Question

Determine the formula weights of each of the following compounds: (a) nitrous oxide, \(\mathrm{N}_{2} \mathrm{O}\), known as laughing gas and used as an anesthetic in dentistry; (b) benzoic acid; \(\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\), a substance used as a food preservative; \(\left(\right.\) c) \(\mathrm{Mg}(\mathrm{OH})_{2}\), the active ingredient in milk of magnesia; (d) urea, \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\), a compound used as a nitrogen fertilizer; (e) isopentyl acetate, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{5} \mathrm{H}_{11}\), responsible for the odor of bananas.

Short answer

The formula weights for the given compounds are: a) Nitrous oxide, \(\mathrm{N}_{2} \mathrm{O}\): 44.02 g/mol b) Benzoic acid, \(\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\): 122.12 g/mol c) Magnesium hydroxide, \(\mathrm{Mg}(\mathrm{OH})_{2}\): 58.33 g/mol d) Urea, \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\): 60.07 g/mol e) Isopentyl acetate, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{5} \mathrm{H}_{11}\): 130.17 g/mol

Step-by-step solution

Finding atomic weights of individual elements

First, we need to determine the atomic weight of each individual element in the given compounds. In general, the atomic weights can be found in the periodic table. Here, we've the atomic weights of the required elements, Oxygen (O) = 16.00 g/mol Nitrogen (N) = 14.01 g/mol Carbon (C) = 12.01 g/mol Hydrogen (H) = 1.008 g/mol Magnesium (Mg) = 24.31 g/mol

Calculate the formula weight for \(\mathrm{N}_{2} \mathrm{O}\)

To determine the formula weight of Nitrous oxide, multiply the atomic weights of all elements present in the formula by the number of atoms of each element and add the contributions made by each element. Formula weight of \(\mathrm{N}_{2} \mathrm{O} = 2 \times \mathrm{N} + 1 \times \mathrm{O}\) Formula weight of \(\mathrm{N}_{2} \mathrm{O} = 2 \times (14.01) + 1 \times (16.00) = 28.02 + 16.00 = 44.02\) g/mol

Calculate the formula weight for \(\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\)

Formula weight of Benzoic acid, \(\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\) can be determined in the same way, Formula weight of \(\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2} = 1 \times \mathrm{H} + 7 \times \mathrm{C} + 5 \times \mathrm{H} + 2 \times \mathrm{O}\) Formula weight of \(\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2} = 1 \times (1.008) + 7 \times (12.01) + 5 \times (1.008) + 2 \times (16.00) = 1.008 + 84.07 + 5.04 + 32.00 = 122.12\) g/mol

Calculate the formula weight for \(\mathrm{Mg}(\mathrm{OH})_{2}\)

Formula weight of Magnesium Hydroxide, \(\mathrm{Mg}(\mathrm{OH})_{2} = 1 \times \mathrm{Mg} + 2 \times (\mathrm{O} + \mathrm{H})\) Formula weight of \(\mathrm{Mg}(\mathrm{OH})_{2} = 1 \times (24.31) + 2 \times (16.00 + 1.008) = 24.31 + 2 \times (17.008) = 24.31 + 34.02 = 58.33\) g/mol

Calculate the formula weight for \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\)

Formula weight of Urea, \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO} = 2 \times (1 \times \mathrm{N} + 2 \times \mathrm{H}) + 1 \times \mathrm{C} + 1 \times \mathrm{O}\) Formula weight of Urea = \(2 \times (1 \times 14.01 + 2 \times 1.008) + 1 \times 12.01 + 1 \times 16.00 = 2 \times (14.01 + 2.016) + 12.01 + 16.00 = 28.04 + 6.032 + 12.01 + 16.00 = 60.07\) g/mol

Calculate the formula weight for \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{5} \mathrm{H}_{11}\)

Formula weight of isopentyl acetate, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{5} \mathrm{H}_{11} = 1 \times (\mathrm{C} + 3 \times \mathrm{H}) + 1 \times (\mathrm{C} + 2 \times \mathrm{O}) + 1 \times (5 \times \mathrm{C} + 11 \times \mathrm{H})\) Formula weight of isopentyl acetate = \((1 \times 12.01 + 3 \times 1.008) + (1 \times 12.01 + 2 \times 16.00) + (5 \times 12.01 + 11 \times 1.008) = (12.01 + 3.024) + (12.01 + 32.00) + (60.05 + 11.088) = 130.17\) g/mol In summary, the formula weights for the given compounds are: a) Nitrous oxide, \(\mathrm{N}_{2} \mathrm{O}\): 44.02 g/mol b) Benzoic acid, \(\mathrm{HC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\): 122.12 g/mol c) Magnesium hydroxide, \(\mathrm{Mg}(\mathrm{OH})_{2}\): 58.33 g/mol d) Urea, \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\): 60.07 g/mol e) Isopentyl acetate, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{5} \mathrm{H}_{11}\): 130.17 g/mol

Key concepts

Nitrous Oxide

Nitrous oxide, commonly known as laughing gas, is a chemical compound with the formula \( \mathrm{N}_2 \mathrm{O} \). It's often used in dentistry as an anesthetic to safely sedate patients during procedures.
Its ability to create a relaxed and slightly euphoric feeling is why it's famously called laughing gas.
When calculating the formula weight of nitrous oxide, we need to consider the atomic weights of nitrogen (N) and oxygen (O):

• Nitrogen (N) has an atomic weight of 14.01 g/mol.
• Oxygen (O) has an atomic weight of 16.00 g/mol.

For nitrous oxide, there are two nitrogen atoms and one oxygen atom in each molecule. So, you multiply the atomic weight of each element by the number of atoms, then sum them up:

• Formula weight = \( 2 \times 14.01 + 1 \times 16.00 = 44.02 \) g/mol.

Understanding this helps in various scientific and industrial applications, ensuring precise usage and minimizing risk.

Benzoic Acid

Benzoic acid, with the chemical formula \( \mathrm{HC}_7 \mathrm{H}_5 \mathrm{O}_2 \), is commonly used as a preservative in foods. Its efficiency in preventing the growth of bacteria and fungi preserves food and extends its shelf life.
It's naturally found in many plants, with cranberries being a prime example.
To find the formula weight of benzoic acid, add together the weights for each atom in the molecule:

• Hydrogen (H) = 1.008 g/mol
• Carbon (C) = 12.01 g/mol
• Oxygen (O) = 16.00 g/mol

In benzoic acid:

• 1 H atom + 7 C atoms + 5 H atoms + 2 O atoms
• Formula weight = \( 1 \times 1.008 + 7 \times 12.01 + 5 \times 1.008 + 2 \times 16.00 = 122.12 \) g/mol.

Knowing the precise formula weight is crucial for its use in food technology, where accurate measurements ensure safety effectiveness.

Atomic Weights

Atomic weights are fundamental units in chemistry, representing the mass of an atom expressed in atomic mass units (amu). This enables scientists to easily conduct calculations, especially in determining molecular weights of compounds.
The atomic weight of an element is typically found on the periodic table.
Some basic atomic weights useful in formula weight calculations include:

• Oxygen (O) = 16.00 g/mol
• Nitrogen (N) = 14.01 g/mol
• Carbon (C) = 12.01 g/mol
• Hydrogen (H) = 1.008 g/mol
• Magnesium (Mg) = 24.31 g/mol

To calculate the formula weight of a compound, multiply the atomic weight of each element by the number of atoms of that element in the compound's chemical formula. Then, add all these values together.
Understanding atomic weights helps streamline many chemical processes, from laboratory experiments to large-scale industrial applications.

Isopentyl Acetate

Isopentyl acetate is an ester with the chemical formula \( \mathrm{CH}_3 \mathrm{CO}_2 \mathrm{C}_5 \mathrm{H}_{11} \). It's renowned for its distinctive fruity smell, often associated with bananas.
This property makes it a common ingredient in flavoring and fragrance industries.
To calculate the formula weight of isopentyl acetate, consider the atomic weights of the elements involved:

• Carbon (C) = 12.01 g/mol
• Hydrogen (H) = 1.008 g/mol
• Oxygen (O) = 16.00 g/mol

For isopentyl acetate, the structure includes:

• 3 C atoms from methyl, 1 from the acetate group, and 5 from the isopentyl part
• 3 H from the methyl, 11 H from isopentyl, and 2 additional O
• Formula weight = \((1 \times 12.01 + 3 \times 1.008) + (1 \times 12.01 + 2 \times 16.00) + (5 \times 12.01 + 11 \times 1.008) = 130.17\) g/mol.

Proper calculations ensure its reliable use in creating synthetic perfumes and food flavorings, playing a vital role in product consistency and quality.