[VISUAL] Based on the bond energies listed in the table above, which of the following is closest to — Thermodynamics Chemistry Question

STEPS:

1. Understand the relationship between reaction enthalpy ($\Delta H^\circ$) and bond energies:
The enthalpy change of a reaction can be estimated by calculating the energy required to break the reactant bonds minus the energy released when the product bonds are formed:
$$\Delta H^\circ \approx \sum(\text{Bond Energies of Bonds Broken}) - \sum(\text{Bond Energies of Bonds Formed})$$
*From Question 36, we know that the enthalpy of this peptide-coupling reaction is $\Delta H^\circ_{298} = \mathbf{+12\text{ kJ/mol}_{\text{rxn}}}$.*

2. Identify which specific bonds are broken and formed:
By examining the chemical structures on page 25 of the exam booklet:
* Reactants side (Bonds Broken):
* The $\text{C–O}$ single bond of the carboxylic acid group ($-\text{COOH}$) in the first glycine molecule is broken to release the circled $\text{–OH}$ group.
* One $\text{N–H}$ bond of the amino group ($-\text{NH}_2$) in the second glycine molecule is broken to release the circled $\text{–H}$ atom.
* *Total bonds broken:* $1 \times \text{C–O}$ and $1 \times \text{N–H}$.
* Products side (Bonds Formed):
* A new peptide bond is formed directly linking the carbonyl carbon and the amino nitrogen ($\text{C–N}$).
* The released $\text{–OH}$ group and $\text{–H}$ atom combine to form a water molecule ($\text{H–O–H}$), creating one new $\text{O–H}$ bond.
* *Total bonds formed:* $1 \times \text{C–N}$ and $1 \times \text{O–H}$.

3. Sum the bond energies of the broken bonds:
Using the values given in the table:
* $\text{Bond Energy (C–O)} = 360\text{ kJ/mol}$
* $\text{Bond Energy (N–H)} = 390\text{ kJ/mol}$
$$\sum(\text{Bonds Broken}) = 360\text{ kJ/mol} + 390\text{ kJ/mol} = \mathbf{750\text{ kJ/mol}}$$

4. Set up the algebraic equation to solve for the $\text{C–N}$ bond energy ($x$):
Let $x$ represent the bond energy of the newly formed $\text{C–N}$ bond:
$$\Delta H^\circ = \sum(\text{Bonds Broken}) - \left[\text{Bond Energy (C–N)} + \text{Bond Energy (O–H)}\right]$$
Substitute the known values into the equation:
$$+12\text{ kJ/mol} = 750\text{ kJ/mol} - (x + 460\text{ kJ/mol})$$
$$+12 = 290 - x$$

5. Solve for $x$ and find the closest option:
$$x = 290 - 12 = \mathbf{278\text{ kJ/mol}}$$
Comparing this calculated value to the options, $278\text{ kJ/mol}$ is closest to $300\text{ kJ/mol}$. This identifies Option B as the correct answer.

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WHY_OTHERS_WRONG:

* Option A is incorrect (200 kJ/mol): This value is significantly lower than the calculated bond energy of $278\text{ kJ/mol}$. A student might arrive at this if they made basic arithmetic errors during subtraction or estimated the parameters incorrectly.
* Option C is incorrect (400 kJ/mol): This value is too high. A student might select this if they mistakenly used the formula $\Delta H^\circ = \text{Formed} - \text{Broken}$ but set up the sign of the enthalpy change incorrectly, or if they confused the $\text{C–N}$ single bond energy with the much higher value of a carbon-nitrogen double/triple bond.
* Option D is incorrect (500 kJ/mol): This is far too high for a single covalent carbon–nitrogen bond. A student might calculate a value in this range if they completely forgot to account for the formation of the new $\text{O–H}$ bond in water:
$$+12 = 750 - x \implies x = 738\text{ kJ/mol}$$
Realizing $738$ is not an option, they might guess $500\text{ kJ/mol}$ as the highest available value.