Given the following information about xenon
normal boiling point = -108 degrees C
normal melting point = -112 degrees C
triple point = -121 degrees C at 281 mmHg
critical point = -16.6 degrees C at 58 atm
a) Construct an appropriate phase diagram for xenon [I did this.]
b) Estimate the vapor pressure of xenon at -115 degrees C.
c) Is the density of solid Xe larger than that of liquid Xe?
For b, I figured I could solve the problem with the Clausius-Clapeyron equation if I was provided with the heat of vaporization. However, I'm not, and I'm not sure that I'd be able to find it with the information given. How can I solve the problem with this information?
For c, should this be done qualitatively or is it not possible [with the info given]/ not necessary? I had written down that yes, solid Xe is more dense than liquid Xe because the solid would always be more dense than its liquid [is this a false assumption?].
For b, look in your text or notes on phase diagrams. The phase diagram will allow you to estimate vapor pressure at any temperature.
For c. you have made a false assumption. Ice, for example, is less dense than water (that's why ice floats). Again, the phase diagram will tell you about the density of the solid. Phasd diagrams consist of three parts. The lower part which is curved slightly upward from below freezing to the freezing point, starting there another section which goes up and above the boiling point, and a third line which is almost vertical that starts at the freezing point and points upward. If the slope of the nearly vertical line is negative, the solid is less dense than the liquid. If the slope of that nearly vertical line is positive, the solid is more dense than the liquid. I hope this helps. The solution to this problem is to understand phase diagrams.
To solve the problem, let's follow the instructions:
a) Given the information about the normal boiling point, normal melting point, triple point, and critical point of xenon, you can construct an appropriate phase diagram. A phase diagram is a graphical representation that shows the different phases (solid, liquid, and gas) of a substance under different conditions of temperature and pressure. Based on the given values, you can plot the different points (boiling point, melting point, triple point, and critical point) on the diagram and connect them to form the appropriate lines.
b) To estimate the vapor pressure of xenon at -115 degrees Celsius, you can use the phase diagram. Look for the temperature -115 degrees Celsius on the diagram and find the corresponding vapor pressure value. Follow the vertical line from -115 degrees Celsius until it intersects with the gas phase boundary. Then, read the corresponding pressure value. This will give you an estimate of the vapor pressure of xenon at -115 degrees Celsius.
c) To determine if the density of solid xenon is larger than that of liquid xenon, you can again refer to the phase diagram. Look for the solid phase region and the liquid phase region. If the line representing the solid phase has a positive slope (meaning it goes up as you go from the freezing point to higher temperatures), then the solid xenon is more dense than liquid xenon. However, if the line representing the solid phase has a negative slope (going down from the freezing point), then the solid xenon is less dense than liquid xenon. Consult the phase diagram to determine the slope of the solid phase line and thus determine the density relationship between solid and liquid xenon.
Remember, phase diagrams are graphical representations that provide information about the phases of a substance at different temperatures and pressures. By analyzing the diagram, you can estimate vapor pressure and density relationships between different phases.