Question

Consider the vapor pressure curves of molecules \(\mathrm{A}, \mathrm{B}\), and C shown below. (a) Which compound \((\mathrm{A}, \mathrm{B},\) or \(\mathrm{C})\) has the weakest forces between molecules? (b) Which compound \((\mathrm{A}, \mathrm{B},\) or \(\mathrm{C})\) has a normal boiling point at about \(15^{\circ} \mathrm{C} ?\) (c) At what temperature will \(\mathrm{B}\) boil if the atmospheric pressure is \(500 \mathrm{~mm} \mathrm{Hg}\) ? (d) At \(25^{\circ} \mathrm{C}\) and \(400 \mathrm{~mm} \mathrm{Hg}\), what is the physical state of \(\mathrm{A}\) ? (e) At what pressure will C boil at \(40^{\circ} \mathrm{C}\) ?

Short answer

(a) Compound A has the weakest intermolecular forces because it has the highest vapor pressure curve among the three compounds. (b) Compound C has a normal boiling point of approximately 15°C as its vapor pressure curve intersects the line representing atmospheric pressure (760 mm Hg) at around this temperature. (c) Compound B has a boiling temperature of approximately 30°C at 500 mm Hg atmospheric pressure. (d) Compound A is in the vapor state at 25°C and 400 mm Hg because the specified point is above its vapor pressure curve. (e) Compound C will boil at a pressure of approximately 650 mm Hg when the temperature is 40°C.

Step-by-step solution

(a) Weakest intermolecular forces

Observe the vapor pressure curves and identify which compound has the highest vapor pressure at a given temperature. The highest vapor pressure corresponds to the weakest intermolecular forces because the molecules are more ready to escape into the vapor state. Based on the graph, compound A has the highest vapor pressure curve, so it has the weakest intermolecular forces.

(b) Normal boiling point at 15°C

The normal boiling point of a compound is the temperature at which its vapor pressure equals atmospheric pressure, which is 760 mm Hg. At this pressure, find the curve that intersects with a temperature of about 15°C. The graph shows that it's compound C that intersects at this temperature, so compound C has a normal boiling point of approximately 15°C.

(c) Boiling temperature of B at 500 mm Hg

To find the boiling temperature of compound B at 500 mm Hg atmospheric pressure, find the point on the vapor pressure curve of B where the pressure is 500 mm Hg. Then read the corresponding temperature on the temperature axis. From the graph, B has a boiling temperature of approximately 30°C at 500 mm Hg.

(d) Physical state of A at 25°C and 400 mm Hg

To determine the physical state of compound A at 25°C and 400 mm Hg, locate the point on the graph where the temperature is 25°C and the pressure is 400 mm Hg. Compare the location of this point with the vapor pressure curve of A. If the point is below the curve, the compound is in the liquid state; if the point is above the curve, it is in the vapor state. The specified point is above the vapor pressure curve of A, so compound A is in the vapor state at 25°C and 400 mm Hg.

(e) Pressure at which C boils at 40°C

To find the pressure at which compound C will boil at 40°C, locate the point on the vapor pressure curve of C where the temperature is 40°C, and read the corresponding pressure on the pressure axis. From the graph, compound C will boil at a pressure of approximately 650 mm Hg when the temperature is 40°C.