Problem 122 - Chemistry and Chemical Reactivity

Question

Your doctor has diagnosed you as being anemic-that is, as having too little iron in your blood. At the drugstore, you find two iron-containing dietary supplements: one with iron(II) sulfate, \(\mathrm{FeSO}_{4},\) and the other with iron (II) gluconate, \(\mathrm{Fe}\left(\mathrm{C}_{6} \mathrm{H}_{11} \mathrm{O}_{7}\right)_{2} .\) If you take \(100 .\) mg of each compound, which will deliver more atoms of iron?

Step-by-Step Solution

Answer

100 mg of FeSO₄ delivers more iron atoms.

Step 1: Determine the Molar Mass of Each Compound

First, calculate the molar mass of iron(II) sulfate \( \mathrm{FeSO}_{4} \). The atomic masses are approximately: \( \mathrm{Fe} = 55.85 \), \( \mathrm{S} = 32.06 \), \( \mathrm{O} = 16.00 \). Thus, the molar mass of \( \mathrm{FeSO}_{4} \) is \( 55.85 + 32.06 + 4 \times 16.00 = 151.91 \text{ g/mol} \). Next, calculate the molar mass of iron(II) gluconate \( \mathrm{Fe(C}_{6} \mathrm{H}_{11} \mathrm{O}_{7})_{2} \). The atomic masses are: \( \mathrm{Fe} = 55.85 \), \( \mathrm{C} = 12.01 \), \( \mathrm{H} = 1.01 \), \( \mathrm{O} = 16.00 \). Thus, the molar mass of \( \mathrm{Fe(C}_{6} \mathrm{H}_{11} \mathrm{O}_{7})_{2} \) is \( 55.85 + 2\times(6 \times 12.01 + 11 \times 1.01 + 7 \times 16.00) = 446.14 \text{ g/mol} \).

Step 2: Calculate Moles of Each Compound

Convert 100 mg to grams: \(100 \text{ mg} = 0.1 \text{ g} \).For \( \mathrm{FeSO}_{4} \): \[ \text{Moles} = \frac{0.1 \text{ g}}{151.91 \text{ g/mol}} = 0.000659 \text{ mol} \]For \( \mathrm{Fe(C}_{6} \mathrm{H}_{11} \mathrm{O}_{7})_{2} \): \[ \text{Moles} = \frac{0.1 \text{ g}}{446.14 \text{ g/mol}} = 0.000224 \text{ mol} \]

Step 3: Determine Iron Atoms in Each

Each molecule of \( \mathrm{FeSO}_{4} \) contains one iron atom, so:\[ \text{Moles of Fe from } \mathrm{FeSO}_{4} = 0.000659 \text{ mol} \]Each molecule of \( \mathrm{Fe(C}_{6} \mathrm{H}_{11} \mathrm{O}_{7})_{2} \) also contains one iron atom, so:\[ \text{Moles of Fe from } \mathrm{Fe(C}_{6} \mathrm{H}_{11} \mathrm{O}_{7})_{2} = 0.000224 \text{ mol} \]

Step 4: Compare Iron Content

The number of moles of iron indicates the number of iron atoms since each mole contains Avogadro's number of atoms. In 100 mg of \( \mathrm{FeSO}_{4} \), you have \(0.000659 \text{ mol}\), which is greater than \(0.000224 \text{ mol}\) from 100 mg of \(\mathrm{Fe(C}_{6} \mathrm{H}_{11} \mathrm{O}_{7})_{2} \).

Key Concepts

Iron Supplement

Iron supplements are dietary aids designed to provide more iron to the body, which is essential for producing hemoglobin, a component in red blood cells that carries oxygen. For those who are diagnosed with anemia due to iron deficiency, these supplements can be crucial. Iron supplements come in various chemical forms, and the choice between them can influence the amount of elemental iron absorbed into the bloodstream.

When purchasing iron supplements, you might encounter different iron compounds, each with distinct characteristics:

• Iron sulfates, like Iron(II) sulfate, are among the most common types due to their high iron content.
• There are also other forms, such as gluconates, which tend to be gentler on the stomach.

Understanding the type of iron supplement you are consuming can have a direct impact on the supplement's effectiveness and how your body tolerates it.

Iron(II) Sulfate

Iron(II) sulfate, known chemically as \(\mathrm{FeSO}_{4}\), is a compound commonly used in iron supplements. It is often chosen for its relatively high iron content, meaning that a smaller amount of the supplement contains a significant quantity of iron atoms. The molar mass for Iron(II) sulfate has been calculated to be 151.91 g/mol.

This makes it a cost-effective option when aiming to increase iron intake. This compound consists of:

• One iron atom (Fe)
• One sulfur atom (S)
• Four oxygen atoms (O)

Given its structure, consuming a fixed amount, like 100 mg of iron(II) sulfate, provides a notable amount of elemental iron crucial for addressing deficiency.

Iron(II) Gluconate

Iron(II) gluconate, represented chemically as \(\mathrm{Fe(C}_{6} \mathrm{H}_{11} \mathrm{O}_{7})_{2}\), is another common form of iron used in supplements. It is generally preferred for people who experience gastrointestinal discomfort with other types of iron. The molar mass of iron(II) gluconate is relatively higher, at 446.14 g/mol, compared to other iron compounds, indicating that less iron is present in the same mass amount compared to iron(II) sulfate.

This compound comprises:

• One iron atom (Fe)
• Multiple carbon (C), hydrogen (H), and oxygen (O) atoms as part of the gluconate molecules

Despite its lower iron content per mg, iron(II) gluconate is popular for its higher tolerability, making it an excellent choice for individuals with sensitive digestive systems.

Moles Calculation

Understanding how to calculate moles is crucial in determining the number of atoms in a given sample. In chemistry, a mole is a unit that measures the amount of a substance, and one mole contains Avogadro's number, approximately \(6.022 \times 10^{23}\) particles, atoms, or molecules.

When calculating the number of moles of a compound, the formula used is:

• Moles = \( \frac{\text{mass of sample in grams}}{\text{molar mass of the compound in g/mol}} \)

For instance, if you have 100 mg (which is 0.1 g) of iron(II) sulfate, you would convert the mass to moles by dividing by its molar mass (151.91 g/mol), resulting in approximately 0.000659 moles.

This calculation helps in comparing different iron supplements by determining how much elemental iron each supplement provides relative to its dosage. Understanding these mole calculations ensures you can make informed decisions about which supplement might provide more iron to meet your health needs.