Problem 137 - General Chemistry: Principles and Modern Applications

Question

The gas with the greatest density at STP is (a) \(\mathrm{N}_{2} \mathrm{O}\) (b) \(\mathrm{Kr} ;\) (c) \(\mathrm{SO}_{3} ;\) (d) \(\mathrm{Cl}_{2}\).

Step-by-Step Solution

Answer

The gas with the greatest density at Standard Temperature and Pressure (STP) is \(Kr\).

Step 1: Calculate The Molar Mass Of \(N_2O\)

The molar mass of a molecule is the sum of the molar masses of its atoms. Nitrogen's molar mass is 14.01 g/mol and Oxygen's molar mass is 16.00 g/mol. The \(N_2O\) molecule has 2 Nitrogen atoms and 1 Oxygen atom, thus the molar mass of \(N_2O\) is \(2*14.01 g/mol + 16.00 g/mol = 44.02 g/mol\).

Step 2: Calculate The Molar Mass Of \(Kr\)

The Kr is a noble gas. Its atomic mass is 83.80 g/mol which is same as molar mass because it is monoatomic. So the molar mass of \(Kr\) is 83.80 g/mol.

Step 3: Calculate The Molar Mass Of \(SO_3\)

Similar to step 1, the molar mass of \(SO_3\) is \(1*32.07 g/mol + 3*16.00 g/mol = 80.07 g/mol\).

Step 4: Calculate The Molar Mass Of \(Cl_2\)

The \(Cl_2\) molecule has 2 Chlorine atoms. As the molar mass of Chlorine is 35.45 g/mol, the molar mass of \(Cl_2\) is \(2 * 35.45 g/mol = 70.90 g/mol\).

Step 5: Compare The Molar Mass Of All four Gases

After comparing all the molar masses calculated above, it appears that \(Kr\) has the highest molar mass (83.80 g/mol). Therefore, \(Kr\) is the densest gas at STP.

Key Concepts

Molar Mass Calculation

The concept of molar mass is crucial in chemistry because it allows us to convert between the mass of a substance and the amount of substance in moles. To calculate the molar mass, add up the atomic masses of all atoms in a molecule. Each element's atomic mass can be found on the periodic table, usually listed in atomic mass units (amu) or g/mol when considering molar mass. For example:
The molar mass of nitrogen ( abla N_2O abla) involves adding twice the atomic mass of nitrogen (14.01 g/mol) and the atomic mass of oxygen (16.00 g/mol), resulting in 44.02 g/mol for abla N_2O abla.

• Chlorine gas ( abla Cl_2 abla) is composed of 2 chlorine atoms, and since each has a molar mass of 35.45 g/mol, the total molar mass is 70.90 g/mol.
• Sulfur trioxide ( abla SO_3 abla) requires summing the molar mass of sulfur (32.07 g/mol) with three times the molar mass of oxygen, giving a total of 80.07 g/mol.
• Krypton ( abla Kr abla), being a monoatomic elemental gas, has the same molar mass as its atomic mass, 83.80 g/mol.

By converting a sample's mass to moles using molar mass, you can easily relate experimental quantities to theoretical chemical equations.

Noble Gases

Noble gases are unique elements characterized by their complete valence electron shells, making them very stable and chemically inert. This family includes helium, neon, argon, krypton, xenon, and radon. Because of their full electron shells, noble gases do not readily form compounds with other elements.
They are found in small amounts in Earth's atmosphere and are used in various applications due to their inert properties.
For example:

• Krypton ( abla Kr abla), a noble gas with an atomic and molar mass of 83.80 g/mol, is known for its luminosity when electrified and is used in certain types of lighting and lasers.
• Another notable feature is that noble gases are typically odorless, colorless, and have very low reactivity under standard conditions.
• Due to their stability, noble gases are often used as a reference for comparing the reactivity of other substances.

Understanding noble gases helps in comprehending why certain elements behave the way they do under different experimental conditions.

Molecular Weight Comparison

Comparing molecular weights is essential in determining the density of gases. Gases with a higher molar mass will generally be denser at standard temperature and pressure (STP).
Molecular weight provides insight into the kinds of physical properties a gas will exhibit, such as its behavior under high pressure or in chemical reactions.
Consider the following example:

• Krypton's molar mass is notable due to being higher than the rest in the list, resulting in its high density at STP, which is why it was identified as the densest gas among the options given, like abla N_2O abla, abla SO_3 abla, and abla Cl_2 abla.
• Comparatively, a lighter gas like nitrogen dioxide ( abla NO_2 abla) would be less dense due to its lower molecular weight relative to krypton.

To measure these comparisons, chemists utilize molar mass as a pivotal factor in predicting and comparing gas behaviors under similar conditions.