3.1 Physical Properties of Gas Hydrates
63
only talk about a range or an average of hydration numbers per guest molecule to
describe the molar ratio of the guests to the hosts. What further complicates the
matter is that more than one molecule of argon, hydrogen, methane, or nitrogen can
occupy a large cavity of sII. What complicates the matter still further is that not all
the cavities of a given clathrate hydrate structure need to be occupied by the guest
molecules—that is, the occupancy ratio can be less than 1. Put it another way, the
maximum number of guests that can be accommodated in a given clathrate hydrate
can be uniquely determined (the hydration number is 5.75 for sI and 5.67 for sII
for full occupancy [1]), but that does not mean a given clathrate hydrate will always
contain the maximum numbers of guest gases. This non-stoichiometric nature of
clathrate hydrates gives rise to variations in their physical properties. Even for a
given occupancy ratio, its physical properties generally depend on the type of guests.
For example, the density of a clathrate hydrate depends on the average molecular
weight of the guests. So, no unique value exists for the density of a Structure I, a
Structure II, or a Structure H hydrate. Therefore, only typical values, as opposed to a
unique value, can be compiled for some physical properties. With this generic point
in mind, we will review several known physical properties of clathrate hydrates.
3.1.3 Thermal Properties
Density depends on the guest in that the clathrate hydrate of a high-molecular-weight
guest is denser than the clathrate hydrate of a low-molecular-weight guest. The value
typically ranges from ≈0.94 g/cm
3 for sI hydrates to ≈1.29 g/cm
3 for sII hydrates,
in contrast to 0.91 g/cm
3 for ice (Ih) [1]. Since ice (Ih) does not contain any guests,
its smaller density than either clathrate hydrate makes sense.
Specific heat of sI hydrate is about ≈2080 Jkg
−1 K
−1 which is similar to that of
sII of about ≈2130 Jkg
−1 K
−1 [1, 16, 17]. These values are substantially greater than
that of ice (Ih) of ≈1700 Jkg
−1 K
−1 . The greater specific heat of clathrate hydrates
is expected because the presence of guests ought to increase the amount of heat
required to raise the temperature of a clathrate hydrate than ice for a given number of
water molecules. For comparison, the specific heat of liquid water is much larger than
either of ice or clathrate hydrate, 4186 Jkg
−1 K
−1 . This rather surprising fact suggests
that the great majority of the hydrogen bonding in ice or clathrate hydrate does not
break when they dissociate but progressively break as the liquid water warms up.
The enthalpy of fusion of clathrate hydrate depends on the guest and increases
with the size of the guest [1, 18–20], probably as expected. For example, the enthalpy
of fusion of methane hydrate is 54.2 kJ per mole of the guest gas, ethane hydrate is
71.8 kJ per mole of the guest gas, propane hydrate is 129.2 kJ per mole of the guest
gas, and iso-butane hydrate is 133.2 kJ per mole of the guest gas [1].
The thermal conductivity of an sI hydrate and an sII hydrate are both about ≈0.5
Wm
−1 K
−1 [1, 16, 17, 21–28]. This value is similar to that of liquid water and about
75% to 80% smaller than that of ice (Ih) of ≈2.3 Wm
−1 K
−1 [1]. That the thermal
conductivity of a clathrate is poorer than that of ice is rather counterintuitive. One
63
only talk about a range or an average of hydration numbers per guest molecule to
describe the molar ratio of the guests to the hosts. What further complicates the
matter is that more than one molecule of argon, hydrogen, methane, or nitrogen can
occupy a large cavity of sII. What complicates the matter still further is that not all
the cavities of a given clathrate hydrate structure need to be occupied by the guest
molecules—that is, the occupancy ratio can be less than 1. Put it another way, the
maximum number of guests that can be accommodated in a given clathrate hydrate
can be uniquely determined (the hydration number is 5.75 for sI and 5.67 for sII
for full occupancy [1]), but that does not mean a given clathrate hydrate will always
contain the maximum numbers of guest gases. This non-stoichiometric nature of
clathrate hydrates gives rise to variations in their physical properties. Even for a
given occupancy ratio, its physical properties generally depend on the type of guests.
For example, the density of a clathrate hydrate depends on the average molecular
weight of the guests. So, no unique value exists for the density of a Structure I, a
Structure II, or a Structure H hydrate. Therefore, only typical values, as opposed to a
unique value, can be compiled for some physical properties. With this generic point
in mind, we will review several known physical properties of clathrate hydrates.
3.1.3 Thermal Properties
Density depends on the guest in that the clathrate hydrate of a high-molecular-weight
guest is denser than the clathrate hydrate of a low-molecular-weight guest. The value
typically ranges from ≈0.94 g/cm
3 for sI hydrates to ≈1.29 g/cm
3 for sII hydrates,
in contrast to 0.91 g/cm
3 for ice (Ih) [1]. Since ice (Ih) does not contain any guests,
its smaller density than either clathrate hydrate makes sense.
Specific heat of sI hydrate is about ≈2080 Jkg
−1 K
−1 which is similar to that of
sII of about ≈2130 Jkg
−1 K
−1 [1, 16, 17]. These values are substantially greater than
that of ice (Ih) of ≈1700 Jkg
−1 K
−1 . The greater specific heat of clathrate hydrates
is expected because the presence of guests ought to increase the amount of heat
required to raise the temperature of a clathrate hydrate than ice for a given number of
water molecules. For comparison, the specific heat of liquid water is much larger than
either of ice or clathrate hydrate, 4186 Jkg
−1 K
−1 . This rather surprising fact suggests
that the great majority of the hydrogen bonding in ice or clathrate hydrate does not
break when they dissociate but progressively break as the liquid water warms up.
The enthalpy of fusion of clathrate hydrate depends on the guest and increases
with the size of the guest [1, 18–20], probably as expected. For example, the enthalpy
of fusion of methane hydrate is 54.2 kJ per mole of the guest gas, ethane hydrate is
71.8 kJ per mole of the guest gas, propane hydrate is 129.2 kJ per mole of the guest
gas, and iso-butane hydrate is 133.2 kJ per mole of the guest gas [1].
The thermal conductivity of an sI hydrate and an sII hydrate are both about ≈0.5
Wm
−1 K
−1 [1, 16, 17, 21–28]. This value is similar to that of liquid water and about
75% to 80% smaller than that of ice (Ih) of ≈2.3 Wm
−1 K
−1 [1]. That the thermal
conductivity of a clathrate is poorer than that of ice is rather counterintuitive. One