What is the energy of a bond formed between a potassium (K+) cation and an iodide (I−) anion? The ionic radii of K+ and I−, are 152 pm and 206 pm, respectively. Assume the Born exponent n is 10. Please report your answer in joules.
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Calculate the cohesive energy of potassium iodide (KI). The ionic radii of K+ and I−, are 152 pm and 206 pm, respectively. Assume the Born exponent n is 10. Assume a Madelung constant of 1.7. Please report your answer in kJ/mol.
y=
To calculate the energy of the bond formed between a potassium (K+) cation and an iodide (I-) anion, we need to use the Born-Lande equation. The Born-Lande equation is given by:
E = (k * z+ * z- * e^2) / (2 * r0) * (1 - 1 / n)
where:
- E is the energy of the bond
- k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2)
- z+ and z- are the charges of the cation and anion, respectively (in this case, z+ = +1 and z- = -1)
- e is the elementary charge (1.6 x 10^-19 C)
- r0 is the distance between the ions (sum of their ionic radii)
- n is the Born exponent (given as 10 for this calculation)
Given that the ionic radii of K+ and I- are 152 pm and 206 pm, respectively, we can calculate the energy of the bond.
To convert the energy to joules, we need to multiply the calculated value by the elementary charge (e). So, x = E * e.
Now let's calculate the cohesive energy of potassium iodide using the Madelung constant.
The cohesive energy of an ionic compound is given by:
Ec = -A * (z+ * z- / r0) * M
where:
- Ec is the cohesive energy per mole
- A is the Madelung constant (given as 1.7 for this calculation)
- z+ and z- are the charges of the cation and anion, respectively (in this case, z+ = +1 and z- = -1)
- r0 is the distance between the ions (sum of their ionic radii)
- M is the Avogadro's number (6.022 x 10^23 mol^-1)
Since we want to report the answer in kilojoules per mole, we will calculate y = Ec / 1000.
Now you can plug in the values and calculate x and y using the given formulas.