Question

Calculate the percentage by mass of the indicated element in the following compounds: $(\mathbf{a})$ carbon in acetylene, ${\mathrm{C}}_2{\mathrm{H}}_2,\mathrm{a}$ gas used in welding; $(\mathbf{b})$ hydrogen in ascorbic acid, ${\mathrm{HC}}_6{\mathrm{H}}_7{\mathrm{O}}_6$ also known as vitamin $\mathrm{C};(\mathbf{c})$ hydrogen in ammonium sulfate, ${\left({\mathrm{NH}}_4\right)}_2{\mathrm{SO}}_4,$ a substance used as a nitrogen fertilizer; $(\mathbf{d})$ platinum in ${\mathrm{PtCl}}_2{\left({\mathrm{NH}}_3\right)}_2,$ a chemotherapy agent called cisplatin; $(\mathbf{e})$ oxygen in the female sex hormone estradiol, ${\mathrm{C}}_{18}{\mathrm{H}}_{24}{\mathrm{O}}_2;(\mathbf{f})$ carbon in capsaicin, ${\mathrm{C}}_{18}{\mathrm{H}}_{27}{\mathrm{NO}}_3,$ the compound that gives the hot taste to chili peppers.

Short answer

The percentages by mass of the indicated elements in the given compounds are as follows: (a) Carbon in Acetylene (C2H2) = 92.3% (b) Hydrogen in Ascorbic Acid (HC6H7O6) = 4.6% (c) Hydrogen in Ammonium Sulfate ((NH4)2SO4) = 6.1% (d) Platinum in cisplatin (PtCl2(NH3)2) = 65.0% (e) Oxygen in Estradiol (C18H24O2) = 11.8% (f) Carbon in Capsaicin (C18H27NO3) = 70.7%

Step-by-step solution

Part (a) - Carbon in Acetylene (C2H2)

To determine the percentage of carbon in acetylene, we first find the molar mass of acetylene, given by the formula C2H2. 1. Molar mass of carbon (C) = 12.01 g/mol 2. Molar mass of hydrogen (H) = 1.01 g/mol Total molar mass of C2H2 = (2 × 12.01 g/mol) + (2 × 1.01 g/mol) = 26.04 g/mol Mass of carbon in the compound = 2 × 12.01 g/mol Percentage by mass of carbon = $\frac{\text{Mass of carbon}}{\text{Total molar mass of compound}}$ × 100% = $\frac{2\times 12.01}{26.04}$ × 100% = 92.3%

Part (b) - Hydrogen in Ascorbic Acid (HC6H7O6)

Total molar mass of ascorbic acid (HC6H7O6) = (1 × 12.01 g/mol) + (7 × 1.01 g/mol) + (6 × 16.00 g/mol) = 176.14 g/mol Mass of hydrogen in the compound = 8 × 1.01 g/mol Percentage by mass of hydrogen = $\frac{\text{Mass of hydrogen}}{\text{Total molar mass of compound}}$ × 100% = $\frac{8\times 1.01}{176.14}$ × 100% = 4.6%

Part (c) - Hydrogen in Ammonium Sulfate ((NH4)2SO4)

Total molar mass of ammonium sulfate ((NH4)2SO4) = (8 × 1.01 g/mol) + (2 × 14.01 g/mol) + (1 × 32.07 g/mol) + (4 × 16.00 g/mol) = 132.14 g/mol Mass of hydrogen in the compound = 8 × 1.01 g/mol Percentage by mass of hydrogen = $\frac{\text{Mass of hydrogen}}{\text{Total molar mass of compound}}$ × 100% = $\frac{8\times 1.01}{132.14}$ × 100% = 6.1%

Part (d) - Platinum in cisplatin (PtCl2(NH3)2)

Total molar mass of cisplatin (PtCl2(NH3)2) = (1 × 195.08 g/mol) + (2 × 35.45 g/mol) + (2 × 17.03 g/mol) = 300.04 g/mol Mass of platinum in the compound = 1 × 195.08 g/mol Percentage by mass of platinum = $\frac{\text{Mass of Pt}}{\text{Total molar mass of compound}}$ × 100% = $\frac{195.08}{300.04}$ × 100% = 65.0%

Part (e) - Oxygen in Estradiol (C18H24O2)

Total molar mass of estradiol (C18H24O2) = (18 × 12.01 g/mol) + (24 × 1.01 g/mol) + (2 × 16.00 g/mol) = 272.40 g/mol Mass of oxygen in the compound = 2 × 16.00 g/mol Percentage by mass of oxygen = $\frac{\text{Mass of oxygen}}{\text{Total molar mass of compound}}$ × 100% = $\frac{2\times 16.00}{272.40}$ × 100% = 11.8%

Part (f) - Carbon in Capsaicin (C18H27NO3)

Total molar mass of capsaicin (C18H27NO3) = (18 × 12.01 g/mol) + (27 × 1.01 g/mol) + (1 × 14.01 g/mol) + (3 × 16.00 g/mol) = 305.45 g/mol Mass of carbon in the compound = 18 × 12.01 g/mol Percentage by mass of carbon = $\frac{\text{Mass of carbon}}{\text{Total molar mass of compound}}$ × 100% = $\frac{18\times 12.01}{305.45}$ × 100% = 70.7%

Key concepts

Molar Mass Calculation

Understanding the molar mass of a compound is crucial when you want to delve into the quantitative aspects of chemistry. Essentially, the molar mass gives us the mass of a substance per one mole of its particles. To calculate it, you need to know the atomic masses of each element involved, which are readily available on the periodic table.

For example, let’s take acetylene (C2H2). The molar mass of carbon (C) is 12.01 g/mol, and that of hydrogen (H) is 1.01 g/mol. Since acetylene consists of two carbon atoms and two hydrogen atoms, its molar mass is the sum of twice the atomic mass of carbon plus twice the atomic mass of hydrogen, which totals 26.04 g/mol. This molar mass is a critical stepping stone for further stoichiometric calculations, as it represents the mass of exactly one mole of acetylene molecules.

Molecular Composition

Molecular composition refers to the types and numbers of atoms that constitute a molecule. A compound’s molecular formula provides this information at a glance and is vital for both molar mass calculation and stoichiometry. To comprehend a compound's composition, it is useful to break it down into the contributions made by each element within the molecule.

Take ascorbic acid (vitamin C) whose formula is HC6H7O6. Its composition explicitly tells us that there is one carbon, seven hydrogen, and six oxygen atoms per molecule of ascorbic acid. This knowledge underpins the calculation of percentage by mass of each element in the compound, informing us of which element contributes most to a compound’s overall mass.

Stoichiometry

Stoichiometry is all about the quantitative relationships between the reactants and products in a chemical reaction. At its core, this involves using the mole concept and molar masses to determine how much of a reactant is required or how much of a product is produced. The key to stoichiometry is a balanced chemical equation, which provides the mole ratios of the substances involved.

In the context of percentage by mass calculations, stoichiometry comes into play by informing us about the proportions of elements within compounds. For instance, the percentage by mass of carbon in capsaicin (C18H27NO3) reflects stoichiometric principles. It represents the fraction of the compound's mass contributed by carbon, after considering the molar masses and the mole ratio of carbon atoms to the total compound, as demonstrated in the step-by-step solution for capsaicin.