Problem 124 - Chemistry The Molecular Science

Question

Which member of each pair has the greater mass? Explain why. (a) \(1 \mathrm{~mol}\) iron or \(1 \mathrm{~mol}\) aluminum (b) \(6.022 \times 10^{24}\) lead atoms or 1 mol lead (c) 1 copper atom or \(1 \mathrm{~mol}\) copper (d) \(1 \mathrm{~mol} \mathrm{Cl}\) or \(1 \mathrm{~mol} \mathrm{Cl}_{2}\) (e) \(1 \mathrm{~g}\) oxygen atoms or \(1 \mathrm{~g}\) oxygen molecules (f) \(23.4 \mathrm{~g} \mathrm{Mg}\) or \(1 \mathrm{~mol} \mathrm{Mg}\) (g) \(1 \mathrm{~mol} \mathrm{Na}\) or \(1 \mathrm{~g} \mathrm{Na}\) (h) \(4.1 \mathrm{~g} \mathrm{He}\) or \(6.022 \times 10^{23} \mathrm{He}\) atoms (i) 1 molecule \(\mathrm{I}_{2}\) or \(1 \mathrm{~mol} \mathrm{I}_{2}\) (j) 1 oxygen molecule or 1 oxygen atom

Step-by-Step Solution

Answer

(a) Iron; (b) 6.022×10^24 lead atoms; (c) 1 mol copper; (d) 1 mol Cl2; (e) 1 g O2 has greater mass; (f) 1 mol Mg; (g) 1 mol Na; (h) 4.1 g He; (i) 1 mol I2; (j) O2 molecule.

Step 1: Molar Mass Comparison

Compare the molar mass of iron and aluminum to determine which 1 mol of these elements has a greater mass. The molar mass of iron (Fe) is approximately 55.85 g/mol, while the molar mass of aluminum (Al) is approximately 26.98 g/mol. Since 55.85 g/mol > 26.98 g/mol, 1 mol of iron has a greater mass than 1 mol of aluminum.

Step 2: Quantity of Lead Atoms

Compare the amount of lead atoms between the two options. 1 mol of lead contains Avogadro's number of atoms, which is approximately \(6.022 \times 10^{23}\). \(6.022 \times 10^{24}\) atoms is ten times more than \(1 \text{ mol}\) of lead. Since both quantities refer to atoms of the same substance, \(6.022 \times 10^{24}\) atoms of lead will have a greater mass.

Step 3: Atomic vs Molar Comparison for Copper

Compare the mass of a single copper atom to 1 mol of copper. 1 mol of copper is equivalent to Avogadro's number of copper atoms, meaning it contains \(6.022 \times 10^{23}\) atoms. Therefore, 1 mol of copper has a much greater mass than a single copper atom, as it is \(63.55 \text{ g/mol}\) (the molar mass of copper).

Step 4: Molecular Mass of Chlorine

Compare the masses of 1 mol \(\text{Cl}\) (35.45 g) and 1 mol \(\text{Cl}_{2}\) (70.90 g). Since \(\text{Cl}_{2}\) is a diatomic molecule, 1 mol of \(\text{Cl}_{2}\) has twice the molar mass of chlorine \(\text{Cl}\) atoms, making it greater.

Step 5: Molecules vs Atoms in Oxygen

Although 1 g of oxygen atoms or oxygen molecules both weigh 1 g, oxygen molecules \(\text{O}_{2}\) have greater mass concentration per mole due to molecular weight. In general, regardless of the weight, molecules have higher aggregate mass than individual atoms, hence per gram, oxygen molecules have greater total substance mass than atoms.

Step 6: Molar Mass in Magnesium

Compare 23.4 g of Mg with 1 mol of Mg (24.31 g/mol). In terms of molar mass, 1 mol of magnesium weighs more than 23.4 g. Thus, \(1 \text{ mol Mg}\) has a greater mass.

Step 7: Mole-Mass Comparison for Sodium

Compare 1 mol \(\text{Na}\) (22.99 g/mol) with 1 g of \(\text{Na}\). Given that 1 mol weighs substantially more than 1 g, 1 mol of sodium has the greater mass.

Step 8: Helium Atom Quantity

Compare 4.1 g of helium to 1 mol \((\approx 6.022 \times 10^{23})\) of helium atoms, or \(4.00 \text{ g/mol}\). 4.1 g is slightly more than 1 mol of helium atoms, which means the mass of 4.1 g of helium is greater.

Step 9: Molecular Mass in Iodine

Compare one molecule of \(\text{I}_{2}\) with one mol of \(\text{I}_{2}\). One mol contains Avogadro's number of molecules \((6.022 \times 10^{23})\), far more significant in mass than a single molecule by a substantial amount due to iodine's molar mass of \(253.8 \text{ g/mol}\).

Step 10: Mass of Oxygen Comparatively

For a single molecule and a single atom of oxygen, the molecule (\(\text{O}_{2}\)) has a greater mass because it contains two atoms instead of one.

Key Concepts

Avogadro's Number

Avogadro's Number is crucial for understanding the mole concept. It is a huge number, specifically:

• Avogadro's Number: \(6.022 \times 10^{23}\)

This constant defines the number of atoms, molecules, or particles in one mole of a substance.
This means if you have one mole of any element or compound, it contains exactly \(6.022 \times 10^{23}\) of its constituent particles.
For example, one mole of lead will have this many atoms of lead. This enormous number helps bridge the gap between the macroscopic world that we can see and the microscopic world of atoms and molecules.

Practical Usage

Here's how Avogadro's number comes into play:

• It allows chemists to count and calculate quantities of substances in a standardized way.
• It's vital for converting between atomic/molecular-scale masses and quantities we can measure in grams.

Molecular Mass

Molecular mass is the sum of the atomic masses of the atoms within a single molecule.
When you add up the masses of each atom in a molecule, you obtain its molecular mass.
This is usually expressed in atomic mass units (amu).

Calculation Example

For instance, the molecular mass of chlorine gas (\(Cl_2\)):

• It's composed of two chlorine atoms.
• Each chlorine atom has an atomic mass of approximately 35.45 amu.
• Therefore, the molecular mass of \(Cl_2\) is \(2 \times 35.45 = 70.90\) amu.

In practice, molecular masses help determine how much of a molecule is present in a given sample when you know its weight in grams.
This helps in calculating concentrations and reactions among various substances.

Atomic Mass

Atomic mass is the mass of an individual atom, typically expressed in atomic mass units (amu).
It roughly corresponds to the sum of protons and neutrons in an atom's nucleus.

Why It's Important

• Each element has a unique atomic mass, such as hydrogen with approximately 1 amu and helium with about 4 amu.
• Atomic masses are essential for calculating how heavy a single atom is, and subsequently, for determining the molecular mass of compounds.

Understanding atomic mass is key to comparing different atoms, especially when converting between different amounts of elements, such as in molar mass calculations.
Such comparisons are necessary to solve problems like determining which substance in a pair has the greater mass, as atomic and molar masses directly influence these calculations.

Mole Concept

The mole concept is a foundational principle in chemistry that connects the amount of substance with its mass.
One mole is defined as the quantity of substance that contains Avogadro's number of particles, whether they're atoms, molecules, or ions.

Real-World Applications

• Enables chemists to count atoms and molecules in bulk, translating atomic masses into measurable quantities:
• For example, knowing the molar mass of copper is 63.55 g/mol allows for determining how much a given quantity weighs.
• Helps in balancing chemical equations and conducting experiments on a scalable level.

Grasping the mole concept ensures accurate calculations and understanding of chemical compositions and reactions, making it invaluable for scientific endeavors and industrial applications.