Problem 96 - Chemistry Matter and Change

Question

RDA of Selenium The recommended daily allowance \((\mathrm{RDA})\) of selenium in your diet is \(8.87 \times 10^{-4} \mathrm{mol} .\) How many atoms of selenium is this?

Step-by-Step Solution

Answer

The RDA of selenium is equivalent to approximately \(5.34 \times 10^{20}\) atoms of selenium.

Step 1: Identify the Number of Moles

The RDA of selenium given is \(8.87 \times 10^{-4}\) moles. This value tells us how many moles of selenium are needed in the diet.

Step 2: Apply Avogadro's Number

To find out how many atoms are present in a given number of moles, we use Avogadro's number. Avogadro's number is \(6.022 \times 10^{23}\) atoms per mole, which is the number of atoms in one mole of any substance.

Step 3: Multiply Moles by Avogadro's Number

Multiply the number of moles of selenium by Avogadro's number to find the total number of selenium atoms.\[8.87 \times 10^{-4} \text{ mol} \times 6.022 \times 10^{23} \text{ atoms/mol} = 5.34 \times 10^{20} \text{ atoms}\]

Step 4: Report the Final Result

The total number of selenium atoms corresponding to the RDA is \(5.34 \times 10^{20}\) atoms.

Key Concepts

Moles

Moles are a fundamental concept in chemistry, providing a bridge between the microscopic world of atoms and the macroscopic world we interact with daily. A mole is essentially a counting unit similar to a dozen, except it is used for particles and represents a much larger quantity.

The Avogadro's number, which is approximately \(6.022 \times 10^{23}\), helps us quantify this relationship. - One mole of any substance contains \(6.022 \times 10^{23}\) entities, whether they be atoms, molecules, ions, or electrons.

This concept of moles allows chemists to count atoms in a measurable way, transforming atomic scale quantities into amounts that we can work with in the lab or consider in dietary contexts, such as the RDA of selenium.

Atoms

Atoms are the basic building blocks of matter and the defining structure of elements. Each element on the periodic table is comprised of a distinct type of atom.- Atoms consist of a nucleus containing protons and neutrons, with electrons orbiting around the nucleus.

When asking how many atoms there are in a certain amount of mole, we use Avogadro's number to make this conversion.- For instance, the exercise provides a scenario where \(8.87 \times 10^{-4}\) moles of selenium are equivalent to \(5.34 \times 10^{20}\) atoms.

Understanding atoms at this microscopic level is essential for explaining both chemical reactions and the properties of different elements.

RDA (Recommended Daily Allowance)

The Recommended Daily Allowance (RDA) is a measure used to indicate the daily level of consumption of a nutrient considered sufficient to meet the needs of most healthy people. Nutrients are essential substances required for growth and health. - RDAs are set by health authorities and help guide dietary intake.
- They ensure that you obtain enough essential nutrients daily. For selenium, an essential mineral crucial for various bodily processes, knowing the RDA helps maintain optimal health, supporting processes like metabolism and protecting cells from damage. - This exercise uses moles to relate the RDA of selenium to the number of selenium atoms needed daily for a healthy diet.

Selenium

Selenium is a trace mineral that plays a critical role in human health through various physiological functions. It is a component of antioxidant enzymes, which help to protect cells against damage. - Selenium can be found in foods like nuts, fish, and grains.

It supports a healthy immune system, thyroid function, and may even play a role in reducing cancer risk. - The amount required in the diet is quite small, but it is vital to ensure these small quantities are consistently met, hence the concept of RDA. With its connection to moles and atoms, the exercise illustrates how even a tiny amount of a substance can still involve billions of atoms, and highlights the precision required in nutritional science to equate dietary quantities with biological needs.