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Chapter 8: Problem 82

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

Expert verified
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

01

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: \( \frac{1}{2}\mathrm{N}_{2}(g) + \frac{3}{2}\mathrm{H}_{2}(g) \rightarrow \mathrm{NH}_{3}(g) \)
02

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: \( \Delta \mathrm{H}^{\circ}_{reaction} = -46.1 - (236.35 + 324.0) = -46.1 - 560.35 = -606.45 \mathrm{kJ/mol} \)
03

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: \( \mathrm{N{-}H \ bond \ energy} \approx -202.15 \mathrm{kJ/mol} \)
04

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.

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