The melting temperature of the fluorides of selected alkali metals and alkaline earths are listed below (see Table). If one considers the trend of the listed melting temperatures in terms of both the ionic character of the bonds and the ionic potentials of the compounds, which of these compounds follow Goldschmidt’s rules and which one do not, and why?
Fluoride compounds Ionic Potential Melting temperature (0C)
LiF 1.31 845
NaF 1.96 993
KF 0.72 858
RbF 0.657 795
CsF 0.598 682
BeF2 4.44 800 (sublimes)
MgF2 2.77 1261
CaF2 2 1423
SrF2 1.69 1573
BaF2 1.48 1355
Goldschmidt's rules state that compounds with similar radii and charges are more likely to form solid solutions and have higher melting temperatures.
Based on the given data, we can analyze the trend of the melting temperatures in relation to the ionic character of the bonds and the ionic potentials of the compounds.
LiF, NaF, KF, RbF, and CsF are the fluorides of alkali metals. Among these, KF, RbF, and CsF have lower ionic potentials compared to LiF and NaF. This suggests that KF, RbF, and CsF have a higher ionic character in their bonds due to the lower electronegativity difference between the metal cation and the fluoride anion. However, their melting temperatures do not follow the trend of increasing ionic character. This deviation from the trend can be attributed to the increasing size of the cations, which leads to weaker electrostatic forces between the ions.
BeF2, MgF2, CaF2, SrF2, and BaF2 are the fluorides of alkaline earth metals. These compounds generally have higher ionic potentials compared to the alkali metal fluorides. The trend of the melting temperatures for these compounds follows the expected trend of increasing ionic character of the bonds. As the ionic potential decreases, the melting temperature decreases, indicating weaker electrostatic forces between the ions.
In summary, the compounds that follow Goldschmidt's rules are BeF2, MgF2, CaF2, SrF2, and BaF2, while the alkali metal fluorides (KF, RbF, and CsF) do not fully follow Goldschmidt's rules due to the increasing size of the cations.
To determine which compounds follow Goldschmidt's rules, we need to understand what these rules are.
Goldschmidt's rules state that when a cation replaces another cation in a crystal lattice, the radius ratio between the cation and the anion should remain within a specific range for the compound to be stable. The general rule is:
- For compounds with a coordination number of 6 (like fluorides), the ideal cation-anion radius ratio should fall between 0.414 and 0.732. If the radius ratio is smaller or larger than this range, the compound is expected to be less stable.
Now, let's analyze the melting temperatures and ionic potentials of the listed compounds:
- LiF: Ionic potential = 1.31, Melting temperature = 845°C
- NaF: Ionic potential = 1.96, Melting temperature = 993°C
- KF: Ionic potential = 0.72, Melting temperature = 858°C
- RbF: Ionic potential = 0.657, Melting temperature = 795°C
- CsF: Ionic potential = 0.598, Melting temperature = 682°C
- BeF2: Ionic potential = 4.44, Melting temperature = 800°C (sublimes)
- MgF2: Ionic potential = 2.77, Melting temperature = 1261°C
- CaF2: Ionic potential = 2, Melting temperature = 1423°C
- SrF2: Ionic potential = 1.69, Melting temperature = 1573°C
- BaF2: Ionic potential = 1.48, Melting temperature = 1355°C
Now, let's compare the ionic potential and the melting temperatures within each group (alkali metals and alkaline earths) to see if the compounds follow Goldschmidt's rules:
For the alkali metal fluorides (LiF, NaF, KF, RbF, CsF):
- The ionic potentials decrease as we move down the group, indicating a larger size of the cation.
- The melting temperatures generally decrease as the ionic potentials decrease.
- All the compounds in this group have low ionic potentials, suggesting that the cation-anion radius ratios would be within the stable range.
- Therefore, all the alkali metal fluorides (LiF, NaF, KF, RbF, CsF) are expected to follow Goldschmidt's rules.
For the alkaline earth fluorides (BeF2, MgF2, CaF2, SrF2, BaF2):
- The ionic potentials decrease from BeF2 to BaF2, indicating a larger size of the cation.
- The melting temperatures generally increase as the ionic potentials decrease, except for BeF2, which sublimes instead of melting.
- BeF2 has a very high ionic potential, indicating that the cation-anion ratio is not within the stable range. Therefore, BeF2 does not follow Goldschmidt's rules.
- MgF2, CaF2, SrF2, and BaF2 have lower ionic potentials and are expected to have cation-anion radius ratios within the stable range. Therefore, these compounds are expected to follow Goldschmidt's rules.
In conclusion, the alkali metal fluorides (LiF, NaF, KF, RbF, CsF) and the alkaline earth fluorides (MgF2, CaF2, SrF2, BaF2) all follow Goldschmidt's rules. However, BeF2 does not follow Goldschmidt's rules due to its high ionic potential.