Problem 25 - Chemistry The Central Science

Question

Calculate the percentage by mass of the indicated element in the following compounds: (a) carbon in acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2},\) a gas used in welding; (b) hydrogen in ascorbic acid, \(\mathrm{HC}_{6} \mathrm{H}_{7} \mathrm{O}_{6},\) also known as vitamin C; (c) hydrogen in ammonium sulfate, \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\), a substance used as a nitrogen fertilizer; (d) platinum in \(\mathrm{PtCl}_{2}\left(\mathrm{NH}_{3}\right)_{2},\) a chemotherapy agent called cisplatin; (e) oxygen in the female sex hormone estradiol, \(\mathrm{C}_{18} \mathrm{H}_{24} \mathrm{O}_{2}\); (f) carbon in capsaicin, \(\mathrm{C}_{18} \mathrm{H}_{27} \mathrm{NO}_{3},\) the compound that gives the hot taste to chili peppers.

Step-by-Step Solution

Answer

(a) Percentage by mass of carbon in acetylene: 92.2% (b) Percentage by mass of hydrogen in ascorbic acid: 4.6% (c) Percentage by mass of hydrogen in ammonium sulfate: 6.1% (d) Percentage by mass of platinum in cisplatin: 65.0% (e) Percentage by mass of oxygen in estradiol: 11.7% (f) Percentage by mass of carbon in capsaicin: 70.8%

Step 1: (a) Carbon in acetylene, C2H2

First, let's find the molar mass of the compound acetylene (C2H2). Use the atomic masses for carbon (C, 12.01 g/mol) and hydrogen (H, 1.01 g/mol): Molar mass of C2H2 = (2 × 12.01 g/mol) + (2 × 1.01 g/mol) = 24.02 g/mol + 2.02 g/mol = 26.04 g/mol Next, calculate the mass of the specified element (carbon) in the compound: Mass of carbon = 2 × 12.01 g/mol = 24.02 g/mol Now, calculate the percentage by mass of the carbon in the acetylene: Percentage by mass of carbon = (24.02 g/mol / 26.04 g/mol) × 100 = 92.2%

Step 2: (b) Hydrogen in ascorbic acid, HC6H7O6

First, let's find the molar mass of the compound ascorbic acid (HC6H7O6). Use the atomic masses for carbon (C, 12.01 g/mol), hydrogen (H, 1.01 g/mol), and oxygen (O, 16.00 g/mol): Molar mass of HC6H7O6 = (1 × 1.01 g/mol) + (6 × 12.01 g/mol) + (7 × 1.01 g/mol) + (6 × 16.00 g/mol) = 1.01 g/mol + 72.06 g/mol + 7.07 g/mol + 96.00 g/mol = 176.14 g/mol Next, calculate the mass of the specified element (hydrogen) in the compound: Mass of hydrogen = (1 + 7) × 1.01 g/mol = 8.08 g/mol Now, calculate the percentage by mass of the hydrogen in the ascorbic acid: Percentage by mass of hydrogen = (8.08 g/mol / 176.14 g/mol) × 100 = 4.6%

Step 3: (c) Hydrogen in ammonium sulfate, (NH4)2SO4

First, let's find the molar mass of the compound ammonium sulfate ((NH4)2SO4). Use the atomic masses for nitrogen (N, 14.01 g/mol), hydrogen (H, 1.01 g/mol), sulfur (S, 32.07 g/mol), and oxygen (O, 16.00 g/mol): Molar mass of (NH4)2SO4 = (2 × (1 × 14.01 g/mol + 4 × 1.01 g/mol)) + (1 × 32.07 g/mol) + (4 × 16.00 g/mol) = 2 × (14.01 g/mol + 4.04 g/mol) + 32.07 g/mol + 64.00 g/mol = 2 × 18.05 g/mol + 96.07 g/mol = 132.14 g/mol Next, calculate the mass of the specified element (hydrogen) in the compound: Mass of hydrogen = 2 × (4 × 1.01 g/mol) = 8.08 g/mol Now, calculate the percentage by mass of the hydrogen in the ammonium sulfate: Percentage by mass of hydrogen = (8.08 g/mol / 132.14 g/mol) × 100 = 6.1%

Step 4: (d) Platinum in PtCl2(NH3)2, cisplatin

First, let's find the molar mass of the compound cisplatin (PtCl2(NH3)2). Use the atomic masses for platinum (Pt, 195.08 g/mol), chlorine (Cl, 35.45 g/mol), nitrogen (N, 14.01 g/mol), and hydrogen (H, 1.01 g/mol): Molar mass of PtCl2(NH3)2 = (1 × 195.08 g/mol) + (2 × 35.45 g/mol) + (2 × (1 × 14.01 g/mol + 3 × 1.01 g/mol)) = 195.08 g/mol + 70.90 g/mol + (2 × (14.01 g/mol + 3.03 g/mol)) = 195.08 g/mol + 70.90 g/mol + 2 × 17.05 g/mol = 300.18 g/mol Next, calculate the mass of the specified element (platinum) in the compound: Mass of platinum = 1 × 195.08 g/mol = 195.08 g/mol Now, calculate the percentage by mass of the platinum in the cisplatin: Percentage by mass of platinum = (195.08 g/mol / 300.18 g/mol) × 100 = 65.0%

Step 5: (e) Oxygen in estradiol, C18H24O2

First, let's find the molar mass of the compound estradiol (C18H24O2). Use the atomic masses for carbon (C, 12.01 g/mol), hydrogen (H, 1.01 g/mol), and oxygen (O, 16.00 g/mol): Molar mass of C18H24O2 = (18 × 12.01 g/mol) + (24 × 1.01 g/mol) + (2 × 16.00 g/mol) = 216.18 g/mol + 24.24 g/mol + 32.00 g/mol = 272.42 g/mol Next, calculate the mass of the specified element (oxygen) in the compound: Mass of oxygen = 2 × 16.00 g/mol = 32.00 g/mol Now, calculate the percentage by mass of the oxygen in the estradiol: Percentage by mass of oxygen = (32.00 g/mol / 272.42 g/mol) × 100 = 11.7%

Step 6: (f) Carbon in capsaicin, C18H27NO3

First, let's find the molar mass of the compound capsaicin (C18H27NO3). Use the atomic masses for carbon (C, 12.01 g/mol), hydrogen (H, 1.01 g/mol), nitrogen (N, 14.01 g/mol), and oxygen (O, 16.00 g/mol): Molar mass of C18H27NO3 = (18 × 12.01 g/mol) + (27 × 1.01 g/mol) + (1 × 14.01 g/mol) + (3 × 16.00 g/mol) = 216.18 g/mol + 27.27 g/mol + 14.01 g/mol + 48.00 g/mol = 305.46 g/mol Next, calculate the mass of the specified element (carbon) in the compound: Mass of carbon = 18 × 12.01 g/mol = 216.18 g/mol Now, calculate the percentage by mass of the carbon in the capsaicin: Percentage by mass of carbon = (216.18 g/mol / 305.46 g/mol) × 100 = 70.8%

Key Concepts

Molar Mass Calculation

When calculating the molar mass of a chemical compound, we essentially sum the atomic masses of all the elements present in the molecule. Each element contributes to the overall molar mass based on its quantity and atomic weight. To find the molar mass, follow these steps:

• Identify the formula of the compound and list the elements present.
• Use the periodic table to determine the atomic mass of each element.
• Multiply the atomic mass of each element by the number of atoms of that element in the compound.
• Add up all the values to get the total molar mass of the compound.

For example, in acetylene, \(\mathrm{C}_2\mathrm{H}_2\), the molar mass is calculated by finding the sum of the atomic masses for carbon and hydrogen. For carbon, it's \((2 \times 12.01 \text{ g/mol})\) and for hydrogen, it's \((2 \times 1.01 \text{ g/mol})\), bringing us to a total of \(26.04 \text{ g/mol}\). This calculated molar mass is crucial for deriving further chemical properties and behaviors of the compound.

Chemical Compounds

Chemical compounds are substances composed of two or more elements chemically bonded together. Unlike a simple mixture where substances can retain their individual properties, in a compound, elements combine proportionally and the resultant compound displays new characteristics. Each compound can be represented by a chemical formula that gives insight into the elements involved and their ratios. In acetylene (C2H2), acetylene is a compound composed primarily of carbon and hydrogen atoms. This fixed ratio determines its properties and reactions.

• Elements in a compound are bonded together in fixed ratios, specific to the compound.
• The chemical formula provides an at-a-glance look at the elements and their proportions.
• This information helps predict how compounds will react chemically.

Understanding these formulas is essential for working with chemical reactions and for the calculation of values such as molar mass and percentage composition by mass.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It plays a crucial role in calculating masses, moles, and percentages of elements within a compound based on their atomic proportions.For calculating percentage composition by mass, stoichiometry helps in evaluating how much mass of a specific element contributes to the total mass of a compound:

• Calculate the mass of each element in the compound using atomic masses.
• Determining the molar mass of the compound provides the total mass reference.
• The formula \(\text{Percentage by Mass} = \left( \frac{\text{Mass of Element}}{\text{Molar Mass of Compound}} \right) \times 100 \) calculates the element's contribution to the total mass.

In practice, this is used to find the mass percentage of elements in compounds like vitamin C or ammonium sulfate. This approach not only simplifies the complexity of dealing with multiple atoms but also guides practical applications such as determining nutritional contents or formulating pharmaceuticals.