Problem 61 - General Chemistry

Question

The heats of vaporization of liquid \(\mathrm{Cl}_{2}\), liquid \(\mathrm{H}_{2}\), and liquid \(\mathrm{N}_{2}\) are \(20.4 \mathrm{~kJ} / \mathrm{mol}, 0.9 \mathrm{~kJ} / \mathrm{mol}\), and \(5.6 \mathrm{~kJ} / \mathrm{mol}\), respectively. Are the relative values as you would expect? Explain.

Step-by-Step Solution

Answer

Yes, the values are expected based on molecular weight and intermolecular forces. Chlorine has the highest heat of vaporization, followed by nitrogen and then hydrogen.

Step 1: Reading the Exercise

The problem provides the heat of vaporization values for three substances: chlorine, hydrogen, and nitrogen. It asks us to determine if these values are reasonable given what we know about the substances.

Step 2: Understanding Heat of Vaporization

Heats of vaporization reflect the energy needed to convert a mole of liquid into gas. Higher values indicate stronger intermolecular forces. We need to compare the given values accordingly.

Step 3: Intermolecular Forces Analysis

Analyzing the intermolecular forces, chlorine (0_2"), is molecular and has London dispersion forces, which are stronger in heavier molecules. Hydrogen (0_2"), has very weak London forces due to low mass. Nitrogen (0_2"), has stronger dispersion forces than hydrogen but weaker than chlorine due to its intermediate molecular weight.

Step 4: Comparing Heat Values

Chlorine, with the highest molecular weight, has the strongest dispersion forces and a heat of vaporization of 20.4 kJ/mol. Nitrogen, lighter than chlorine but heavier than hydrogen, has an intermediate heat of vaporization of 5.6 kJ/mol. Hydrogen, the lightest, exhibits the weakest dispersion forces and thus has the lowest heat of 0.9 kJ/mol.

Step 5: Conclusion on Relative Values

The heats of vaporization (0_2, 0_2, and 0_2 respectively) are consistent with the expected intermolecular force strengths based on molecular weights. Chlorine > Nitrogen > Hydrogen in both weight and boiling points.

Key Concepts

Intermolecular Forces

Intermolecular forces are the forces that hold molecules together. These forces are crucial because they determine many physical properties of substances, such as boiling points and heat of vaporization.
These forces come in different types, with varying strengths. Some of the main types include hydrogen bonding, dipole-dipole interactions, and London dispersion forces.

• Hydrogen Bonding: A strong type of intermolecular force occurring between molecules containing a hydrogen atom bonded to a highly electronegative atom (like oxygen, nitrogen or fluorine).


• Dipole-Dipole Interactions: These occur between polar molecules, where positive and negative charges attract each other.


• London Dispersion Forces: A type of van der Waals force that occurs in all molecules, especially notable in nonpolar substances.

The strength of intermolecular forces affects how easy or difficult it is to vaporize a liquid. Higher heats of vaporization reflect stronger intermolecular forces, requiring more energy to change from liquid to gas.

London Dispersion Forces

London dispersion forces, also known as dispersion forces or van der Waals forces, are the weakest type of intermolecular force.
They occur when the electron clouds of atoms or molecules momentarily fluctuate and induce temporary dipoles in neighboring particles. These forces are present in all molecules, polar and nonpolar alike, but significantly impact nonpolar compounds.

• Temporary Dipoles: The random movement of electrons leads to temporary, short-lived dipoles that result in weak attractions between molecules.


• Importance in Nonpolar Molecules: In nonpolar molecules, London dispersion forces are often the only type of intermolecular force present.

The strength of London dispersion forces generally increases with larger and heavier molecules. This is due to their larger electron clouds, which are more easily polarizable.
Therefore, as molecular weight and size increase, so does the impact of these forces on the physical properties such as the heat of vaporization.

Molecular Weight Comparison

Molecular weight plays a significant role in determining the strength of intermolecular forces, especially London dispersion forces.
The heat of vaporization tends to increase with molecular weight due to stronger intermolecular attractions. Here's how it works for the specific molecules in our problem:

• Chlorine (\(\mathrm{Cl}_2\)): This molecule has the highest molecular weight among the three gases. It possesses stronger dispersion forces and, subsequently, the highest heat of vaporization.


• Nitrogen (\(\mathrm{N}_2\)): With a molecular weight between that of chlorine and hydrogen, nitrogen has stronger dispersion forces than hydrogen but weaker than chlorine, resulting in an intermediate heat of vaporization.


• Hydrogen (\(\mathrm{H}_2\)): As the lightest molecule, hydrogen has the weakest dispersion forces and thus the lowest heat of vaporization.

In general, molecules with greater molecular weight exhibit stronger intermolecular forces. This trend is evident when comparing the boiling points and heats of vaporization as seen in our examples. Recognizing these patterns helps in anticipating the physical properties of other similar molecules.