Problem 148 - Introductory Chemistry Atoms First

Question

Nicotine has the formula \(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{~N}_{2}\). Determine the mass percent of each element.

Step-by-Step Solution

Answer

The mass percentages of each element in nicotine (\(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{N}_{2}\)) are approximately: Carbon: \(74.03\%\) Hydrogen: \(8.699\%\) Nitrogen: \(17.27\%\)

Step 1: Find the molar mass of nicotine

To determine the molar mass of nicotine, we need to add the molar mass of each element present in the compound, multiplied by the number of atoms of each element. The molar masses of carbon (C), hydrogen (H), and nitrogen (N) are approximately 12.01 g/mol, 1.008 g/mol, and 14.01 g/mol respectively. The molar mass of nicotine (\(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{N}_{2}\)) can be calculated as follows: Nicotine molar mass = (10 × 12.01 g/mol) + (14 × 1.008 g/mol) + (2 × 14.01 g/mol)

Step 2: Calculate the molar mass of each element in nicotine

Now, we will multiply the molar mass of each element by the number of atoms of that element in nicotine. Carbon: 10 × 12.01 g/mol = 120.1 g/mol Hydrogen: 14 × 1.008 g/mol = 14.112 g/mol Nitrogen: 2 × 14.01 g/mol = 28.02 g/mol

Step 3: Calculate mass percentages of each element

Lastly, we will divide the molar mass of each element in nicotine by the molar mass of nicotine and multiply the result by 100 to obtain the mass percentages of each element. Carbon (%): \(\frac{120.1}{162.232} × 100\% = 74.03\%\) Hydrogen (%): \(\frac{14.112}{162.232} × 100\% = 8.699\%\) Nitrogen (%): \(\frac{28.02}{162.232} × 100\% = 17.27\%\) Therefore, the mass percentages of each element in nicotine are approximately: Carbon: 74.03% Hydrogen: 8.699% Nitrogen: 17.27%

Key Concepts

Understanding Molar Mass

Molar mass holds the key to uncovering how much of each element is part of a compound. It is essentially the weight of one mole of a substance, measured in grams per mole (g/mol). To find the molar mass of a compound, add up the molar masses of all the elements that make it up. Each element is multiplied by the number of its atoms in the formula. This concept is crucial in calculating mass percent composition, enabling us to understand the relative makeup of each element in a compound.

When working with elements like carbon, hydrogen, and nitrogen found in nicotine (\(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{~N}_{2}\)), find the molar mass of each based on:

• Carbon (C): approximately 12.01 g/mol
• Hydrogen (H): approximately 1.008 g/mol
• Nitrogen (N): approximately 14.01 g/mol

Multiply the molar mass of each element by the number of atoms of that element to get the overall molar mass for compounds like nicotine.

Exploring Elemental Analysis

Elemental analysis is a method that allows chemists to determine which elements are present in a compound and in what quantity. It's like detective work for chemistry! By evaluating the composition of elements based on mass, scientists can decipher the structure and formula of a compound like nicotine.

This involves taking the molar mass results (from calculations in the molar mass section) and examining each element's contribution to the total weight. For nicotine, an elemental analysis reveals that within each molecule:

• Carbon contributes a notable portion due to its presence in larger amounts.
• Hydrogen and nitrogen, while present in smaller quantities, are still essential components.

Using this information helps determine the mass percent of each element, guiding further understanding of the compound's characteristics.

The Role of Percentage Composition

The percentage composition of a compound highlights what fraction of its mass comes from each element. This percentage helps chemists understand the relative importance of each element in a compound. Nicotine's composition is a great example to explore this concept.

To find the percentage composition, calculate the individual mass of each element in the formula, then divide by the total molar mass of the compound. Multiply this result by 100 to convert it into a percentage. For nicotine, the mass percentages are approximately:

• Carbon: 74.03%
• Hydrogen: 8.699%
• Nitrogen: 17.27%

Recognizing these percentages aids in grasping how much of the compound is made up by each type of atom, further enriching our understanding of its formulation and properties.

Decoding the Nicotine Molecular Formula

The nicotine molecular formula, \(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{~N}_{2}\), is a concise representation of the compound's structure. It tells us how many atoms of each element are present in a single molecule, providing a snapshot of the chemical makeup.

With 10 carbon atoms, 14 hydrogen atoms, and 2 nitrogen atoms, this formula provides essential information for calculating both molar mass and elemental composition. Understanding molecular formulas allows scientists and students to visualize the microscopic world of molecules and their interactions.

In essence, the nicotine molecular formula is the roadmap to all the quantitative analyses we perform, such as molar mass calculation and determining percentage composition, giving us deeper insight into the material's intrinsic nature.