Chemistry 9701/11 — October/November 2022

Background Concept

The mole is the amount of substance that contains the Avogadro constant, $N_A = 6.02 \times 10^{23}$, of particles. To compare the number of particles in different samples, we convert each mass to an amount in moles using

$$n=\frac{m}{M}$$

where $m$ is the mass and $M$ is the molar mass of the species being counted.

The key subtlety is that the "named species" is not always the same type of particle:

• Molecular substances such as chlorine and carbon dioxide exist as molecules, so $\text{Cl}_2$ and $\text{CO}_2$ are the particles counted.
• Atomic elements such as sodium and sulfur can be counted as atoms.
• Ionic compounds such as potassium chloride do not contain molecules. They contain ions, so we count ions or formula units.

Equal amounts in moles mean equal numbers of particles, because the Avogadro constant applies to all species.

Understanding the Question

The question asks which sample contains the same number of the named species as the number of molecules in $35.5\text{ g}$ of chlorine. The phrase "named species" is important: in each option the particle being counted is different — atoms in A and B, ions in C, and molecules in D.

First we must find how many moles of chlorine molecules are present in $35.5\text{ g}$. Chlorine is a diatomic molecule, $\text{Cl}_2$, so its molar mass is $2 \times 35.5 = 71.0\text{ g mol}^{-1}$. Therefore:

$$n(\text{Cl}_2)=\frac{35.5}{71.0}=0.50\text{ mol}$$

So we need the option that contains $0.50$ mol of the named species.

Approach

1. Calculate the target amount: moles of $\text{Cl}_2$ molecules in $35.5\text{ g}$.
2. For each option, identify the correct particle and its molar mass.
3. Convert the given mass to moles of that named species.
4. Compare each result with $0.50$ mol.

Step-by-Step Reasoning

Target:

$$n(\text{Cl}_2)=\frac{35.5}{71.0}=0.50\text{ mol molecules}$$

Option A — atoms in $16\text{ g}$ of sulfur.
The named species is sulfur atoms. The atomic molar mass of sulfur is about $32.1\text{ g mol}^{-1}$.

$$n(\text{S})=\frac{16}{32.1}\approx 0.50\text{ mol atoms}$$

This matches the target, so A is correct. Note that sulfur commonly exists as $\text{S}_8$ molecules, but the option specifically asks for atoms, so we use the atomic mass.

Option B — atoms in $23\text{ g}$ of sodium.
Sodium is metallic and the named species is atoms.

$$n(\text{Na})=\frac{23}{23}=1.0\text{ mol atoms}$$

This is twice the target, so B is incorrect.

Option C — ions in $74.5\text{ g}$ of potassium chloride.
Potassium chloride is ionic, so it does not contain molecules. Its formula unit is $\text{KCl}$, with molar mass about $39.1 + 35.5 = 74.6\text{ g mol}^{-1}$, often taken as $74.5\text{ g mol}^{-1}$.

$$n(\text{KCl})=\frac{74.5}{74.5}=1.0\text{ mol formula units}$$

Each formula unit contains one $\text{K}^+$ ion and one $\text{Cl}^-$ ion, so the total number of ions is:

$$1.0 \times 2 = 2.0\text{ mol ions}$$

This is four times the target, so C is incorrect.

Option D — molecules in $88\text{ g}$ of carbon dioxide.
Carbon dioxide is molecular, with molar mass $12.0 + 2(16.0) = 44.0\text{ g mol}^{-1}$.

$$n(\text{CO}_2)=\frac{88}{44}=2.0\text{ mol molecules}$$

This is four times the target, so D is incorrect.

Therefore the correct answer is A.

Key Takeaways

• Always identify the actual particle being counted: atoms, molecules, or ions.
• Chlorine is diatomic, $\text{Cl}_2$, so its molar mass is double the atomic mass of chlorine.
• Equal numbers of moles always mean equal numbers of particles.
• For ionic compounds, count the ions released per formula unit, not just the formula units themselves.

Common Mistakes

• Using $\text{Cl}$ instead of $\text{Cl}_2$: this would give $1.0$ mol instead of $0.50$ mol and lead to the wrong option.
• Treating potassium chloride as molecules: $\text{KCl}$ is ionic, so it contains ions, not molecules.
• Forgetting to multiply by the number of ions: for option C, $1$ mol of $\text{KCl}$ gives $2$ mol of ions, not $1$ mol.
• Using $\text{S}_8$ for option A: although sulfur often exists as $\text{S}_8$, the option asks for atoms, so the atomic mass must be used.

Things to Be Careful About

• Use the molar mass that matches the named species: $71.0\text{ g mol}^{-1}$ for $\text{Cl}_2$, $32.1\text{ g mol}^{-1}$ for S atoms, $23.0\text{ g mol}^{-1}$ for Na atoms, $74.5\text{ g mol}^{-1}$ for $\text{KCl}$, and $44.0\text{ g mol}^{-1}$ for $\text{CO}_2$.
• Read the phrase "named species" carefully; it tells you exactly which particle to count.
• State symbols are not needed here, but the chemical identity of each substance is essential.
• Approximate values are acceptable as long as the comparison clearly identifies the correct option.