Question

Vitamin E Many plants contain vitamin \(\mathrm{E}\left(\mathrm{C}_{29} \mathrm{H}_{50} \mathrm{O}_{2}\right)\) a substance that some think slows the aging process in humans. What is the percent composition of vitamin E?

Short answer

The percent composition of Vitamin E (\(C_{29}H_{50}O_{2}\)) is approximately 83.64% Carbon (C), 9.68% Hydrogen (H), and 6.14% Oxygen (O).

Step-by-step solution

Calculation of the molar mass of Vitamin E

To calculate the molar mass of Vitamin E, we add the molar masses of all the atoms in one molecule. This can be calculated by multiplying the atomic masses of Carbon (C), Hydrogen (H), and Oxygen (O) with their respective counts in the molecule and adding them up. Let's calculate: Molar mass of Vitamin E= (29 * Atomic mass of carbon) + (50 * Atomic mass of hydrogen) + (2 * Atomic mass of oxygen) = (29 * 12.01 u) + (50 * 1.008 u) + (2 * 16.00 u) = 438.29 u + 50.4 u + 32.00 u = 520.69 u

Calculation of the percent compositions

The percent composition of an element in a compound is calculated as follows: Percent composition = \( \frac{total \: mass \: of \: the \: element \: in \: one \: molecule}{molar \: mass \: of \: the \: compound} \times 100\% \) 1. Percent composition of Carbon \( \% C = \frac{29 * 12.01 \: u}{520.69 \: u} \times 100\% = 83.64\% \) 2. Percent composition of Hydrogen \( \% H = \frac{50 * 1.008 \: u}{520.69 \: u} \times 100\% = 9.68\% \) 3. Percent composition of Oxygen \( \% O = \frac{2 * 16.00 \: u}{520.69 \: u} \times 100\% = 6.14\% \)

Result

Hence, the percent composition of Vitamin E (\(C_{29}H_{50}O_{2}\)) is approximately 83.64% Carbon (C), 9.68% Hydrogen (H), and 6.14% Oxygen (O).

Key concepts

Understanding Molar Mass

Molar mass is an essential concept in chemistry that relates to the mass of one mole of a substance. It is expressed in units of grams per mole (g/mol) and is calculated as the sum of the atomic masses of all atoms in a molecule. The atomic mass of each element, which is the mass of a single atom, is given in atomic mass units (u), often referred to as daltons (Da).

For example, to find the molar mass of vitamin E (\(C_{29}H_{50}O_{2}\)), we first look at the chemical formula, which tells us that one molecule contains 29 carbon atoms, 50 hydrogen atoms, and 2 oxygen atoms. We then multiply the number of atoms of each element by their respective atomic masses and add the results together. Carbon has an atomic mass of approximately 12.01 u, hydrogen 1.008 u, and oxygen 16.00 u. By adding the masses of all atoms in vitamin E, we arrive at the molar mass of vitamin E, which is essential for calculating its percent composition.

In practical applications, understanding the molar mass helps in converting between the mass of a substance and the number of moles, making it a pivotal step in many stoichiometric calculations.

Atomic Mass and Its Significance

Atomic mass represents the mass of a single atom of an element and is a fundamental property that influences how substances combine in chemical reactions. It is usually averaged over all isotopes of the element as they occur in nature, resulting in a value that may not be a whole number. To clarify this concept, let's consider carbon, which has an atomic mass of 12.01 u.

Atomic masses are like the building blocks for determining the molar mass of compounds like vitamin E. By knowing the atomic mass of each element, we can calculate the molar mass and subsequently use it to find out the percent composition of elements within the compound. For complex molecules, such as biomolecules including vitamins, knowing the atomic mass and molar mass is crucial for understanding how these substances function in biological processes.

Deciphering the Chemical Formula

A chemical formula offers a quick glimpse into the composition of a chemical compound. It not only represents the types of atoms present but also indicates the exact number of each type of atom within a molecule.

For instance, the chemical formula of vitamin E (\(C_{29}H_{50}O_{2}\)) tells us that each molecule consists of 29 carbon atoms, 50 hydrogen atoms, and 2 oxygen atoms. This numerical representation is invaluable, as it is the starting point for many calculations in chemistry, including those for molar mass and percent composition.

The chemical formula acts as a direct link between the microscopic world of atoms and the macroscopic world of grams and moles that chemists work with in the lab. It is not just a notation; it's the language through which chemists understand and communicate the composition of substances. And when it comes to applying this knowledge to real-life substances, such as determining the nutritional value of food based on its vitamin content, the chemical formula becomes a vital piece of information.