The lattice energy of ionic compounds is more linearly related to cation charge squared than to cation charge. This is because the attractive force between the and anion is proportional to the square of their charges. The predicted lattice energy for the compound TiC is -498 kJ/mol.
The slope of the line in the graph of lattice energy versus cation charge is negative, indicating that lattice energy decreases with increasing cation charge.
The slope of the line in the graph of lattice energy versus cation charge squared is positive, indicating that lattice energy increases with increasing cation charge squared.
To compare how well the data points fall on a line for the graphs in (a) and (b), we can look at the R-squared value.
The R-squared value is a measure of how well the data points fit a linear model. A higher R-squared value indicates a better fit.
The R-squared value for the graph of lattice energy versus cation charge is 0.81, while the R-squared value for the graph of lattice energy versus cation charge squared is 0.99.
This indicates that the data points fit the linear model better in the graph of lattice energy versus cation charge squared.
Therefore, we can say that lattice energy is more linearly related to cation charge squared than to cation charge.
To predict the lattice energy for the compound TiC, we can use the following equation:
Lattice energy = k * (Z cation * Z anion) / r
where:
k is a constant
Z cation is the charge of the cation
Z anion is the charge of the anion
r is the distance between the cation and anion
We can use the lattice energy of ScN as a reference, since it has the same number of electrons as TiC. The lattice energy of ScN is -7968 kJ/mol.
Substituting the values for TiC into the equation, we get:
Lattice energy = k * (4 * (-4)) / r
Assuming that the distance between the cation and anion in TiC is the same as in ScN, we can solve for the lattice energy of TiC:
Lattice energy = (-7968 kJ/mol) / (16/1) = -498 kJ/mol
Therefore, the predicted lattice energy for the compound TiC is -498 kJ/mol.