Problem 24 - Chemistry The Central Science In Si Units

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

(a) 88.12 g/mol, (b) 81.80 g/mol, (c) 100.09 g/mol, (d) 120.91 g/mol, (e) 84.01 g/mol, (f) 119.99 g/mol.

Step 1: Calculate Formula Weight of Butyric Acid (CH3CH2CH2COOH)

To find the formula weight, sum the atomic weights of all atoms in the compound: - C (Carbon) has an atomic weight of 12.01 and there are 4 C atoms: \( 4 \times 12.01 = 48.04 \) - H (Hydrogen) has an atomic weight of 1.01 and there are 8 H atoms: \( 8 \times 1.01 = 8.08 \) - O (Oxygen) has an atomic weight of 16.00 and there are 2 O atoms: \( 2 \times 16.00 = 32.00 \) Add them: \( 48.04 + 8.08 + 32.00 = 88.12 \) g/mol.

Step 2: Calculate Formula Weight of Sodium Perborate (NaBO3)

Sum the atomic weights for NaBO3: - Na (Sodium) has an atomic weight of 22.99: \( 22.99 \) - B (Boron) has an atomic weight of 10.81: \( 10.81 \) - O (Oxygen) has an atomic weight of 16.00 and there are 3 O atoms: \( 3 \times 16.00 = 48.00 \) Add them together: \( 22.99 + 10.81 + 48.00 = 81.80 \) g/mol.

Step 3: Calculate Formula Weight of Calcium Carbonate (CaCO3)

Sum the atomic weights for CaCO3: - Ca (Calcium) has an atomic weight of 40.08: \( 40.08 \) - C (Carbon) has an atomic weight of 12.01: \( 12.01 \) - O (Oxygen) has an atomic weight of 16.00 and there are 3 O atoms: \( 3 \times 16.00 = 48.00 \) Add them: \( 40.08 + 12.01 + 48.00 = 100.09 \) g/mol.

Step 4: Calculate Formula Weight of Freon (CF2Cl2)

Sum the atomic weights for CF2Cl2: - C (Carbon) has an atomic weight of 12.01: \( 12.01 \) - F (Fluorine) has an atomic weight of 19.00 and there are 2 F atoms: \( 2 \times 19.00 = 38.00 \) - Cl (Chlorine) has an atomic weight of 35.45 and there are 2 Cl atoms: \( 2 \times 35.45 = 70.90 \) Add them: \( 12.01 + 38.00 + 70.90 = 120.91 \) g/mol.

Step 5: Calculate Formula Weight of Baking Soda (NaHCO3)

Sum the atomic weights for NaHCO3: - Na (Sodium) has an atomic weight of 22.99: \( 22.99 \) - H (Hydrogen) has an atomic weight of 1.01: \( 1.01 \) - C (Carbon) has an atomic weight of 12.01: \( 12.01 \) - O (Oxygen) has an atomic weight of 16.00 and there are 3 O atoms: \( 3 \times 16.00 = 48.00 \) Add them: \( 22.99 + 1.01 + 12.01 + 48.00 = 84.01 \) g/mol.

Step 6: Calculate Formula Weight of Iron Pyrite (FeS2)

Sum the atomic weights for FeS2: - Fe (Iron) has an atomic weight of 55.85: \( 55.85 \) - S (Sulfur) has an atomic weight of 32.07 and there are 2 S atoms: \( 2 \times 32.07 = 64.14 \) Add them: \( 55.85 + 64.14 = 119.99 \) g/mol.

Key Concepts

Molecular Weight Determination

Determining molecular weight, or formula weight, is a fundamental task in chemistry. It involves the sum of the atomic weights of all atoms in a molecule. For instance, consider a compound like Butyric acid, \( \text{CH}_{3}\text{CH}_{2}\text{CH}_{2}\text{COOH} \). To find its molecular weight, we simply need to add up the atomic weights of carbon, hydrogen, and oxygen present in the molecule.
This technique lets chemists identify the mass of one mole of a substance, foundational for making accurate chemical calculations and reactions. Here’s how you can determine molecular weight:

• List all elements present in the compound.
• Determine the number of each type of atom.
• Multiply the number of atoms by their respective atomic weights.
• Add up all the results to get the molecular weight.

Each element’s atomic weight can be found on the periodic table, which tells you how much one mole of that element weighs.

Chemical Compounds

Chemical compounds result from atoms bonding together. They can be composed of different elements, which remain in fixed ratios. For example, Butyric acid as \( \text{CH}_{3}\text{CH}_{2}\text{CH}_{2}\text{COOH} \) features a consistent ratio of carbon, hydrogen, and oxygen.
This fixed ratio defines the specific properties and reactions of a compound.
Compounds can be categorized mainly by:

• Ionic compounds, formed from a metal and a non-metal, like sodium chloride \( (\text{NaCl}) \).
• Covalent or molecular compounds, composed of non-metals sharing electrons, such as water \( (\text{H}_2\text{O}) \).

Compounds can exist as solids, liquids, or gases depending on their constituents and the strength of the chemical bonds within them.

Atomic Weights

Atomic weight is a measure of the average mass of atoms of an element. It accounts for the different isotopes of an element found in nature. Elemental atomic weights are crucial for numerous scientific calculations, as they help chemists compute the molecular weight of compounds.
You can find the atomic weight of an element on the periodic table, usually listed below the elemental symbol.
Using atomic weights:

• Each element has a specific atomic weight that reflects its position on the periodic table.
• By knowing these weights, chemists can ascertain how much of an element is present in a compound.
• Atomic weights are typically expressed in atomic mass units (amu), where 1 amu is one twelfth the mass of a carbon-12 atom.

An understanding of atomic weights is crucial for balancing chemical reactions and for the quantitative analysis in chemistry.