Draw a diagram of the Born-Haber cycle for potassium bromide. Include labels (DHf,
DHSub, DHVap, DHI.E., DHE.A., DHL.E, etc.) of the different energies involved. Include the
equation needed showing how the lattice energy would be calculated (DHL.E,).
I apologize, as a text-based AI, I am unable to draw diagrams directly. However, I can provide you with a step-by-step description of the Born-Haber cycle for potassium bromide and explain the labels and energies involved. Let's begin:
The Born-Haber cycle is used to determine the lattice energy of an ionic compound, such as potassium bromide (KBr). The lattice energy is the energy required to break one mole of the solid ionic compound into its gaseous ions.
Here is the step-by-step description of the Born-Haber cycle for potassium bromide:
1. Start with the formation of potassium bromide from its elements:
K(s) + 1/2Br2(g) → KBr(s)
This step involves the formation enthalpy (ΔHf) of potassium bromide, which represents the energy change when one mole of KBr is formed from its constituent elements.
2. Sublimation of potassium:
K(s) → K(g)
This step involves the sublimation enthalpy (ΔHsub) of potassium, which represents the energy change when one mole of solid potassium is converted into gaseous potassium atoms.
3. Dissociation of bromine:
1/2Br2(l) → Br(g)
This step involves the dissociation enthalpy (ΔHdissoc) of bromine, which represents the energy change when one mole of liquid bromine is converted into gaseous bromine atoms.
4. Ionization of potassium:
K(g) → K+(g) + e-
This step involves the first ionization energy (ΔHI.E.) of potassium, which represents the energy required to remove one mole of electrons from one mole of potassium atoms to form one mole of gaseous potassium ions.
5. Electron affinity of bromine:
Br(g) + e- → Br-(g)
This step involves the electron affinity (ΔHE.A.) of bromine, which represents the energy change when one mole of gaseous bromine atoms accepts one mole of electrons to form one mole of bromide ions.
6. Lattice energy of potassium bromide:
K+(g) + Br-(g) → KBr(g)
This step involves the lattice energy (ΔHL.E.) of potassium bromide, which represents the energy change when one mole of gaseous ions (K+ and Br-) combine to form one mole of solid ionic compound (KBr). The lattice energy is a measure of the bond strength in the solid.
In this cycle, the overall energy change should be zero. The equation for calculating the lattice energy (ΔHL.E.) is as follows:
ΔHL.E. = -ΔHf - ΔHsub - ΔHdissoc - ΔHI.E. - ΔHE.A.
The negative sign is used because energy is released when the ionic compound is formed, from its constituent elements.
I hope this explanation helps you understand the Born-Haber cycle for potassium bromide and the different energies involved.
To draw a diagram of the Born-Haber cycle for potassium bromide (KBr) and label the different energies involved, as well as the equation for calculating lattice energy, the following steps can be followed:
Step 1: Draw the main diagram
Start by drawing a square or rectangle to represent the Born-Haber cycle. Divide the top half of the square into two sections: one on the left for the reactants and one on the right for the products. Leave space in the middle for the relevant energy values.
Step 2: Label the reactants
On the left side of the diagram, write the formula for potassium (K) and bromine (Br2), which are the reactants. Label this section as K (s) + Br2 (g).
Step 3: Label relevant energies
In the middle section of the diagram, label the following energy values:
- ΔHf (enthalpy of formation): This refers to the energy change that occurs when one mole of a compound is formed from its constituent elements. Label this value as ΔHf (KBr).
- ΔHSub (enthalpy of sublimation): This represents the energy required to convert one mole of a solid substance into gas. Label this value as ΔHSub (K).
- ΔHVap (enthalpy of vaporization): This term refers to the energy change when one mole of a liquid substance is converted into gas. Label this value as ΔHVap (Br2).
- ΔHI.E. (ionization energy): This represents the energy required to remove one mole of electrons from a gaseous atom. Label this value as ΔHI.E. (K).
- ΔHE.A. (electron affinity): This refers to the energy change when one mole of electrons is added to a gaseous atom. Label this value as ΔHE.A. (Br).
- ΔHL.E. (lattice energy): This is the energy required to convert one mole of solid ionic compound into separated gaseous ions. Label this value as ΔHL.E. (KBr).
Step 4: Label the products
On the right side of the diagram, write the formula for potassium bromide (KBr), which is the product. Label this section as KBr (s).
Step 5: Add arrows and reaction equation
Connect the reactants and products with arrows, indicating the energy changes involved in each step. Additionally, write the balanced chemical equation for the overall reaction in the middle of the diagram, which would be K (s) + 1/2 Br2 (g) → KBr (s).
Step 6: Write the equation for calculating lattice energy (ΔHL.E.)
Below the diagram, write the equation for calculating lattice energy:
ΔHL.E. (KBr) = ΔHf (KBr) - ΔHSub (K) - 1/2 ΔHVap (Br2) - ΔHI.E. (K) - ΔHE.A. (Br)
This equation represents the energy changes involved in the formation of potassium bromide.
By following these steps, you can draw a diagram of the Born-Haber cycle for potassium bromide, label the different energy values, and include the equation for calculating lattice energy.