Problem 110 - Chemistry and Chemical Reactivity

Question

The recommended daily allowance (RDA) of iron for women \(19-30\) years old is 18 mg. How many moles is this? How many atoms?

Step-by-Step Solution

Answer

The RDA of iron is approximately 3.22 \times 10^{-4} moles or 1.94 \times 10^{20} atoms.

Step 1: Convert Mass to Moles

First, we need to convert the mass of iron in milligrams to moles. The molecular weight of iron is approximately 55.85 g/mol. The RDA of iron is 18 mg, which is equal to 0.018 g. We use the formula:\[\text{moles of iron} = \frac{\text{mass of iron (g)}}{\text{molar mass of iron (g/mol)}} = \frac{0.018}{55.85} \approx 3.22 \times 10^{-4} \text{ moles}\]

Step 2: Calculate the Number of Atoms

Next, we need to convert the moles of iron to the number of atoms. We use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms/mol. Multiply the number of moles by Avogadro's number:\[\text{number of atoms} = 3.22 \times 10^{-4} \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 1.94 \times 10^{20} \text{ atoms}\]

Key Concepts

Molar Mass

The concept of molar mass is crucial in converting between the mass of a substance and the number of moles, which are units of measurement in chemistry. Molar mass is essentially the mass of one mole of a given element or compound. It allows us to bridge the gap between the macroscopic world (the mass we can measure) and the microscopic world (individual atoms and molecules). The molar mass is usually expressed in grams per mole (g/mol). For example, the molar mass of iron is approximately 55.85 g/mol.

To determine how many moles of an element you have from a given mass, you use the formula:

• \( \text{moles} = \frac{\text{mass of the substance (g)}}{\text{molar mass (g/mol)}} \)

This equation tells us that the number of moles is equal to the mass of the substance divided by its molar mass. Understanding this concept helps us convert practical measurements into something we can use for further calculations or predictions about chemical reactions.

Avogadro's Number

Avogadro's Number is a fundamental constant in chemistry that provides a link between the mass of a substance and the amount of particles it contains. Named after the scientist Amedeo Avogadro, this number is approximately \( 6.022 \times 10^{23} \) and represents the number of atoms, molecules, or particles in one mole of any substance.

Understanding Avogadro's Number is essential when converting moles of a substance into the number of atoms. It allows chemists to accurately estimate the count of particles in a sample without needing to physically count each one.

• To find the number of atoms in a given mole, simply multiply the number of moles by Avogadro's Number.
• This conversion is key in understanding how much of a substance is truly present at the atomic level.

For instance, in the case of iron, knowing the moles helps us compute how many individual atoms you have, using Avogadro’s number, yielding a large number that supports its use in everyday nutritional intake.

Chemical Calculations

Chemical calculations form a backbone of chemistry as they help chemists figure out the quantities of reactants and products involved in chemical reactions. These calculations enable scientists to transition from the mass of substances utilized in the lab to the microscopic world of atoms and molecules.

The process typically involves several steps:

• First, convert the mass of the substance to moles, using the molar mass as a conversion factor.
• Then, use Avogadro's number to find the number of atoms or molecules in the given moles.
• This multi-step approach ensures precision and accuracy in chemical experimentation and applications.

Practicing these steps enhances your skills in performing chemical calculations, allowing for accurate formulation of chemicals whether you’re adjusting dietary components, like the recommended daily allowance of iron, or predicting outcomes in chemical reactions. Understanding how mass, molar mass, and Avogadro’s Number interrelate is fundamental to mastering chemical calculations.