Question

Calculate the percentage by mass of the indicated element in the following compounds: (a) hydrogen in methane, \(\mathrm{CH}_{4}\), the major hydrocarbon in natural gas; \((\mathbf{b})\) oxygen in vitamin \(\mathrm{E}, \mathrm{C}_{29} \mathrm{H}_{50} \mathrm{O}_{2} ;\) (c) sulphur in magnesium sulphate, \(\mathrm{MgSO}_{4}\), a substance used as a drying agent; \((\mathbf{d})\) nitrogen in epinephrine, \(\mathrm{C}_{9} \mathrm{H}_{13} \mathrm{NO}_{3},\) also known as adrenalin, a hormone that is important for the fightor-flight response; (e) oxygen in the insect pheromone sulcatol, \(\mathrm{C}_{8} \mathrm{H}_{16} \mathrm{O} ;\) (f) carbon in sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11},\) the compound that is responsible for the sweet taste of table sugar.

Short answer

The mass percentages of the indicated elements in the given compounds are as follows: (a) Hydrogen in methane (CH4): 25.17% (b) Oxygen in vitamin E (C29H50O2): 7.43% (c) Sulphur in magnesium sulphate (MgSO4): 26.65% (d) Nitrogen in epinephrine (C9H13NO3): 7.65% (e) Oxygen in sulcatol (C8H16O): 12.48% (f) Carbon in sucrose (C12H22O11): 42.12%

Step-by-step solution

Molar Mass Calculation

First, we need to calculate the molar mass of each compound and the mass of the indicated element in each compound. (a) Methane (CH4): Molar mass of C = 12.01 g/mol Molar mass of H = 1.01 g/mol Molar mass of CH4 = (12.01 + 4 * 1.01) g/mol = 16.05 g/mol (b) Vitamin E (C29H50O2): Molar mass of C = 12.01 g/mol Molar mass of H = 1.01 g/mol Molar mass of O = 16.00 g/mol Molar mass of C29H50O2 = (29 * 12.01 + 50 * 1.01 + 2 * 16.00) g/mol = 430.72 g/mol (c) Magnesium sulphate (MgSO4): Molar mass of Mg = 24.31 g/mol Molar mass of S = 32.07 g/mol Molar mass of O = 16.00 g/mol Molar mass of MgSO4 = (24.31 + 32.07 + 4 * 16.00) g/mol = 120.38 g/mol (d) Epinephrine (C9H13NO3): Molar mass of C = 12.01 g/mol Molar mass of H = 1.01 g/mol Molar mass of N = 14.01 g/mol Molar mass of O = 16.00 g/mol Molar mass of C9H13NO3 = (9 * 12.01 + 13 * 1.01 + 14.01 + 3 * 16.00) g/mol = 183.22 g/mol (e) Sulcatol (C8H16O): Molar mass of C = 12.01 g/mol Molar mass of H = 1.01 g/mol Molar mass of O = 16.00 g/mol Molar mass of C8H16O = (8 * 12.01 + 16 * 1.01 + 16.00) g/mol = 128.22 g/mol (f) Sucrose (C12H22O11): Molar mass of C = 12.01 g/mol Molar mass of H = 1.01 g/mol Molar mass of O = 16.00 g/mol Molar mass of C12H22O11 = (12 * 12.01 + 22 * 1.01 + 11 * 16.00) g/mol = 342.34 g/mol

Mass Percentage Calculation

Now, we will calculate the mass percentage of each indicated element in the given compounds. (a) Hydrogen in methane: Percentage of H in CH4 = (4 * 1.01 / 16.05) * 100 = 25.17% (b) Oxygen in vitamin E: Percentage of O in C29H50O2 = (2 * 16.00 / 430.72) * 100 = 7.43% (c) Sulphur in magnesium sulphate: Percentage of S in MgSO4 = (32.07 / 120.38) * 100 = 26.65% (d) Nitrogen in epinephrine: Percentage of N in C9H13NO3 = (14.01 / 183.22) * 100 = 7.65% (e) Oxygen in sulcatol: Percentage of O in C8H16O = (16.00 / 128.22) * 100 = 12.48% (f) Carbon in sucrose: Percentage of C in C12H22O11 = (12 * 12.01 / 342.34) * 100 = 42.12% These calculated percentages are the mass percentages of the indicated element in each compound.

Key concepts

Molar Mass Calculation

To calculate the percentage by mass of an element in a compound, we first need to find the molar mass of that compound. Molar mass is the mass of one mole of a compound expressed in grams per mole (g/mol).
To determine the molar mass of a chemical compound, simply add up the molar masses of all the atoms present in the compound, taking into account how many atoms of each type are present.
For example, methane (\( \text{CH}_4 \)) is composed of one carbon atom and four hydrogen atoms:

• Molar mass of carbon (C) = 12.01 g/mol
• Molar mass of hydrogen (H) = 1.01 g/mol

Molar mass of methane = 12.01 + 4(1.01) g/mol = 16.05 g/mol.
Repeat this process for other compounds such as Vitamin E, magnesium sulfate, epinephrine, sulcatol, and sucrose by summing up the molar masses of individual elements to get the total molar mass of the compound.

Mass Percentage Calculation

Mass percentage calculation is all about determining what fraction of the total mass of a compound is due to a specific element.
To find the mass percentage of an element in a compound, use the following steps:

• Calculate the total molar mass of the compound as previously described.
• Identify the number of moles of the element in the compound and calculate their combined mass.
• Divide the mass of the element by the total molar mass of the compound, then multiply by 100 to express it as a percentage.

For example, to find the mass percentage of hydrogen in methane (\( \text{CH}_4 \)), we take the mass of the 4 hydrogen atoms divided by the molar mass of methane: \[\text{Percentage of H in CH}_4 = \left( \frac{4 \times 1.01}{16.05} \right) \times 100 \approx 25.17\%\]This formula helps us understand how much of any particular element is present by mass in a compound, and it is useful for both chemists and students alike.

Chemical Compounds

Chemical compounds are substances formed when two or more elements combine in definite proportions. Compounds can be simple combinations like water (\( \text{H}_2\text{O} \)) or complex organic structures, such as those found in biochemistry like Vitamin E or epinephrine.
Every compound has a fixed composition and exhibits unique properties different from the individual properties of the constituent elements.
In chemistry, compounds are often represented by chemical formulas, which display the types and numbers of atoms present. For instance:

• Methane is represented as \( \text{CH}_4 \), indicating one carbon atom combined with four hydrogen atoms.
• Magnesium sulfate is represented as \( \text{MgSO}_4 \), indicating one magnesium atom combined with one sulfur atom and four oxygen atoms.
• Sucrose is represented as \( \text{C}_{12}\text{H}_{22}\text{O}_{11} \), showing twelve carbon, twenty-two hydrogen, and eleven oxygen atoms.

Understanding chemical compounds and their compositions is essential for predicting reactions and for the study of chemistry as a whole. Knowing how these elements combine and their percentages allows us to understand the world in molecular detail.