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 \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{C}=\mathrm{O}(\mathrm{MM}=58.0 \mathrm{~g} / \mathrm{mol})\). (b) The vapor pressure of \(\mathrm{X}\) 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 \(\mathrm{Y}(l) \quad\) the density of \(\mathrm{Y}(s)\). (d) The normal boiling point of \(\mathrm{A}\) is \(85^{\circ} \mathrm{C}\), while the normal boiling point of \(\mathrm{B}\) is \(45^{\circ} \mathrm{C}\). The vapor pressure of \(\mathrm{A}\) at \(85^{\circ} \mathrm{C}\) pressure of \(\mathrm{B}\) at \(45^{\circ} \mathrm{C}\). (e) The triple point of \(A\) is \(25 \mathrm{~mm} \mathrm{Hg}\) and \(5^{\circ} \mathrm{C}\). The melting point of \(\mathrm{A}\) \(5^{\circ} \mathrm{C}\)

Short answer

Question: Compare the following properties of given substances using the relationships LT (less than), GT (greater than), EQ (equal), or MI (more information required): (a) Boiling point of a compound with a molar mass of 150 g/mol ______ boiling point of a compound with a molar mass of 190 g/mol. (b) Vapor pressure of substance X at 57°C (250 mm Hg) ______ total pressure in a flask containing only gas at 57°C (245 mm Hg). (c) Density of substance Y in the liquid state ______ density of Y in the solid state, given that the melting-point curve for Y tilts to the right of a straight line. (d) Vapor pressure of substance A at its normal boiling point (125°C) ______ vapor pressure of substance B at its normal boiling point (90°C). (e) Melting point of substance A (5°C) ______ temperature at the triple point of A (25 mm Hg, 5°C). Answer: (a) MI (b) GT (c) LT (d) EQ (e) EQ

Step-by-step solution

(a) Boiling Point Comparison

In question (a), we are given the molar mass of two compounds, and we need to compare their boiling points. However, without knowing their chemical properties and boiling point trends, we cannot infer the comparison of their boiling points. So, the correct answer for (a) is MI (more information required).

(b) Vapor Pressure Comparison

In question (b), we are given the vapor pressure of substance X at 57°C and the total pressure in a flask that contains only gas at the same temperature. Since the vapor pressure of the substance X is 250 mm Hg and the total pressure in the flask is 245 mm Hg, we can infer that the pressure of X is GT (greater than) the pressure in the flask.

(c) Density Comparison

In question (c), we are given the melting-point curve for substance Y tilts to the right of a straight line. This implies that the substance is expanding as it melts. Therefore, the density of Y in the liquid state is LT (less than) the density of Y in the solid state.

(d) Vapor Pressure Comparison

In question (d), we are given the normal boiling points of substances A and B and asked to compare their vapor pressures at these points. At the normal boiling point, the vapor pressure of a substance is equal to 1 atmosphere (760 mm Hg). Since both substances are at their respective boiling points, their vapor pressures are EQ (equal) at these temperatures.

(e) Melting Point Comparison

In question (e), we are given that the triple point of A is at 25 mm Hg and 5°C. The melting point of A is also given as 5°C. At the triple point, all three phases of a substance coexist. Since the melting point and the temperature of the triple point are the same, we can conclude that the melting point of A is EQ (equal) to the temperature at the triple point, which is 5°C.

Key concepts

Boiling Point Comparison

The boiling point of a substance is the temperature at which it changes from a liquid to a gas. This is a critical physical property that is influenced by intermolecular forces. Stronger intermolecular forces result in higher boiling points because more energy is required to separate the molecules.
For compounds such as \[\text{C}_3\text{H}_7\text{OH}\]and \[\text{C}_2\text{H}_6\text{C}=\text{O}\], simply looking at their molar masses is not enough to determine their boiling points.

• Hydrogen bonding generally raises the boiling point significantly, which may occur in alcohols like \[ \text{C}_3\text{H}_7\text{OH} \] .
• Other relevant factors include molecular geometry and polarities.

Due to these complexities, further information about the nature of these specific compounds is necessary to make an accurate comparison.

Vapor Pressure

Vapor pressure is defined as the pressure exerted by the vapor of a liquid when the liquid and vapor are in dynamic equilibrium.
Substance X at 57°C exhibits a vapor pressure of 250 mm Hg. If placed in a flask where the total pressure is only 245 mm Hg, it indicates that not all of the substance is in vapor form, and conditions are such that leaked vapor or condensation has altered the expected pressure.

• When vapor pressure is higher than the pressure in an enclosed space, it signifies that the liquid can evaporate more freely.
• Vapor pressure also increases with temperature, so it varies at different stages of heating or cooling.

Knowing the vapor pressure allows one to potentially predict phase changes and how the substance would behave at various temperatures.

Density Comparison

Density is calculated as mass per unit volume and it varies between solid, liquid, and gas phases. Typically, a solid is denser than its liquid form, except in certain cases like water.
The description of the melting-point curve tilting to the right for substance Y suggests it expands upon melting.

• As the volume increases while melting, the density decreases because density is inversely proportional to volume.
• Thus, for substance Y, \[\text{density in liquid form} < \text{density in solid form}\]

Considering these insights, we can interpret physical behaviors and processes involved in melting and solidification for various substances.

Phase Transitions

Phase transitions include changes between solid, liquid, and gas states. The conditions under which these transitions occur, such as temperature and pressure, are critical for understanding a substance’s behavior.
A triple point, for example, characterizes a unique set of conditions where all three phases coexist in equilibrium. For substance A, this occurs at 25 mm Hg and 5°C.

• Understanding phase diagrams can help predict these transitions and the conditions required for them.
• Boiling points at normal atmospheric pressure mark transition points from liquid to gas and are dependent on ambient conditions.

The knowledge of phase transitions illuminates why specific physical changes occur under certain environmental settings, offering deeper insight into material properties.