Problem 76 - Chemistry and Chemical Reactivity

Question

How many ammonium ions and how many sulfate ions are present in a 0.20 mol sample of \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4} ?\) How many atoms of \(\mathrm{N}, \mathrm{H}, \mathrm{S}\) and \(\mathrm{O}\) are contained in this sample?

Step-by-Step Solution

Answer

There are 0.40 mol ammonium ions and 0.20 mol sulfate ions. Atoms: N = 2.41×10^23, H = 9.63×10^23, S = 1.20×10^23, O = 4.82×10^23.

Step 1: Calculate Total Moles of Ions

Given a 0.20 mol sample of \((\mathrm{NH}_4)_2 \mathrm{SO}_4\), since each formula unit contains 2 ammonium ions and 1 sulfate ion, multiply the number of moles by the ions in the formula:\[\text{Ammonium ions} = 0.20 \times 2 = 0.40 \text{ moles}\]\[\text{Sulfate ions} = 0.20 \times 1 = 0.20 \text{ moles}\]

Step 2: Calculate Total Moles of Atoms

Break down the moles of ions into individual atoms for each element in \((\mathrm{NH}_4)_2 \mathrm{SO}_4\):- Each ammonium ion \( (\mathrm{NH}_4)^+ \) contains 1 N and 4 H.- Each sulfate ion \( \mathrm{SO}_4^{2-} \) contains 1 S and 4 O.For 0.20 mol of \((\mathrm{NH}_4)_2 \mathrm{SO}_4\), we have:- Nitrogen: \(0.20 \text{ mol} \times 2 = 0.40 \text{ mol} \text{ N}\)- Hydrogen: \(0.20 \text{ mol} \times 8 = 1.60 \text{ mol} \text{ H}\)- Sulfur: \(0.20 \text{ mol} \times 1 = 0.20 \text{ mol} \text{ S}\)- Oxygen: \(0.20 \text{ mol} \times 4 = 0.80 \text{ mol} \text{ O}\)

Step 3: Convert Moles to Number of Atoms/Ions

Use Avogadro's number \(6.022 \times 10^{23}\) to convert moles to individual ions or atoms:- Ammonium Ions: \(0.40 \text{ moles} \times 6.022 \times 10^{23} = 2.41 \times 10^{23} \text{ ammonium ions}\)- Sulfate Ions: \(0.20 \text{ moles} \times 6.022 \times 10^{23} = 1.20 \times 10^{23} \text{ sulfate ions}\)- Nitrogen Atoms: \(0.40 \text{ moles} \times 6.022 \times 10^{23} = 2.41 \times 10^{23} \text{ N atoms}\)- Hydrogen Atoms: \(1.60 \text{ moles} \times 6.022 \times 10^{23} = 9.63 \times 10^{23} \text{ H atoms}\)- Sulfur Atoms: \(0.20 \text{ moles} \times 6.022 \times 10^{23} = 1.20 \times 10^{23} \text{ S atoms}\)- Oxygen Atoms: \(0.80 \text{ moles} \times 6.022 \times 10^{23} = 4.82 \times 10^{23} \text{ O atoms}\)

Key Concepts

Mole Concept

The mole concept is a fundamental idea in chemistry that helps us count atoms, ions, and molecules. In simple terms, a mole is a unit that represents a specific number of particles, similar to a dozen representing 12 items. One mole contains Avogadro's number of particles, which is approximately \(6.022 \times 10^{23}\). This large number is used because atoms and molecules are extremely small, and it allows chemists to work with chemicals on a macroscopic scale that is easily observable.

In our exercise, we dealt with 0.20 moles of ammonium sulfate \((NH_4)_2 SO_4\). Using the mole concept, we converted this amount into moles of ammonium ions and sulfate ions by recognizing that each formula unit of ammonium sulfate contains two ammonium ions \((NH_4^+)\) and one sulfate ion \((SO_4^{2-})\). By multiplying the given moles of the compound by the number of ions per formula unit, we easily determined the moles of each type of ion. Understanding this concept allows us to accurately measure substances and predict the amounts of products formed in a reaction.

Chemical Formulas

Chemical formulas are a shorthand way to represent compounds using symbols for the elements and numbers to show the relative amounts. For example, the formula \((NH_4)_2 SO_4\) represents ammonium sulfate. This indicates that each formula unit contains:

• 2 ammonium ions \((NH_4^+)\)
• 1 sulfate ion \((SO_4^{2-})\)

Each ammonium ion is made up of one nitrogen \(N\) and four hydrogen \(H\) atoms, while each sulfate ion contains one sulfur \(S\) and four oxygen \(O\) atoms. The subscript numbers in the formula indicate how many of each atom are present. For instance, in ammonium \(NH_4\), there are four hydrogen atoms bonded to one nitrogen atom.

Chemical formulas allow for the precise communication of the composition of compounds and play a crucial role in chemical equations that represent reactions. By breaking down the formula \((NH_4)_2 SO_4\), we can understand the specific make-up of the compound and calculate the total number of each atom within a mole of a compound, providing vital information when predicting changes during a chemical reaction.

Ionic Compounds

Ionic compounds are formed when metals transfer electrons to non-metals, resulting in positive and negative ions that attract and form a neutral compound. These compounds are held together by strong ionic bonds due to the electrostatic forces between oppositely charged ions.

In our example, the compound \((NH_4)_2 SO_4\) is made up of ammonium ions \((NH_4^+)\) and sulfate ions \((SO_4^{2-})\). The ammonium ion is unusual because it’s a polyatomic ion, meaning it consists of more than one atom that behaves as a single charged entity. Understanding polyatomic ions is essential because they frequently occur in ionic compounds.

Ionic compounds tend to be crystalline solids at room temperature and generally have high melting and boiling points due to the strong forces between ions. They also typically dissolve well in water, dissociating into their respective ions. These properties are crucial in many chemical processes, especially in solution chemistry, where the ionic nature of compounds determines how they react. Understanding their structure helps us predict the behavior of these materials in various chemical reactions.