Problem 62 - 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 2.686 x 10^-4 moles and contains about 1.617 x 10^20 atoms.

Step 1: Convert milligrams to grams

The first step is to convert 15 milligrams to grams because molar mass is typically expressed in grams per mole. Since 1 milligram (mg) is equal to 0.001 gram (g), we have:\[ 15 \text{ mg} = 15 \times 0.001 \text{ g} = 0.015 \text{ g} \]

Step 2: Calculate moles of iron

Next, use the molar mass of iron to calculate the number of moles. The molar mass of iron (Fe) is approximately 55.85 g/mol. Using the formula for moles:\[ \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]Substitute the values into the formula:\[ \text{moles of Fe} = \frac{0.015 \text{ g}}{55.85 \text{ g/mol}} \approx 2.686 \times 10^{-4} \text{ moles} \]

Step 3: Convert moles to atoms

Finally, calculate the number of atoms using Avogadro's number, which is \(6.022 \times 10^{23}\) atoms/mol. Multiply the moles obtained in Step 2 by Avogadro's number:\[ \text{atoms of Fe} = 2.686 \times 10^{-4} \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 1.617 \times 10^{20} \text{ atoms} \]

Key Concepts

Understanding Molar Mass

When we talk about molar mass, we're referring to the weight of one mole of a particular substance. It's essentially the mass in grams of one mole of atoms, molecules, or compounds of a given substance. The molar mass is an essential factor when converting between the mass of a substance and the number of moles, as seen in chemical calculations.
To find the molar mass of an element, look at the atomic mass of the element on the periodic table. For compounds, sum the atomic masses of all atoms in the chemical formula.

• The molar mass of iron (Fe) is approximately 55.85 grams per mole (g/mol).
• This means that one mole, or 6.022 x 10^23 atoms, of iron weighs 55.85 grams.

Having a clear understanding of molar mass allows you to accurately perform calculations like those in the exercise, converting between grams and moles effectively.

Avogadro's Number: The Big Picture

Avogadro's number is a super useful tool in chemistry. It's the number that links the macroscopic world of grams and liters to the microscopic world of atoms and molecules. Specifically, Avogadro's number is approximately 6.022 x 10^23.
This number tells us how many particles, usually atoms or molecules, there are in one mole of a substance. It's a constant that allows for the conversion between the number of moles and the actual number of atoms.

• This is crucial for converting moles to atoms, just as seen in the exercise.
• For one mole of iron, Avogadro's number gives the number of iron atoms.

Using Avogadro's number, we can easily calculate the number of atoms from the moles of a substance, making it a vital part of any chemist's toolkit.

Mass to Moles Conversion

Understanding how to convert mass to moles is a cornerstone of chemistry calculations. This process allows you to determine the number of moles from a given mass of material.
The conversion uses the formula:
\[ \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Here’s a step-by-step on how to perform this calculation:

• Start by measuring the mass of your substance in grams.
• Identify the molar mass of the substance from the periodic table or other sources.
• Divide the mass by the molar mass to find the number of moles.

In the problem example, we converted 15 mg of iron to grams first, then used the molar mass of iron to find that 0.015 grams equals approximately 2.686 x 10^{-4} moles of iron. With these conversions, you can easily switch between grams and moles with confidence.