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Chapter 2: Problem 39

Calculate the molecular weight of the active ingredients in the following prescription drugs. (a) Darvon, \(\mathrm{C}_{22} \mathrm{H}_{30} \mathrm{ClNO}_{2}\) (b) Valium, \(\mathrm{C}_{16} \mathrm{H}_{13} \mathrm{ClN}_{2} \mathrm{O}\) (c) Tetracycline, \(\mathrm{C}_{22} \mathrm{H}_{24} \mathrm{~N}_{2} \mathrm{O}_{8}\)

Short Answer

Expert verified
Darvon: 375.92, Valium: 284.73, Tetracycline: 444.43.

Step by step solution

01

Understand Atomic Weights

Before calculating the molecular weight, understand that atomic weights are the average mass of atoms, usually found on the periodic table. Common atomic weights used here are Carbon (C) = 12.01, Hydrogen (H) = 1.008, Chlorine (Cl) = 35.45, Nitrogen (N) = 14.01, and Oxygen (O) = 16.00.
02

Calculate Molecular Weight of Darvon

For Darvon: \( \mathrm{C}_{22} \mathrm{H}_{30} \mathrm{ClNO}_{2} \).- Carbon: \(22 \times 12.01 = 264.22\)- Hydrogen: \(30 \times 1.008 = 30.24\)- Chlorine: \(1 \times 35.45 = 35.45\)- Nitrogen: \(1 \times 14.01 = 14.01\)- Oxygen: \(2 \times 16.00 = 32.00\)Add them together to get the molecular weight: \(264.22 + 30.24 + 35.45 + 14.01 + 32.00 = 375.92\).
03

Calculate Molecular Weight of Valium

For Valium: \( \mathrm{C}_{16} \mathrm{H}_{13} \mathrm{ClN}_{2} \mathrm{O} \).- Carbon: \(16 \times 12.01 = 192.16\)- Hydrogen: \(13 \times 1.008 = 13.104\)- Chlorine: \(1 \times 35.45 = 35.45\)- Nitrogen: \(2 \times 14.01 = 28.02\)- Oxygen: \(1 \times 16.00 = 16.00\)Add them together to get the molecular weight: \(192.16 + 13.104 + 35.45 + 28.02 + 16.00 = 284.734\).
04

Calculate Molecular Weight of Tetracycline

For Tetracycline: \( \mathrm{C}_{22} \mathrm{H}_{24} \mathrm{N}_{2} \mathrm{O}_{8} \).- Carbon: \(22 \times 12.01 = 264.22\)- Hydrogen: \(24 \times 1.008 = 24.192\)- Nitrogen: \(2 \times 14.01 = 28.02\)- Oxygen: \(8 \times 16.00 = 128.00\)Add them together to get the molecular weight: \(264.22 + 24.192 + 28.02 + 128.00 = 444.432\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atomic Weights
Atomic weights are essential components when calculating molecular weights, as they reflect the average mass of atoms of an element based on the abundance of its isotopes. When you refer to an element like Carbon or Oxygen on the periodic table, you'll notice a number under its symbol. This is the atomic weight.
  • Carbon (C) has an atomic weight of approximately 12.01.
  • Hydrogen (H) is about 1.008.
  • Chlorine (Cl) is 35.45.
  • Nitrogen (N) stands at 14.01.
  • Oxygen (O) is 16.00.
Atomic weights are crucial because chemical reactions and molecular weights depend heavily on them. These weights allow us to calculate how much of each element is present in a compound, enabling us to determine a molecule鈥檚 total weight.
Molecular Formula
A molecular formula provides vital information about a chemical compound's composition. It lists each element's symbol followed by a subscript indicating the number of atoms present. For example, in the compound (\(\mathrm{C}_{22} \mathrm{H}_{30} \mathrm{ClNO}_{2}\)), the subscripts 22, 30, 1, 1, and2represent the counts of Carbon, Hydrogen, Chlorine, Nitrogen, and Oxygen, respectively. The molecular formula helps in:
  • Determining the exact composition of each chemical compound.
  • Allowing the calculation of the total molecular weight by summing the products of each element's atomic weight and their respective subscripts.
Understanding how to read and use molecular formulas is key in chemistry for identifying the makeup of compounds and facilitating further calculations and chemical reactions.
Chemical Compounds
Chemical compounds are entities composed of two or more different atoms bonded together. The nature of the bonds can vary, including ionic and covalent bonds, and they have distinct physical and chemical properties.
  • For example, Valium (\(\mathrm{C}_{16} \mathrm{H}_{13} \mathrm{ClN}_{2} \mathrm{O} \)) is a compound composed of Carbon, Hydrogen, Chlorine, Nitrogen, and Oxygen combined in a specific arrangement to form the drug's active ingredient.
  • Chemical compounds function in distinct ways in the body, providing therapeutic effects or participating in diverse reactions.
Understanding chemical compounds involves recognizing the symbolic molecular formulas, learning their properties, and how different combinations of elements mediate different functions.
Periodic Table
The periodic table is a comprehensive chart representing all known elements organized by their atomic number, electron configuration, and recurring chemical properties. Dmitri Mendeleev created it to provide predictability in chemistry by identifying patterns among the elements. The table allows chemists to:
  • Easily locate an element's atomic weight, facilitating various calculations, such as in molecular weight determination.
  • Predict how different elements might react chemically based on their group and period placement.
  • Understand periodic trends, such as electronegativity and atomic radius, providing insight into element behavior.
Whether you're dealing with simple molecules or complex compounds, the periodic table is a fundamental tool in understanding and predicting chemical behavior.

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