Problem 31 - Chemistry Matter and Change

Question

Iron(III) sulfate \(\left[\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\right]\) is sometimes used in the water purification process. Determine the number of moles of sulfate ions present in 3.00 mol of \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\).

Step-by-Step Solution

Answer

There are 9.00 moles of sulfate ions in 3.00 moles of \(\text{Fe}_2(\text{SO}_4)_3\).

Step 1: Understanding the Mole Ratio

Iron(III) sulfate has the chemical formula \( ext{Fe}_2( ext{SO}_4)_3\). This formula indicates that 1 mole of \( ext{Fe}_2( ext{SO}_4)_3\) contains 3 moles of sulfate ions \(( ext{SO}_4^{2-})\). The subscript '3' after \(( ext{SO}_4)\) tells us that there are 3 sulfate ions in each formula unit of iron(III) sulfate.

Step 2: Calculating the Total Moles of Sulfate Ions

To find the total number of moles of sulfate ions in 3.00 moles of \( ext{Fe}_2( ext{SO}_4)_3\), multiply the number of moles of iron(III) sulfate by the mole ratio of sulfate ions: \(3.00 \, \text{mol} imes 3 \, \text{mol of} \, \text{(SO}_4^{2-}\text{) / mol of} \, \text{Fe}_2( ext{SO}_4)_3 = 9.00 \, \text{mol of} \, \text{(SO}_4^{2-}\text{)}\).

Key Concepts

Understanding Chemical Formula

A chemical formula is a way of expressing information about the atoms that constitute a particular chemical compound. It is a symbolic representation of the elements in a molecule. For example, the chemical formula of iron(III) sulfate is \(\text{Fe}_2(\text{SO}_4)_3\). This formula gives us several pieces of valuable information.

• Elements Present: The formula shows that it contains iron (Fe), sulfur (S), and oxygen (O).
• Numbers of Each Atom: The subscripts indicate the number of atoms. In iron(III) sulfate, "2" after Fe shows two iron atoms, and "3" outside the brackets indicates that there are three sulfate groups, each consisting of one sulfur and four oxygen atoms.

Understanding chemical formulas is essential in chemistry because they convey both quantitative and qualitative information about a compound, which helps in calculating mole ratios and understanding compound compositions.

Calculating Using Mole Ratio

A mole ratio is a conversion factor derived from the coefficients of a balanced chemical equation. It is used to relate quantities in a chemical reaction or compound. In the context of our problem, for every 1 mole of iron(III) sulfate \(\text{Fe}_2(\text{SO}_4)_3\), there are 3 moles of sulfate ions \((\text{SO}_4^{2-})\).

The mole ratio formula can be expressed as:
\[\text{Mole Ratio} = \frac{\text{Moles of Desired Substance}}{\text{Moles of Given Substance}}\]
To find how many moles of sulfate ions are present in 3.00 moles of \(\text{Fe}_2(\text{SO}_4)_3\), we apply this mole ratio:
3.00 moles of \(\text{Fe}_2(\text{SO}_4)_3\) \(\times\) \(\frac{3 \text{ moles (SO}_4^{2-})}{1 \text{ mole Fe}_2(\text{SO}_4)_3}\) = 9.00 moles of \((\text{SO}_4^{2-})\).

This calculation reveals that understanding mole ratios is crucial for interpreting chemical reactions and for determining how many atoms or ions are needed or produced, which is vital for applications like water purification.

Role of Sulfate Ions in Water Purification

Sulfate ions \((\text{SO}_4^{2-})\) are polyatomic ions consisting of one sulfur atom covalently bonded to four oxygen atoms. In water purification, compounds like iron(III) sulfate, which contain sulfate ions, are often used as coagulants to remove impurities from water.

• Coagulation Process: In water treatment, iron(III) sulfate dissociates into sulfate ions and ferric ions. These ions help to neutralize the charges on particles, allowing them to form larger aggregates, or flocs, which can be easily removed from water.
• Safe and Effective: The use of sulfate ions in water treatment is considered safe and is effective in removing a wide range of impurities, including organic matter, reducing turbidity, and improving water clarity.

While sulfate ions can already be present in water, their controlled addition through compounds like iron(III) sulfate plays a significant role in maintaining water quality and safety.