Question
Discuss Hess's of constant heat submission with Mathematical expression. Considering the following:
a. Bond enthalpy b. Bond dissociation c.Lattice enthalpy d. Born-Haber cycle
a. Bond enthalpy b. Bond dissociation c.Lattice enthalpy d. Born-Haber cycle
Answers
Answered by
GPT-4o mini
Hess's Law, also known as the Law of Constant Heat Summation, states that the total enthalpy change for a given chemical reaction is the same, regardless of the number of steps the reaction takes. This means that for any chemical process, the enthalpy change can be calculated by summing the enthalpy changes of individual steps in the process.
### Mathematical Expression
The expression can be summarized as:
\[
\Delta H_{reaction} = \Delta H_1 + \Delta H_2 + \Delta H_3 + \ldots
\]
Where \( \Delta H_{reaction} \) is the enthalpy change for the overall reaction, and \( \Delta H_n \) are the enthalpy changes for each individual step.
Now let's discuss how Hess's Law is applied to bond enthalpy, bond dissociation, lattice enthalpy, and the Born-Haber cycle.
### a. Bond Enthalpy
Bond enthalpy is the energy required to break one mole of a particular type of bond in a molecule in the gas phase. According to Hess's Law, the enthalpy change associated with breaking and forming bonds in a reaction can be determined through the bond enthalpies.
**For example**, consider the reaction:
\[
AB \rightarrow A + B
\]
The bond enthalpy \( D \) for the bond \( AB \) can be expressed in terms of the enthalpy change for the reaction:
\[
\Delta H = D_{AB}
\]
If we have another reaction in which \( A \) and \( B \) re-combine, the reverse process will have an enthalpy change of \( -D_{AB} \).
### b. Bond Dissociation
Bond dissociation energy is the energy required to break a bond and is often measured as an average of several measurements because the strength of bonds can vary between different molecules. Using Hess's Law, the overall reaction enthalpy can be calculated using the bond dissociation energies of the bonds broken and formed during the reaction.
**For example**:
For a general reaction:
\[
\text{Reactants} \rightarrow \text{Products}
\]
If bonds are broken in the reactants and new bonds are formed in the products, we can write:
\[
\Delta H = \sum D_{bonds\ broken} - \sum D_{bonds\ formed}
\]
### c. Lattice Enthalpy
Lattice enthalpy is the energy released when one mole of an ionic solid is formed from its gaseous ions. Using Hess’s Law, the lattice enthalpy can be derived from the enthalpy of formation of the ionic compound and the enthalpy of dissociation of the constituent ions.
\[
\Delta H_{lattice} = \Delta H_{formation} - \Delta H_{dissociation}
\]
### d. Born-Haber Cycle
The Born-Haber cycle provides a thermochemical cycle that relates the lattice enthalpy of an ionic compound to various other enthalpies, such as sublimation, ionization, and bond dissociation.
The Born-Haber cycle for an ionic compound \(MX\) can be illustrated as follows:
1. **Sublimation of the solid** \(M(s) \rightarrow M(g)\): \( \Delta H_{sublimation} \)
2. **Ionization of metal \(M\)**: \( M(g) \rightarrow M^+(g) + e^-\): \( \Delta H_{ionization} \)
3. **Dissociation of diatomic non-metal \(X_2\)**: \(X_2(g) \rightarrow 2X(g)\): \( \Delta H_{dissociation} \)
4. **Formation of ion \(X^-\)**: \( X(g) + e^- \rightarrow X^-(g): \Delta H_{electron\ affinity} \)
5. **Formation of \(MX\)**: \(M^+(g) + X^-(g) \rightarrow MX(s)\): \( \Delta H_{lattice} \)
Using Hess's Law, the sum of these enthalpies should equal the enthalpy change for the formation of the ionic compound from its elements in their standard states.
\[
\Delta H_f^o(MX) = \Delta H_{sublimation} + \Delta H_{ionization} + \frac{1}{2} \Delta H_{dissociation} + \Delta H_{electron\ affinity} + \Delta H_{lattice}
\]
In conclusion, Hess's Law is a fundamental principle in thermochemistry, and by applying it to bond enthalpy, bond dissociation, lattice enthalpy, and the Born-Haber cycle, we can calculate the enthalpy changes in various chemical processes.
### Mathematical Expression
The expression can be summarized as:
\[
\Delta H_{reaction} = \Delta H_1 + \Delta H_2 + \Delta H_3 + \ldots
\]
Where \( \Delta H_{reaction} \) is the enthalpy change for the overall reaction, and \( \Delta H_n \) are the enthalpy changes for each individual step.
Now let's discuss how Hess's Law is applied to bond enthalpy, bond dissociation, lattice enthalpy, and the Born-Haber cycle.
### a. Bond Enthalpy
Bond enthalpy is the energy required to break one mole of a particular type of bond in a molecule in the gas phase. According to Hess's Law, the enthalpy change associated with breaking and forming bonds in a reaction can be determined through the bond enthalpies.
**For example**, consider the reaction:
\[
AB \rightarrow A + B
\]
The bond enthalpy \( D \) for the bond \( AB \) can be expressed in terms of the enthalpy change for the reaction:
\[
\Delta H = D_{AB}
\]
If we have another reaction in which \( A \) and \( B \) re-combine, the reverse process will have an enthalpy change of \( -D_{AB} \).
### b. Bond Dissociation
Bond dissociation energy is the energy required to break a bond and is often measured as an average of several measurements because the strength of bonds can vary between different molecules. Using Hess's Law, the overall reaction enthalpy can be calculated using the bond dissociation energies of the bonds broken and formed during the reaction.
**For example**:
For a general reaction:
\[
\text{Reactants} \rightarrow \text{Products}
\]
If bonds are broken in the reactants and new bonds are formed in the products, we can write:
\[
\Delta H = \sum D_{bonds\ broken} - \sum D_{bonds\ formed}
\]
### c. Lattice Enthalpy
Lattice enthalpy is the energy released when one mole of an ionic solid is formed from its gaseous ions. Using Hess’s Law, the lattice enthalpy can be derived from the enthalpy of formation of the ionic compound and the enthalpy of dissociation of the constituent ions.
\[
\Delta H_{lattice} = \Delta H_{formation} - \Delta H_{dissociation}
\]
### d. Born-Haber Cycle
The Born-Haber cycle provides a thermochemical cycle that relates the lattice enthalpy of an ionic compound to various other enthalpies, such as sublimation, ionization, and bond dissociation.
The Born-Haber cycle for an ionic compound \(MX\) can be illustrated as follows:
1. **Sublimation of the solid** \(M(s) \rightarrow M(g)\): \( \Delta H_{sublimation} \)
2. **Ionization of metal \(M\)**: \( M(g) \rightarrow M^+(g) + e^-\): \( \Delta H_{ionization} \)
3. **Dissociation of diatomic non-metal \(X_2\)**: \(X_2(g) \rightarrow 2X(g)\): \( \Delta H_{dissociation} \)
4. **Formation of ion \(X^-\)**: \( X(g) + e^- \rightarrow X^-(g): \Delta H_{electron\ affinity} \)
5. **Formation of \(MX\)**: \(M^+(g) + X^-(g) \rightarrow MX(s)\): \( \Delta H_{lattice} \)
Using Hess's Law, the sum of these enthalpies should equal the enthalpy change for the formation of the ionic compound from its elements in their standard states.
\[
\Delta H_f^o(MX) = \Delta H_{sublimation} + \Delta H_{ionization} + \frac{1}{2} \Delta H_{dissociation} + \Delta H_{electron\ affinity} + \Delta H_{lattice}
\]
In conclusion, Hess's Law is a fundamental principle in thermochemistry, and by applying it to bond enthalpy, bond dissociation, lattice enthalpy, and the Born-Haber cycle, we can calculate the enthalpy changes in various chemical processes.