Question

C.2 Shown is a portion of the phase diagram for CO$_2$. Pressure (bar) 10 CO$_2$ Liquid Solid -90 -80 -70 -60 -50 -40 -30 Temperature (°C) Gas In a simplified model for solid CO$_2$ (dry ice), CO$_2$ molecules are spheres arranged in a face centred cubic structure, interacting with neighbours through a Lennard-Jones pair potential $U_{pair} = 4\epsilon \left[ \left( \frac{\sigma}{r} \right)^{12} - \left( \frac{\sigma}{r} \right)^6 \right]$, where $\sigma = 3.6$ Å and $\epsilon = 0.044$ eV. c. Calculate the equilibrium lattice parameter of solid face-centred cubic CO$_2$, and hence calculate the molar volume of solid CO$_2$. d. Show that the latent heat of vapourisation, $L_v$, of solid CO$_2$ is roughly 25 kJ/mol. The Clausius-Clapeyron equation is given as $\frac{dp}{dT} = \frac{L}{T\Delta V}$, where $dp/dT$ is the slope of the phase boundary at pressure $p$ and temperature $T$, $\Delta V$ is the difference in volume between phases at $p$ and $T$, and $L$ is the latent heat of transfor- mation. You may assume 1 bar = 10$^5$ Pa e. At ambient pressure, calculate the change in molar volume upon vapourisation in CO$_2$. f. By what factor does the volume increase upon vapourisation at ambient pressure? Evaluate your answer for plausibility.

          C.2 Shown is a portion of the phase diagram for CO$_2$.
Pressure (bar)
10
CO$_2$
Liquid
Solid
-90 -80 -70 -60 -50 -40 -30
Temperature (°C)
Gas
In a simplified model for solid CO$_2$ (dry ice), CO$_2$ molecules are spheres arranged in a
face centred cubic structure, interacting with neighbours through a Lennard-Jones pair
potential
$U_{pair} = 4\epsilon \left[ \left( \frac{\sigma}{r} \right)^{12} - \left( \frac{\sigma}{r} \right)^6 \right]$,
where $\sigma = 3.6$ Å and $\epsilon = 0.044$ eV.
c. Calculate the equilibrium lattice parameter of solid face-centred cubic CO$_2$, and
hence calculate the molar volume of solid CO$_2$.
d. Show that the latent heat of vapourisation, $L_v$, of solid CO$_2$ is roughly 25 kJ/mol.
The Clausius-Clapeyron equation is given as
$\frac{dp}{dT} = \frac{L}{T\Delta V}$,
where $dp/dT$ is the slope of the phase boundary at pressure $p$ and temperature $T$, $\Delta V$ is
the difference in volume between phases at $p$ and $T$, and $L$ is the latent heat of transfor-
mation. You may assume 1 bar = 10$^5$ Pa
e. At ambient pressure, calculate the change in molar volume upon vapourisation in
CO$_2$.
f. By what factor does the volume increase upon vapourisation at ambient pressure?
Evaluate your answer for plausibility.

C.2 Shown is a portion of the phase diagram for CO2.
Pressure (bar)
10
CO2
Liquid
Solid
-90 -80 -70 -60 -50 -40 -30
Temperature (°C)
Gas
In a simplified model for solid CO2 (dry ice), CO2 molecules are spheres arranged in a
face centred cubic structure, interacting with neighbours through a Lennard-Jones pair
potential
Upair = 4ϵ[ ( (σ)/(r))^12 - ( (σ)/(r))^6 ],
where σ = 3.6 Å and ϵ = 0.044 eV.
c. Calculate the equilibrium lattice parameter of solid face-centred cubic CO2, and
hence calculate the molar volume of solid CO2.
d. Show that the latent heat of vapourisation, Lv, of solid CO2 is roughly 25 kJ/mol.
The Clausius-Clapeyron equation is given as
(dp)/(dT) = (L)/(TΔ V),
where dp/dT is the slope of the phase boundary at pressure p and temperature T, Δ V is
the difference in volume between phases at p and T, and L is the latent heat of transfor-
mation. You may assume 1 bar = 10^5 Pa
e. At ambient pressure, calculate the change in molar volume upon vapourisation in
CO2.
f. By what factor does the volume increase upon vapourisation at ambient pressure?
Evaluate your answer for plausibility.

Added by Domingo C.

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