Problem 106 - Chemistry and Chemical Reactivity

Question

Which of the following is impossible? (a) silver foil that is \(1.2 \times 10^{-4} \mathrm{m}\) thick (b) a sample of potassium that contains \(1.784 \times\) \(10^{24}\) atoms (c) a gold coin of mass \(1.23 \times 10^{-3} \mathrm{kg}\) (d) \(3.43 \times 10^{-27}\) mol of \(S_{8}\) molecules

Step-by-Step Solution

Answer

(d) is impossible as you cannot have a fraction of a molecule.

Step 1: Understanding Avogadro's Number

First, we need to recall that Avogadro's number, which is approximately \(6.022 \times 10^{23}\), represents the number of atoms or molecules in one mole of a substance. Compare quantities given with realistic molecular or atomic counts using this constant.

Step 2: Analyze Option (a) - Silver Foil Thickness

Option (a) provides the thickness of a silver foil, \(1.2 \times 10^{-4}\) meters. This is a realistic value for the thickness of a thin metal foil and does not constitute an impossibility.

Step 3: Analyze Option (b) - Potassium Atoms

Option (b) mentions \(1.784 \times 10^{24}\) atoms of potassium. By dividing this number by Avogadro's number, \( \frac{1.784 \times 10^{24}}{6.022 \times 10^{23}} \approx 2.96 \), we find about 3 moles of potassium, which is possible.

Step 4: Analyze Option (c) - Gold Coin Mass

Option (c) gives the mass of a gold coin as \(1.23 \times 10^{-3}\) kg, or 1.23 grams. Given the density and common usage of gold, a coin of this mass is possible as it resembles a very small coin or medal.

Step 5: Analyze Option (d) - S8 Mole Fraction

Option (d) states \(3.43 \times 10^{-27}\) moles of \(S_8\) molecules. Check this against Avogadro's number: \(3.43 \times 10^{-27} \times 6.022 \times 10^{23} \approx 2.07 \times 10^{-3}\) molecules, which is far less than one molecule. Fractions of a molecule cannot exist, marking this as impossible.

Key Concepts

Avogadro's Number

Avogadro's number is a foundational concept in chemistry that makes it possible to count atoms and molecules in a practicable way. It is defined as the number of constituent particles—usually atoms or molecules—that are contained in one mole of a substance, approximately equal to \(6.022 \times 10^{23}\). This vast number was named after Amedeo Avogadro, who first hypothesized that equal volumes of gases, at the same temperature and pressure, contain an equal number of particles. Avogadro's number

• helps chemists bridge the gap between the microscopic world of atoms and the macroscopic world that we engage with daily
• enables the calculation of specific molecular and atomic quantities

For example, when given \(1.784 \times 10^{24}\) potassium atoms, we divide by Avogadro's number to find moles: \( \frac{1.784 \times 10^{24}}{6.022 \times 10^{23}} \approx 2.96 \text{ moles} \). Here, Avogadro's number serves as a conversion factor to help us understand and express quantities that are unfathomable in practical terms.By grounding chemical calculations in real, measurable traits, Avogadro's number allows chemists to make effective predictions and analyses in the laboratory.

Molecular Quantities

Molecular quantities refer to the measurable aspects of molecules, such as their mass, number, or energy levels. Understanding these properties is crucial for fields ranging from material science to pharmacology. The mole concept in chemistry, which is fundamentally connected to Avogadro's number, is key in expressing these molecular quantities in a coherent manner. For instance, when expressing the mass of a substance in grams:

• A mole of any element contains Avogadro's number of atoms
• A mole of a compound contains that number in its molecules, such as \(1 \text{ mole of } S_8 \text{ consists of } 6.022 \times 10^{23} S_8 \text{ molecules}\)

This unit of measurement allows chemists to utilize mass spectrometry to decode complicated mixtures and intervene in chemical reactions.Consider a gold coin with mass \(1.23 \times 10^{-3}\) kg. Its molecular quantity is evaluated based on its atom count and molar mass. Given Avogadro’s number, we can also assess potential molecules formed by combining different atoms.

Chemical Calculations

Chemical calculations are central to understanding reactions and creating compounds with desired properties. They involve mathematically determining the amounts of reactants and products in chemical processes, utilizing crucial concepts like Avogadro's number and molecular masses as tools. Through these calculations, chemists ensure balanced reactions where no atom is lost or created.To illustrate, option (d) of the problem involves calculating the impossibility of a very small mole fraction: \(3.43 \times 10^{-27}\) moles of \(S_8\). When we multiply this by Avogadro's number \((6.022 \times 10^{23})\), we arrive at merely \(2.07 \times 10^{-3}\) molecules—a fractional number meaning less than one molecule, which is impossible as molecules themselves are indivisible by definition.

• Selective conversion of atoms to moles is necessary to preview the quantities involved in reactions
• Equations adjust amounts, ensuring every reagent contributes fully to reactions

These are not just hypothetical exercises; rather, they lay the foundation for real-world applications such as developing new pharmaceuticals or materials.