Problem 152 - Introductory Chemistry Atoms First

Question

The compound \(3^{\prime}\) -azido- \(3^{\prime}\) -thymidine (AZT) is used in the treatment of AIDS. The molecular formula of \(\mathrm{AZT}\) is \(\mathrm{C}_{10} \mathrm{H}_{13} \mathrm{~N}_{5} \mathrm{O}_{4}\). What is the mass percent of each element in AZT?

Step-by-Step Solution

Answer

The mass percent of each element in AZT is: Carbon: \(44.9\% \), Hydrogen: \(4.9\% \), Nitrogen: \(26.2\% \), and Oxygen: \(24.0\% \).

Step 1: Calculate the molar mass of AZT

To find the molar mass of AZT, we need to find the sum of the molar masses of all the elements in the molecule. Molar mass of Carbon (C) = 12.01 g/mol Molar mass of Hydrogen (H) = 1.01 g/mol Molar mass of Nitrogen (N) = 14.01 g/mol Molar mass of Oxygen (O) = 16.00 g/mol Molar mass of AZT = (10 * 12.01) + (13 * 1.01) + (5 * 14.01) + (4 * 16.00)

Step 2: Determining the mass of each element in AZT

Mass of Carbon (C) = 10 * 12.01 g/mol = 120.1 g/mol Mass of Hydrogen (H) = 13 * 1.01 g/mol = 13.13 g/mol Mass of Nitrogen (N) = 5 * 14.01 g/mol = 70.05 g/mol Mass of Oxygen (O) = 4 * 16.00 g/mol = 64.00 g/mol Now, let's find the molar mass of AZT from the previous step: Molar mass of AZT = 120.1 + 13.13 + 70.05 + 64.00 = 267.28 g/mol

Step 3: Calculate the mass percent of each element

Mass percent of Carbon (C) = (Mass of C / Molar mass of AZT) * 100 = (120.1 / 267.28) * 100 = 44.9 % Mass percent of Hydrogen (H) = (Mass of H / Molar mass of AZT) * 100 = (13.13 / 267.28) * 100 = 4.9 % Mass percent of Nitrogen (N) = (Mass of N / Molar mass of AZT) * 100 = (70.05 / 267.28) * 100 = 26.2 % Mass percent of Oxygen (O) = (Mass of O / Molar mass of AZT) * 100 = (64.00 / 267.28) * 100 = 24.0 % Now we have the mass percent of each element in AZT: Carbon: 44.9 % Hydrogen: 4.9 % Nitrogen: 26.2 % Oxygen: 24.0 %

Key Concepts

Molar Mass Defined

Understanding molar mass is key in chemistry calculations. Molar mass refers to the mass of one mole of a substance. For elements, it's the atomic mass given on the periodic table, but for compounds, it's a bit more involved. You need to add the molar masses of each element, multiplied by how many times that element appears in the compound. For example, in the compound 3′-azido-3′-thymidine (AZT), the molecular formula is \(\mathrm{C}_{10}\mathrm{H}_{13}\mathrm{N}_{5}\mathrm{O}_{4}\). Each element's atomic mass is found on the periodic table, and then you multiply these masses by the number of atoms of that element present. Here's a simple way to remember it:

• Find the atomic mass of each element in the compound.
• Multiply by the number of times the element appears.
• Add these values together for the total molar mass.

Breaking down the numbers, you find that AZT has a molar mass of 267.28 g/mol.

Mass Percent Composition

Mass percent composition gives insight into what fraction of a compound's mass comes from each element. It's calculated by dividing the total mass of each element in a compound by the compound's total molar mass, then multiplying by 100 to convert that ratio into a percentage. Here's how to go about it:

• Calculate the total molar mass of the compound.
• Determine the mass contribution of each element.
• Compute the percentage by multiplying the mass fraction by 100.

In our AZT example, elements like carbon and nitrogen have significant mass percentages because their atomic masses and quantities in the formula are high. Carbon, for instance, makes up 44.9% due to its higher molar mass total, whereas hydrogen contributes a smaller percentage due to its lighter atomic mass.

Understanding Molecular Formulas

A molecular formula provides the exact number of each type of atom in a molecule. Unlike an empirical formula, which shows the simplest whole-number ratio of elements, a molecular formula is much more detailed. For AZT, the molecular formula \(\mathrm{C}_{10}\mathrm{H}_{13}\mathrm{N}_{5}\mathrm{O}_{4}\) indicates it has:

• 10 carbon atoms
• 13 hydrogen atoms
• 5 nitrogen atoms
• 4 oxygen atoms

This formula is crucial for both the synthesis and analysis of chemical compounds, especially in pharmaceuticals where precision can mean the difference between efficacy and ineffectiveness. The details in a molecular formula assist not only in determining molar mass but also in further chemical reactions and compound manipulations.

Elemental Analysis Simplified

Elemental analysis is the process of determining the relative abundance of different elements within a compound. It's essential for checking the purity of a compound or verifying its identity. By understanding the percentage of each element present, you can draw conclusions about its structure and chemical properties. Elemental analysis is often the starting point in determining the molecular formula. Typically, it involves techniques like combustion analysis or spectroscopy, but here we're focusing on the simplicity of calculating mass percent compositions as a method of analysis. In our AZT context, knowing that carbon constitutes 44.9% tells us a lot about the compound’s backbone. Recognizing the significant contributions from nitrogen and oxygen also hints at the functional groups present, essential information when designing relevant treatments or conducting further research.