Problem 168 - Chemistry Matter and Change

Question

Caffeine The stimulant effect of coffee is due to caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}\) . Calculate the molar mass of caffeine. Determine its percent composition.

Step-by-Step Solution

Answer

The molar mass of caffeine, \(C_8H_{10}N_4O_2\), is 194.20 g/mol. The percent composition of caffeine is: Carbon (C): 49.44%, Hydrogen (H): 5.19%, Nitrogen (N): 28.85%, and Oxygen (O): 16.47%.

Step 1: Find the atomic masses of the elements in caffeine

In order to find the molar mass of caffeine, we first need to know the atomic mass of each element present in the molecule. The elements and their atomic masses are: - Carbon (C): 12.01 g/mol - Hydrogen (H): 1.008 g/mol - Nitrogen (N): 14.01 g/mol - Oxygen (O): 16.00 g/mol

Step 2: Calculate the molar mass of caffeine

Now that we have the atomic masses of each element, we can calculate the molar mass of caffeine by multiplying the atomic mass of each element by the number of atoms in the molecule and then adding the results together. Molar mass of Caffeine = (8 * C) + (10 * H) + (4 * N) + (2 * O) = (8 * 12.01 g/mol) + (10 * 1.008 g/mol) + (4 * 14.01 g/mol) + (2 * 16.00 g/mol) = 96.08 g/mol + 10.08 g/mol + 56.04 g/mol + 32.00 g/mol = 194.20 g/mol The molar mass of caffeine is 194.20 g/mol.

Step 3: Calculate the percent composition of each element

To find the percent composition, we will divide the mass contribution of each element by the total molar mass of caffeine and multiply by 100. Percent composition of Carbon (C): = (96.08 g/mol / 194.20 g/mol) * 100 = 49.44 % Percent composition of Hydrogen (H): = (10.08 g/mol / 194.20 g/mol) * 100 = 5.19 % Percent composition of Nitrogen (N): = (56.04 g/mol / 194.20 g/mol) * 100 = 28.85 % Percent composition of Oxygen (O): = (32.00 g/mol / 194.20 g/mol) * 100 = 16.47 % The percent composition of caffeine is: - Carbon (C): 49.44% - Hydrogen (H): 5.19% - Nitrogen (N): 28.85% - Oxygen (O): 16.47%

Key Concepts

Percent Composition

The percent composition of a compound tells us the proportion of each element present in the compound relative to its total mass. It is an essential concept in chemistry used to compare the consistency of chemical formulas. Calculating the percent composition helps us understand the ratio of atoms in a compound.

To determine the percent composition of caffeine, we follow these steps:

• Find the molar mass of the entire caffeine molecule, which involves summing up the contribution of each atom within the formula.
• For each element, calculate its mass contribution. Then divide this by the total molar mass of caffeine.
• Multiply the result by 100 to convert it to a percentage.

By performing these calculations, you can find the relative abundance of each element within caffeine. This helps in better understanding the chemical makeup and potential interactions of the molecule.

Caffeine Molecule

The caffeine molecule, known chemically as \(\mathrm{C}_8\mathrm{H}_{10}\mathrm{N}_4\mathrm{O}_2\), is a well-known stimulant found in coffee and tea. Its unique properties affect the central nervous system, leading to increased alertness and energy. The structural formula of caffeine consists of:

• 8 Carbon atoms \((C)\)
• 10 Hydrogen atoms \((H)\)
• 4 Nitrogen atoms \((N)\)
• 2 Oxygen atoms \((O)\)

The arrangement and type of atoms in the caffeine molecule contribute to its ability to bind to adenosine receptors, thereby blocking them and reducing the sensation of tiredness. Understanding its chemical formula not only reveals how caffeine functions biologically but also aids in its quantification in various contexts, like in pharmacology and food sciences.

Atomic Mass

Atomic mass is a critical aspect when it comes to calculating the molar mass of compounds. It represents the weight of a single atom of an element, typically measured in atomic mass units (amu) or grams per mole (g/mol). This value can be found on the periodic table for each element.

In our caffeine calculation, the atomic masses were determined for each of its constituent elements:

• Carbon (C): 12.01 g/mol
• Hydrogen (H): 1.008 g/mol
• Nitrogen (N): 14.01 g/mol
• Oxygen (O): 16.00 g/mol

Knowing these values allows us to calculate precisely the molar mass of the caffeine molecule by accounting for the number of each type of atom it includes. Thus, atomic masses are like building blocks, providing essential data for deeper chemical analysis.

Chemical Formula Analysis

Chemical formula analysis is a foundational skill in chemistry, used to interpret the composition of molecules and predict chemical behavior. For caffeine, the chemical formula is \(\mathrm{C}_8\mathrm{H}_{10}\mathrm{N}_4\mathrm{O}_2\), indicating the molecular structure clearly and concisely. This formula represents:

• 8 atoms of carbon
• 10 atoms of hydrogen
• 4 atoms of nitrogen
• 2 atoms of oxygen

From the chemical formula, one can derive many insights, such as determining mole ratios, understanding potential bonding interactions, and facilitating stoichiometric calculations. This information is crucial for synthesizing the molecule in laboratory settings, analyzing its properties, and comparing it with other compounds.