from baking a cake to launching rockets follows these stoichiometric principles.

To navigate stoichiometry, one must be adept at mole-to-mass conversions and understand the relations expressed in a balanced chemical equation. Each coefficient in a balanced equation tells us the ratio of moles required or produced. Knowing the molar mass of each substance then allows us to convert these mole ratios into mass ratios and vice versa. This precise conversion is crucial to not just understanding chemical reactions but in applying this knowledge in practical scenarios such as pharmaceuticals design or environmental engineering.

Atomic Weight

Atomic weight, also referred to as relative atomic mass, is essentially the 'weight' of an atom of a chemical element, scaled on a relative scale where the carbon-12 isotope equals exactly 12. It is the average weight of an element's atoms, taking into account the various isotopes and their abundances.

The atomic weight of each element is a weighted average that takes into account the abundance of each of the element’s isotopes. For example, carbon's atomic weight of approximately 12.01 g/mol is based on it having mostly carbon-12 isotopes with a dash of carbon-13. This value is crucial because it determines the molar mass of compounds. For instance, the atomic weight of carbon contributes to the calculation of the molar mass of carbon tetrafluoride (CF₄). Since the atomic weight is an average, it enables accurate measurements and preparations in chemistry, which is a testament to its importance in the field.

Chemical Formula

The chemical formula is like a recipe for a compound; it tells you exactly what and how much of each ingredient you need. It denotes the types of atoms present in a compound and the exact number of each type. For instance, in the chemical formula of magnesium fluoride (MgF₂), 'Mg' represents magnesium, and 'F' represents fluorine, and the subscript '2' tells us there are two atoms of fluorine for each atom of magnesium.

A correct chemical formula is essential for calculations in stoichiometry. It helps us understand what's in a compound and allows us to calculate its molar mass. Knowing the formula, we can dissect a compound like sulfur trioxide (SO₃) into its components, understand its structure, and predict its reactive behaviors. The beauty of chemical formulas lies in their ability to offer a window into the microscopic world and a way to characterize the macroscopic world’s substances.