Question

Answer the questions below, by filling in the blanks with LT for is less than, GT for is greater than, \(\mathrm{EQ}\) for is equal to, or MI for more information required. (a) At \(50^{\circ} \mathrm{C},\) benzene has a vapor pressure of \(269 \mathrm{~mm} \mathrm{Hg}\). A flask that contains both benzene liquid and vapor at \(50^{\circ} \mathrm{C}\) has a pressure _______________ \(269 \mathrm{~mm} \mathrm{Hg} .\) (b) Ether has a vapor pressure of \(537 \mathrm{~mm} \mathrm{Hg}\) at \(25^{\circ} \mathrm{C}\). A flask that contains only ether vapor at \(37^{\circ} \mathrm{C}\) has a pressure ______________ \(537 \mathrm{~mm} \mathrm{Hg} .\) (c) The boiling point of \(\mathrm{H}_{2} \mathrm{O} \) ________ the boiling point of \(\mathrm{C}_{3} \mathrm{H}_{8}\). (e) The dispersion forces present in naphthalene, \(\mathrm{C}_{10} \mathrm{H}_{8}\), ____________ the dispersion forces present in butane, \(\mathrm{C}_{4} \mathrm{H}_{10}\).

Short answer

Question: Fill in the blanks with LT (is less than), GT (is greater than), EQ (is equal to), or MI (more information required) based on the given conditions. a) The pressure in the flask with benzene at \(50^{\circ}\mathrm{C}\) is ___ the vapor pressure of benzene at \(50^{\circ}\mathrm{C}\) (equal/less than/greater than/more information required). b) The vapor pressure of ether at \(37^{\circ}\mathrm{C}\) is ___ the vapor pressure of ether at \(25^{\circ}\mathrm{C}\) (equal/less than/greater than/more information required). c) The boiling point of \(\mathrm{H}_2 \mathrm{O}\) is ___ the boiling point of \(\mathrm{C}_3 \mathrm{H}_8\) (equal/less than/greater than/more information required). e) The dispersion forces in naphthalene are ___ the dispersion forces in butane (equal/less than/greater than/more information required). Answer: a) EQ b) MI c) GT e) GT

Step-by-step solution

(a) Comparing vapor pressure of benzene

Since both liquid and vapor benzene exist in the flask, the pressure inside the flask will be the same as the vapor pressure of the benzene at \(50^{\circ}\mathrm{C}\). So, the pressure in the flask is \(\mathrm{EQ}\) to \(269\,\mathrm{mm}\,\mathrm{Hg}\).

(b) Comparing vapor pressure of ether at different temperatures

Ether has a vapor pressure of \(537\,\mathrm{mm}\,\mathrm{Hg}\) at \(25^{\circ}\mathrm{C}\). But we need to compare this with the pressure of only ether vapor at \(37^{\circ}\mathrm{C}\). Since we have no information about the vapor pressure of ether at \(37^{\circ}\mathrm{C}\), we need more information. So, the answer is \(\mathrm{MI}\).

(c) Comparing boiling points of \(\mathrm{H}_2 \mathrm{O}\) and \(\mathrm{C}_3 \mathrm{H}_8\)

The boiling point of a substance depends on the strength of intermolecular forces. \(\mathrm{H}_2 \mathrm{O}\) has strong hydrogen bonding, while \(\mathrm{C}_3 \mathrm{H}_8\) (propane) only has weak dispersion forces. Stronger intermolecular forces result in higher boiling points. Thus, the boiling point of \(\mathrm{H}_2 \mathrm{O}\) is \(\mathrm{GT}\) the boiling point of \(\mathrm{C}_3 \mathrm{H}_8\).

(e) Comparing the dispersion forces in naphthalene and butane

Naphthalene (\(\mathrm{C}_{10} \mathrm{H}_{8}\)) has a larger molecular size and more electrons than butane (\(\mathrm{C}_{4} \mathrm{H}_{10}\)). Since dispersion forces are stronger in larger molecules with more electrons, the dispersion forces in naphthalene are \(\mathrm{GT}\) the dispersion forces in butane.

Key concepts

Intermolecular Forces

Understanding intermolecular forces is essential when studying the behavior of liquids and solids. These forces represent the attractions between molecules, influencing various physical properties such as melting points, boiling points, vapor pressures, and viscosities.

At a basic level, there are several types of intermolecular forces:

• Dispersion forces, which occur between all molecules, whether polar or nonpolar. They increase with the molecule's size and number of electrons.
• Dipole-dipole interactions are between polar molecules, aligning so that the positive end of one molecule is near the negative end of another.
• Hydrogen bonds, which are strong dipole-dipole interactions involving a hydrogen atom bonded to a highly electronegative atom like oxygen, nitrogen, or fluorine.

Dispersion forces can explain differences in melting and boiling points among similar-sized nonpolar molecules, while hydrogen bonding plays a crucial role in determining the properties of substances like water. The more robust the intermolecular forces, the higher the boiling point and the lower the vapor pressure as more energy is required to overcome these attractions.

Boiling Point Comparison

Boiling points provide insights into the molecular interactions of a substance. A substance boils when its vapor pressure equals the external pressure. Compounds with stronger intermolecular forces often have higher boiling points because more thermal energy—or heat—is needed to overcome these forces.

For example, water has a higher boiling point than propane (a fact referenced in the exercise) due to the hydrogen bonds present between water molecules. Propane, conversely, has weaker dispersion forces. The comparison of boiling points is a useful way to predict the relative intermolecular strengths:

• If substance A has a higher boiling point than substance B, we can infer stronger intermolecular forces are at play in substance A.
• Substances with strong hydrogen bonding or ionic interactions will generally boast higher boiling points compared to those with mere dipole-dipole interactions or dispersion forces.

Boiling point comparisons are essential in distillation processes and understanding how substances interact in mixtures.

Vapor Pressure Comparison

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase at a given temperature. It is an excellent indicator of a liquid's tendency to evaporate; substances with higher vapor pressures at a particular temperature are more volatile and evaporate more readily. Vapor pressure is influenced by the intermolecular forces present within the liquid.

Here are some key points to remember about vapor pressure comparisons:

• The lesser the intermolecular forces within a liquid, the higher its vapor pressure, because fewer of those forces need to be overcome for the molecules to escape into the vapor phase.
• Conversely, a liquid with strong intermolecular attractions will have a lower vapor pressure as the molecules do not readily escape to the gas phase.
• Temperature plays a vital role in vapor pressure; an increase in temperature generally increases vapor pressure as molecules gain more kinetic energy.

The benzene and ether scenarios from the exercise demonstrate how temperature and the presence of other substances (like the ether vapor at a different temperature) can impact the pressure measured and require different considerations for accurate vapor pressure comparison.