Question

In the blanks provided, answer the questions below, using LT (for is less than), GT (for is greater than), \(\mathrm{EQ}\) (for is equal to), or MI (for more information required). (a) The boiling point of \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(\mathrm{MM}=60.0 \mathrm{~g} / \mathrm{mol})\) _______ the boiling point of \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{C}=\mathrm{O} \quad(\mathrm{MM}=\) \(58.0 \mathrm{~g} / \mathrm{mol})\) (b) The vapor pressure of \(X\) is \(250 \mathrm{~mm} \mathrm{Hg}\) at \(57^{\circ} \mathrm{C}\). Given a sealed flask ________ at \(57^{\circ} \mathrm{C}\) that contains only gas, the pressure in the flask \(245 \mathrm{~mm} \mathrm{Hg}\). (c) The melting-point curve for \(Y\) tilts to the right of a straight line. The density of \(Y(l)\) _______ the density of \(\mathrm{Y}(s)\) (d) The normal boiling point of \(A\) is \(85^{\circ} \mathrm{C},\) while the normal boiling point of \(\mathrm{B}\) is \(45^{\circ} \mathrm{C}\). The vapor pressure of A at \(85^{\circ} \mathrm{C}\) ______ the vapor pressure of \(\mathrm{B}\) at \(45^{\circ} \mathrm{C}\). (e) The triple point of \(\mathrm{A}\) is \(25 \mathrm{~mm} \mathrm{Hg}\) and \(5^{\circ} \mathrm{C}\). The melting point of \(\mathrm{A}\) _______ \(5^{\circ} \mathrm{C}\).

Short answer

Answer: GT

Step-by-step solution

(a) Boiling Point Comparison

To compare the boiling points of C3H7OH and C2H6CO, we should consider the types of intermolecular forces present in each compound. C3H7OH exhibits hydrogen bonding due to the presence of the hydroxyl group, while C2H6CO has a polar carbonyl group (CO) but does not have hydrogen bonding. Generally, hydrogen bonding causes higher boiling points. Therefore, the boiling point of C3H7OH is greater than the boiling point of C2H6CO. Answer: GT.

(b) Vapor Pressure and Pressure in a Sealed Flask

Given that the vapor pressure of substance X is 250 mmHg at 57°C, we can determine the pressure in a sealed flask containing only gas X at 57°C, which is given as 245 mmHg. Since the vapor pressure is the pressure exerted by a vapor in equilibrium with its condensed phase, we can infer that the total pressure inside the flask is less than the vapor pressure of substance X at the same temperature. Answer: LT.

(c) Melting-point Curve and Density Comparison

In a phase diagram, if the melting-point curve tilts to the right of a straight line, it indicates that the liquid phase has a higher density than the solid phase. This is because the slope is positive, signifying that with increasing pressure, the melting point increases and the substance will favor the denser phase (liquid). Thus, the density of Y(l) is greater than the density of Y(s). Answer: GT.

(d)Vapor Pressure Comparison

The normal boiling point indicates the temperature at which a substance's vapor pressure equals 1 atm (760 mmHg). Substance A has a higher normal boiling point than substance B (85°C vs. 45°C). In general, substances with higher boiling points will have lower vapor pressures at a given temperature due to the increased intermolecular forces. Therefore, the vapor pressure of A at 85°C will be 760 mmHg (1 atm) while the vapor pressure of B at 45°C will also be 760 mmHg (1 atm). Thus, the vapor pressures of A and B at their normal boiling points are equal. Answer: EQ.

(e) Melting Point and Triple Point

At the triple point, the three phases of a substance (solid, liquid, and gas) coexist in equilibrium. The given triple point of A is 25 mmHg and 5°C. Since the melting point is the temperature at which a solid-liquid phase transition occurs, the melting point of A must be the same as the triple point in this case. Therefore, the melting point of A is equal to 5°C. Answer: EQ.

Key concepts

Boiling Point Comparison

Understanding the boiling point comparison involves analyzing the temperature at which a substance changes from the liquid phase to the vapor phase. Intermolecular forces play a key role in determining the boiling points of various substances. Typically, stronger intermolecular forces will lead to higher boiling points.

For example, when comparing the boiling points of alcohols and ketones with similar molecular weights, you will notice that alcohols, like C3H7OH, generally have higher boiling points because they can form hydrogen bonds, an exceptionally strong type of intermolecular force. In contrast, ketones, such as C2H6CO, lack hydrogen bonding, making their boiling points lower even if their molecular weights are close to those of alcohols.

Vapor Pressure Equilibrium

Vapor pressure equilibrium refers to the condition in which the rate of evaporation of a liquid equals the rate of condensation of its vapor. This occurs at a specific temperature and pressure, and the resulting vapor pressure is a unique characteristic of every substance.

Understanding vapor pressure is crucial for scientists and engineers in designing processes and equipment related to distillation, evaporation, and other phase-changing operations. For instance, if a substance inside a flask has a vapor pressure less than the measured total pressure, it suggests that the conditions are not yet at equilibrium, possibly due to the presence of other gases or changes in the environment. This intricate balance is key to comprehending how substances behave in various conditions.

Phase Diagram Analysis

A phase diagram is an invaluable tool in materials science and physical chemistry that maps the states of matter of a substance (solid, liquid, and gas) under different conditions of temperature and pressure. Melting-point curves and triple points are critical aspects of these diagrams.

When analyzing a phase diagram, one must consider the slope of the melting-point curve, which informs us about the relative densities of the solid and liquid phases; a right-tilt indicates a rare instance in which the liquid phase is denser. Additionally, the triple point marks the unique set of conditions at which all three phases can coexist in equilibrium. By examining a phase diagram, one can predict the phase behavior of a substance over a wide range of conditions.

Melting Point Determination

The melting point of a substance is a fundamental physical property that indicates when a solid becomes a liquid. Understanding melting points is essential for material identification and purity analysis. For substances with a known triple point, it is possible to conclude that the melting point at one atmosphere of pressure will occur at the same temperature.

However, outside of such specific points, the melting point can be influenced by various factors, such as pressure and the presence of impurities, which can depress or elevate the melting point. In the case of substance A with a given triple point, its melting point under standard atmospheric conditions would indeed be equal to its triple point temperature.

Intermolecular Forces

Intermolecular forces (IMFs) are the forces that mediate interactions between molecules, including London dispersion forces, dipole-dipole interactions, and hydrogen bonds. These forces impact the physical properties of substances, such as boiling points, melting points, and solubilities.

For instance, a molecule with a large number of hydrogen bonds, like C3H7OH (an alcohol), will exhibit a higher boiling point compared to C2H6CO (a ketone) which cannot form hydrogen bonds, indicating that intermolecular forces heavily influence the phase behavior of substances. A deep understanding of IMFs is necessary to predict how substances will behave under different environmental conditions and to tailor materials with desired properties.