Problem 24 - Chemistry: The Central Science in SI Units, Global Edition

Question

Determine the formula weights of each of the following compounds: (a) Butyric acid, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH},\) which is responsible for the rotten smell of spoiled food; (b) sodium perborate, \(\mathrm{NaBO}_{3}\), a substance used as bleach; (c) calcium carbonate, \(\mathrm{CaCO}_{3},\) a substance found in marble. (c) \(\mathrm{CF}_{2} \mathrm{Cl}_{2},\) a refrigerant known as Freon; \((\mathbf{d}) \mathrm{NaHCO}_{3},\) known as baking soda and used in bread and pastry baking; \((\mathbf{e})\) iron pyrite, \(\mathrm{FeS}_{2}\) which has a golden appearance and is known as "Fool's Gold."

Step-by-Step Solution

Answer

The formula weights for the given compounds are as follows: (a) Butyric acid, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\): 88.12 (b) Sodium perborate, \(\mathrm{NaBO}_{3}\): 81.80 (c) Calcium carbonate, \(\mathrm{CaCO}_{3}\): 100.09 (d) Freon, \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\): 120.91 (e) Iron pyrite, \(\mathrm{FeS}_{2}\): 119.99

Step 1: Identify atomic weights

Consult the periodic table to find the atomic weights of each element in butyric acid: - C: 12.01 - H: 1.01 - O: 16.00 Remember that there are 4 Carbon atoms, 8 Hydrogen atoms, and 2 Oxygen atoms in the formula.

Step 2: Multiply and sum

Multiply the atomic weights by the number of atoms and then sum the results: Formula weight = (4 × 12.01) + (8 × 1.01) + (2 × 16.00) = 48.04 + 8.08 + 32.00 = 88.12 (b) Sodium perborate, \(\mathrm{NaBO}_{3}\)

Step 1: Identify atomic weights

Consult the periodic table to find the atomic weights of each element in sodium perborate: - Na: 22.99 - B: 10.81 - O: 16.00

Step 2: Multiply and sum

Multiply the atomic weights by the number of atoms and sum the results: Formula weight = 22.99 + 10.81 + (3 × 16.00) = 22.99 + 10.81 + 48.00 = 81.80 (c) Calcium carbonate, \(\mathrm{CaCO}_{3}\)

Step 1: Identify atomic weights

Consult the periodic table to find the atomic weights of each element in calcium carbonate: - Ca: 40.08 - C: 12.01 - O: 16.00

Step 2: Multiply and sum

Multiply the atomic weights by the number of atoms and sum the results: Formula weight = 40.08 + 12.01 + (3 × 16.00) = 40.08 + 12.01 + 48.00 = 100.09 (d) Freon, \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\)

Step 1: Identify atomic weights

Consult the periodic table to find the atomic weights of each element in Freon: - C: 12.01 - F: 19.00 - Cl: 35.45

Step 2: Multiply and sum

Multiply the atomic weights by the number of atoms and sum the results: Formula weight = 12.01 + (2 × 19.00) + (2 × 35.45) = 12.01 + 38.00 + 70.90 = 120.91 (e) Iron pyrite, \(\mathrm{FeS}_{2}\)

Step 1: Identify atomic weights

Consult the periodic table to find the atomic weights of each element in iron pyrite: - Fe: 55.85 - S: 32.07

Step 2: Multiply and sum

Multiply the atomic weights by the number of atoms and sum the results: Formula weight = 55.85 + (2 × 32.07) = 55.85 + 64.14 = 119.99

Key Concepts

Atomic Weight

Atomic weight is the average mass of atoms of an element, expressed in atomic mass units (amu). To accurately determine atomic weights, scientists consider the distribution of isotopes of an element found in nature with their relative abundances. This value helps in calculating the molecular or formula weights of compounds. When we mention atomic weight, it's important to remember that it is often used interchangeably with "atomic mass," although they have slight differences. Atomic weight takes a weighted average considering all isotopes, whereas atomic mass refers directly to a singular atom's mass. For example, the atomic weight of carbon is approximately 12.01 amu, considering its isotopes like Carbon-12 and Carbon-13. This value is found directly on the periodic table, aiding in the quick calculation of molecular weights.

Formula Weights

Formula weights, also known as molecular weights, are the total weights of all atoms in a chemical formula. To compute the formula weight of a compound, first, identify all the elements present in the molecule. Then, look up each element's atomic weight on the periodic table. Multiply the atomic weight of each element by the number of times the element appears in the compound. Finally, sum all these products to get the formula weight.For instance, in sodium perborate (\(\mathrm{NaBO}_{3}\)), calculate its formula weight as follows:

• Identify atomic weights: Na (22.99 amu), B (10.81 amu), O (16.00 amu).
• Calculate the total weight: 22.99 + 10.81 + (3 × 16.00) = 81.80 amu.

This systematic approach helps in determining the precise weight of various compounds, crucial for chemical reactions and stoichiometric calculations.

Periodic Table

The periodic table is a vital tool in chemistry, providing essential information about all known elements. Conceived by Dmitri Mendeleev, the periodic table arranges elements by increasing atomic number, and groups them based on similar chemical properties. Each element's square on the table displays its atomic number, chemical symbol, and often its atomic weight.By consulting the periodic table, chemists can quickly find the atomic weights necessary for calculations such as those required to determine the formula weight of a compound. For example, if calculating the formula weight of calcium carbonate (\(\mathrm{CaCO}_{3}\)), you find:

• Calcium (Ca) at about 40.08 amu
• Carbon (C) at about 12.01 amu
• Oxygen (O) at about 16.00 amu

Thus, the periodic table is an indispensable resource in both educational contexts and professional chemical problem-solving.