Question

Determine the formula weights of each of the following compounds: (a) nitric acid, \(\mathrm{HNO}_{3} ;\) (b) \(\mathrm{KMnO}_{4}\); (c) \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\); (d) quartz, \(\mathrm{SiO}_{2} ;\) (e) gallium sulfide, (f) chromium(III) sulfate, (g) phosphorus trichloride.

Short answer

The formula weights of the compounds are as follows: (a) Nitric Acid (HNO3) is 63.02 g/mol, (b) KMnO4 is 158.04 g/mol, (c) Ca3(PO4)2 is 310.18 g/mol, (d) Quartz (SiO2) is 60.09 g/mol, (e) Gallium Sulfide (Ga2S3) is 235.65 g/mol, (f) Chromium(III) Sulfate (Cr2(SO4)3) is 392.202 g/mol, and (g) Phosphorus Trichloride (PCl3) is 137.32 g/mol.

Step-by-step solution

Identify the elements and their atomic weights in each compound

We will be referencing the periodic table to find the atomic weights of the elements in each compound. (a) Nitric Acid (HNO3): H (Hydrogen) = 1.01 N (Nitrogen) = 14.01 O (Oxygen) = 16.00 (b) KMnO4: K (Potassium) = 39.10 Mn (Manganese) = 54.94 O (Oxygen) = 16.00 (c) Ca3(PO4)2: Ca (Calcium) = 40.08 P (Phosphorus) = 30.97 O (Oxygen) = 16.00 (d) Quartz (SiO2): Si (Silicon) = 28.09 O (Oxygen) = 16.00 (e) Gallium Sulfide (Ga2S3): Ga (Gallium) = 69.72 S (Sulfur) = 32.07 (f) Chromium(III) Sulfate (Cr2(SO4)3): Cr (Chromium) = 51.996 S (Sulfur) = 32.07 O (Oxygen) = 16.00 (g) Phosphorus Trichloride (PCl3): P (Phosphorus) = 30.97 Cl (Chlorine) = 35.45

Calculate the formula weights of the compounds

Now that we have the atomic weights of each element, we can calculate the formula weights of the compounds using the appropriate molar ratios. (a) Nitric Acid (HNO3): Formula weight = (1 x H) + (1 x N) + (3 x O) = (1 x 1.01) + (1 x 14.01) + (3 x 16.00) = 1.01 + 14.01 + 48.00 = 63.02 g/mol (b) KMnO4: Formula weight = (1 x K) + (1 x Mn) + (4 x O) = (1 x 39.10) + (1 x 54.94) + (4 x 16.00) = 39.10 + 54.94 + 64.00 = 158.04 g/mol (c) Ca3(PO4)2: Formula weight = (3 x Ca) + (2 x ((1 x P) + (4 x O))) = (3 x 40.08) + (2 x ((1 x 30.97) + (4 x 16.00))) = 120.24 + (2 x (30.97 + 64.00)) = 120.24 + (2 x 94.97) = 120.24 + 189.94 = 310.18 g/mol (d) Quartz (SiO2): Formula weight = (1 x Si) + (2 x O) = (1 x 28.09) + (2 x 16.00) = 28.09 + 32.00 = 60.09 g/mol (e) Gallium Sulfide (Ga2S3): Formula weight = (2 x Ga) + (3 x S) = (2 x 69.72) + (3 x 32.07) = 139.44 + 96.21 = 235.65 g/mol (f) Chromium(III) Sulfate (Cr2(SO4)3): Formula weight = (2 x Cr) + (3 x ((1 x S) + (4 x O))) = (2 x 51.996) + (3 x ((1 x 32.07) + (4 x 16.00))) = 103.992 + (3 x (32.07 + 64.00)) = 103.992 + (3 x 96.07) = 103.992 + 288.21 = 392.202 g/mol (g) Phosphorus Trichloride (PCl3): Formula weight = (1 x P) + (3 x Cl) = (1 x 30.97) + (3 x 35.45) = 30.97 + 106.35 = 137.32 g/mol

Key concepts

Chemical Compounds

Chemical compounds are substances formed from two or more chemical elements that are bound together in a fixed ratio. When elements combine, they do so to form a product with distinct properties, different from those of the individual elements. For example, water (H_2O) is a compound consisting of hydrogen and oxygen atoms linked together. In chemistry, understanding the composition of various compounds is fundamental, as it allows us to predict how these compounds will behave under different conditions.

To illustrate how compounds are constituted, let’s consider nitric acid (HNO_3), quartz (SiO_2), and gallium sulfide. In each case, specific ratios of atoms are combined to produce a substance with unique physical and chemical properties. The process of formation and the resulting properties are governed by the rules of chemical bonding and molecular structure, which are topics of great interest in the study of chemistry.

Molar Mass

Molar mass is a fundamental concept in chemistry, representing the mass of one mole of a substance, measured in grams per mole (g/mol). It is an aggregate measure that reflects the combined atomic weights of the atoms making up a chemical compound. Calculating the molar mass of compounds is a basic yet crucial skill for students as it is used in stoichiometry to convert between grams and moles. To compute the molar mass, you must know the atomic weight of each element comprising the compound and the number of atoms of each element.

For example, the molar mass of nitric acid (HNO_3) is calculated by summing the atomic weights of hydrogen (H), nitrogen (N), and oxygen (O), each multiplied by their respective number of atoms in one molecule of the compound. This step is crucial in many laboratory calculations, such as preparing solutions with precise molar concentrations or performing chemical reactions that require balanced quantities of reactants.

Periodic Table

The periodic table is an organized table of elements, structured in rows (periods) and columns (groups). Each element on the periodic table is represented by its chemical symbol and exhibits its unique atomic number, which signifies the number of protons in its nucleus. For students and scientists alike, the periodic table serves as a comprehensive tool for understanding elemental properties, predicting chemical reactions, and selecting elements for various applications.

The key to using the periodic table effectively lies in understanding its layout. Elements are arranged in order of increasing atomic number, and elements with similar chemical behaviors are grouped together. This principle aids in quickly retrieving vital information, like relative atomic weights, which are essential for calculating formula weights of chemical compounds. For instance, to determine the formula weight of KMnO_4 (potassium permanganate), you would locate potassium (K), manganese (Mn), and oxygen (O) on the table to find their atomic weights.

Atomic Weights

Atomic weights, also referred to as relative atomic masses, are numerical values that describe the average mass of atoms of an element compared to one twelfth of the mass of a carbon-12 atom. These weights take into account the presence of different isotopes and their abundances. Atomic weights are not constants; rather, they are averages that reflect isotopic distribution for elements from Earth's crust, atmosphere, and oceans.

These weights are especially important when calculating the formula weight of a given chemical compound. For instance, in compounds like chromium(III) sulfate (Cr_2(SO_4)_3), the relative weights of chromium (Cr), sulfur (S), and oxygen (O) are needed. The atomic weights can be found on the periodic table, and for most elements, they are shown as a decimal number because they are an average of the isotope masses. This knowledge is vital in translating the microscopic world of atoms and molecules into a format we can measure, manipulate, and apply in real-world scenarios.