Question

Use the following standard enthalpies of formation to estimate the \(\mathrm{N}-\mathrm{H}\) bond energy in ammonia: \(\mathrm{N}(g), 472.7 \mathrm{kJ} / \mathrm{mol} ; \mathrm{H}(g),\) \(216.0 \mathrm{kJ} / \mathrm{mol} ; \mathrm{NH}_{3}(g),-46.1 \mathrm{kJ} / \mathrm{mol}\) . Compare your value to the one in Table \(8.5 .\)

Short answer

We estimated the N-H bond energy in ammonia to be approximately -202.15 kJ/mol using the given standard enthalpies of formation. This value can be compared to the one in Table 8.5 to assess the accuracy of our estimation and the reliability of standard enthalpies for calculating bond energies.

Step-by-step solution

Write the balanced equation for the formation of ammonia from its elements

The formation of ammonia from its elements can be represented by the following balanced chemical equation: \( \frac{1}{2}\mathrm{N}_{2}(g) + \frac{3}{2}\mathrm{H}_{2}(g) \rightarrow \mathrm{NH}_{3}(g) \)

Find the change in enthalpy for the reaction

Using the standard enthalpies of formation for nitrogen gas, hydrogen gas, and ammonia gas, we can calculate the enthalpy change for the reaction: \( \Delta \mathrm{H}^{\circ}_{reaction} = \mathrm{H}^{\circ}_{products} - \mathrm{H}^{\circ}_{reactants} \) where, \( \mathrm{N}_{2}(g) = 472.7 \mathrm{kJ/mol} \) \( \mathrm{H}_{2}(g) = 216.0 \mathrm{kJ/mol}\) \( \mathrm{NH}_{3}(g) = -46.1 \mathrm{kJ/mol} \) \( \Delta \mathrm{H}^{\circ}_{reaction} = -46.1 - \left(\frac{1}{2}(472.7) + \frac{3}{2}(216.0)\right) \) Calculating the enthalpy change gives: \( \Delta \mathrm{H}^{\circ}_{reaction} = -46.1 - (236.35 + 324.0) = -46.1 - 560.35 = -606.45 \mathrm{kJ/mol} \)

Estimate the N-H bond energy in ammonia

In one ammonia molecule, there are three N-H bonds. Therefore, we can estimate the N-H bond energy by dividing the enthalpy change by 3: \( \mathrm{N{-}H \ bond \ energy} \approx \frac{-606.45 \mathrm{kJ/mol}}{3} \) This gives: \( \mathrm{N{-}H \ bond \ energy} \approx -202.15 \mathrm{kJ/mol} \)

Compare the estimated value with the one in Table 8.5

Now that we have estimated the N-H bond energy in ammonia, we can compare it to the given value in Table 8.5. The comparison will reveal how accurate our estimation is and whether the standard enthalpies of formation are reliable sources of information for estimating bond energies in molecules.

Key concepts

N-H Bond Energy

The N-H bond energy represents the energy required to break a nitrogen-hydrogen bond in ammonia, or oppositely, the energy released when the bond is formed. This can give you important insight into the stability and strength of the bond. By using the standard enthalpies of formation, we can estimate the N-H bond energy in ammonia. For example, the enthalpy change in the formation of ammonia is calculated and then divided by the number of N-H bonds, which is 3 in the ammonia molecule. This results in an approximate bond energy of \(-202.15 \ \mathrm{kJ/mol}\). Understanding bond energy is crucial as it affects how we predict the behavior of molecules in chemical reactions. A higher bond energy indicates a stronger bond, thus more energy needed to break it resulting in greater stability. This concept is applied in various fields, including chemistry and materials science.

Ammonia Formation

Ammonia is a key chemical in industry and its formation is an essential process. It occurs when nitrogen gas \(\mathrm{N}_2(g)\) and hydrogen gas \(\mathrm{H}_2(g)\) react together. The balanced chemical equation for the formation of ammonia is: \(\frac{1}{2}\mathrm{N}_2(g) + \frac{3}{2}\mathrm{H}_2(g) \rightarrow \mathrm{NH}_3(g)\).This equation tells us that each molecule of ammonia is formed from one nitrogen molecule and three hydrogen molecules, ensuring the conservation of mass and atoms in the reaction. The process of forming ammonia involves a change in energy, moving from the separated gases \(\mathrm{N}_2\) and \(\mathrm{H}_2\) to the formed \(\mathrm{NH}_3\). The calculated enthalpy change for this process is \(-606.45 \ \mathrm{kJ/mol}\), illustrating that the reaction is exothermic, meaning it releases energy, which is why ammonia formation is often harnessed as a source of energy in chemical plants.

Chemical Bond Energies

Chemical bond energies are vital for understanding how atoms are held together in molecules. These energies provide a measure of the bond strength between two atoms and influence how molecules interact in chemical reactions.

• Bond energy is defined as the energy required to break a chemical bond.
• A stronger bond means a higher bond energy.
• Energy release occurs when bonds are formed, contributing to the overall energetics of a reaction.

For example, when we consider ammonia and its formation, we recognize the vital role of N-H bond energy. By using standard enthalpies of formation, chemists can predict the N-H bond energy and compare it to known values. This helps in understanding both the practicality of ammonia's use in industrial applications and the basics of chemical energetics. Knowing bond energies lets us determine reaction conditions, optimize industrial processes, and even design new molecules for various applications. It's all about understanding the energy dynamics that drive chemical changes and transforming that knowledge into technological advances.