Question

Calculate the mass percent of each element in the following compounds: (a) \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{2} \mathrm{O}_{2},\) caffeine (b) \(\mathrm{C}_{10} \mathrm{H}_{20} \mathrm{O},\) menthol (c) \(\mathrm{CoCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\)

Short answer

(a) Caffeine: 57.80% C, 6.08% H, 16.86% N, 19.26% O. (b) Menthol: 76.86% C, 12.92% H, 10.23% O. (c) CoCl2·6H2O: 24.76% Co, 29.80% Cl, 45.44% H2O.

Step-by-step solution

Determine Molar Mass of Each Compound

For (a) Caffeine (\(\mathrm{C}_8 \mathrm{H}_{10} \mathrm{N}_2 \mathrm{O}_2\)), calculate the molar mass: Carbon (C): 8 * 12.01 g/mol = 96.08 g/mol, Hydrogen (H): 10 * 1.01 g/mol = 10.10 g/mol, Nitrogen (N): 2 * 14.01 g/mol = 28.02 g/mol, Oxygen (O): 2 * 16.00 g/mol = 32.00 g/mol. Total = 166.20 g/mol. For (b) Menthol (\(\mathrm{C}_{10} \mathrm{H}_{20} \mathrm{O}\)), calculate the molar mass: Carbon: 10 * 12.01 g/mol = 120.10 g/mol, Hydrogen: 20 * 1.01 g/mol = 20.20 g/mol, Oxygen: 1 * 16.00 g/mol = 16.00 g/mol. Total = 156.30 g/mol. For (c) Cobalt (II) chloride hexahydrate (\(\mathrm{CoCl}_2 \cdot 6 \mathrm{H}_2\mathrm{O}\)), calculate the molar mass: Cobalt (Co): 1 * 58.93 g/mol = 58.93 g/mol, Chlorine (Cl): 2 * 35.45 g/mol = 70.90 g/mol, Water (H₂O): 6 * 18.02 g/mol = 108.12 g/mol. Total = 237.95 g/mol.

Calculate Mass Percent of Each Element

For (a) Caffeine:- Carbon: \((96.08 / 166.20) \times 100 = 57.80\%\)- Hydrogen: \((10.10 / 166.20) \times 100 = 6.08\%\)- Nitrogen: \((28.02 / 166.20) \times 100 = 16.86\%\)- Oxygen: \((32.00 / 166.20) \times 100 = 19.26\%\)For (b) Menthol:- Carbon: \((120.10 / 156.30) \times 100 = 76.86\%\)- Hydrogen: \((20.20 / 156.30) \times 100 = 12.92\%\)- Oxygen: \((16.00 / 156.30) \times 100 = 10.23\%\)For (c) Cobalt (II) chloride hexahydrate:- Cobalt: \((58.93 / 237.95) \times 100 = 24.76\%\)- Chlorine: \((70.90 / 237.95) \times 100 = 29.80\%\)- Water (as part of the whole compound): \((108.12 / 237.95) \times 100 = 45.44\%\)

Key concepts

Molar Mass Determination

Determining the molar mass of a compound is the first essential step in calculating mass percent of its elements. Molar mass represents the mass of one mole of a compound and is expressed in grams per mole (g/mol). To find it, sum up the atomic masses of all atoms present in the chemical formula of the compound. Each element's atomic mass can be found on the periodic table, expressed as g/mol.
As demonstrated in the exercise, begin with the element carbon (C) in caffeine. Multiply the number of carbon atoms by carbon's atomic mass (12.01 g/mol), completing the same process for all elements present in each compound. This approach is applied similarly to other compounds, such as menthol and cobalt (II) chloride hexahydrate, effectively calculating their total molar masses. Thoroughly understanding this procedure is fundamental for later calculations of mass percent, which relies directly on knowing the accurate molar mass of each element in the compound.

Elemental Composition

Elemental composition refers to the different elements present in a compound and their relative proportions by mass. This aspect of compound analysis can be crucial for understanding the compound's properties and behaviors.
Knowing how to compute the mass number of each element and recognizing their quantity in a compound enhances comprehension of its overall makeup. To do so, consider calculating the portion of each element's molar mass compared to the total molar mass. This figure offers insight into how much an element contributes to the compound's whole mass.
By understanding these proportions, you can infer more about the compound's structure and anticipate its interactions in chemical reactions. Observing the elemental composition is essential for assessing the substance's purity or concentration in different applications.

Compound Analysis

Compound analysis involves investigating a compound's chemical structure to determine its elemental makeup and their quantitative ratios. This type of analysis reveals crucial details about how elements are bonded and their arrangement within the compound.
Understanding compound analysis techniques aids in extracting detailed information, such as identifying the active component in mixtures or verifying the compound's identity against its expected formula. This fundamental skill in chemistry ensures that accurate conclusions are drawn about a compound's purity and its potential uses.
Chemists usually employ various analytical methods such as spectroscopy and chromatography to complement stoichiometric calculations, thereby ensuring that the chemical composition matches practical expectations. Compound analysis, therefore, aligns theoretical calculations with experimental data.

Chemical Formula Interpretation

Interpreting chemical formulas means translating the symbolic language of chemistry into practical, comprehensible information about molecular structures. A chemical formula conveys all the essential details about a compound's elemental makeup and quantity.
Reading these formulas accurately is crucial for identifying how elements combine to form the complete compound. For instance, the subscript numbers in a formula illustrate how many atoms of each element exist in one molecule of the compound. This attention to number and symbol allows effective communication of complex information concisely.
Chemical formula interpretation is at the heart of many chemical calculations and analyses. It serves as a foundation upon which further calculations, like molar mass determination and mass percent calculation, are built. Grasping this skillful interpretation is vital for students and professionals aiming to advance in chemical sciences.