Problem 106 - Chemistry and Chemical Reactivity

Question

The recommended daily allowance (RDA) of iron in your diet is 15 mg. How many moles is this? How many atoms?

Step-by-Step Solution

Answer

15 mg of iron is approximately \(2.69 \times 10^{-4}\) moles or \(1.62 \times 10^{20}\) atoms.

Step 1: Convert Milligrams to Grams

First, convert the recommended daily allowance of iron from milligrams to grams. Since there are 1,000 milligrams in a gram, 15 mg is equal to 0.015 grams.

Step 2: Determine Molar Mass of Iron

Next, determine the molar mass of iron, which is approximately 55.85 grams per mole. This information tells us how much one mole of iron weighs.

Step 3: Calculate Moles of Iron

To find the number of moles of iron, divide the mass of iron in grams by the molar mass of iron. This is given by: \( \text{moles} = \frac{\text{mass in grams}}{\text{molar mass}} = \frac{0.015 \text{ g}}{55.85 \text{ g/mol}} \approx 2.69 \times 10^{-4} \text{ moles} \).

Step 4: Use Avogadro's Number to Find Number of Atoms

Using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms per mole, calculate the number of atoms by multiplying the moles of iron by Avogadro's number: \( \text{atoms} = 2.69 \times 10^{-4} \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} \approx 1.62 \times 10^{20} \text{ atoms} \).

Key Concepts

The concept of Recommended Daily Allowance (RDA)

The Recommended Daily Allowance (RDA) is a vital guideline that helps individuals understand how much of a nutrient they need to consume each day to maintain good health. It is essentially a benchmark to ensure nutritional intake is sufficient for most people. When it comes to nutrients like vitamins and minerals, such as iron, the RDA helps prevent deficiencies. Iron, in particular, is important for various bodily functions, including the production of hemoglobin, which carries oxygen in the blood.
The RDA of iron is based on factors like age, gender, and physiological state. For most adults, the standard RDA is around 15 mg. Consuming this amount daily ensures balance, helping to avoid both an iron deficiency and excess iron, which can be harmful. Knowing how to convert this allowance into moles or atoms, as seen in the original exercise, helps in understanding the chemistry behind nutritional requirements.

Understanding Molar Mass

Molar mass is a fundamental concept in chemistry, representing the mass of one mole of a substance. It is typically expressed in grams per mole (g/mol). This value is incredibly helpful because it links the macroscopic and microscopic worlds. For iron, the molar mass is approximately 55.85 g/mol.

• The molar mass allows us to convert between the mass of a substance and the number of moles, which is a crucial step in most chemical calculations.
• To calculate the number of moles from a given mass, we divide the mass by the molar mass. This provides a deeper understanding of how substances interact at a molecular level.

In the exercise, knowing the molar mass of iron helps calculate how many moles are present in the recommended daily allowance, bridging dietary information with chemical data.

Using Avogadro's Number in Calculations

Avogadro's Number is key in chemistry, offering a bridge between the atomic scale and quantities we can observe and measure. Named after Amedeo Avogadro, it is defined as approximately \(6.022 \times 10^{23}\) atoms or molecules per mole. This immense number reflects how numerous atoms or molecules are in small masses of substances.
Avogadro's Number is used to calculate the number of atoms in a sample when the number of moles is known. This makes it essential for translating between moles and the exact number of elementary entities, such as atoms or molecules.
In the context of the exercise, multiplying the moles of iron by Avogadro's Number helps determine the exact number of atoms in the specified dietary amount. These calculations enhance our grasp of quantity at the atomic level, vital for disciplines ranging from nutrition to molecular chemistry.