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Chapter 20: Problem 47

Many oxides of nitrogen have positive values for the standard free energy of formation. Using \(\mathrm{NO}\) as an example, explain why this is the case.

Short Answer

Expert verified
The standard free energy of formation (∆G) indicates the spontaneity of a compound's formation from its elements in their standard states. For nitric oxide (NO), the reaction is given by: \[ N_2(g) + O_2(g) \rightarrow 2NO(g) \] Considering the bond energies of N≡N triple bond (941 kJ/mol), O=O double bond (498 kJ/mol), and N=O double bond (607 kJ/mol), the formation of NO requires an energy input of 225 kJ/mol. This positive ∆G value signifies that the formation of NO is non-spontaneous under standard conditions, a common characteristic among many oxides of nitrogen.

Step by step solution

01

Define standard free energy of formation

The standard free energy of formation is the change in Gibbs free energy (∆G) that occurs when one mole of a compound is formed from its elements in their standard states. A positive value for the standard free energy of formation indicates that the formation of the compound is not spontaneous and requires energy input, while a negative value indicates that the formation is spontaneous.
02

Describe the nature of NO

Nitric oxide (NO) is a simple molecule consisting of one nitrogen (N) atom and one oxygen (O) atom, bound together by a double bond. It is a highly reactive and unstable compound in biological and chemical processes, often behaving as a radical. Given its high reactivity, we need to evaluate its formation in relation to the standard free energy of formation.
03

Explain the formation of NO

In order to explain the positive value of the standard free energy of formation for NO, let us consider the formation process of NO through the following reaction: \[ N_2(g) + O_2(g) \rightarrow 2NO(g) \] In this reaction, one N≡N triple bond and one O=O double bond are broken. In return, four N=O bonds are formed. Now, we need to consider the bond energies of these bonds in order to assess the energy balance of this reaction.
04

Analyze the bond energies

The bond energies are as follows: 1. N≡N triple bond: Approx. 941 kJ/mol 2. O=O double bond: Approx. 498 kJ/mol 3. N=O double bond: Approx. 607 kJ/mol In the formation of NO, one mole of N≡N triple bond and one mole of O=O double bond are broken, while two moles of N=O double bonds are formed. Breaking one mole of N≡N and O=O bonds requires energy: \[ 941\,\text{kJ/mol} + 498\,\text{kJ/mol} = 1439\,\text{kJ/mol} \] Forming two moles of N=O double bonds releases energy: \[ 2 \times 607\,\text{kJ/mol} = 1214\,\text{kJ/mol} \] We can now calculate the difference in energy: \[ \Delta G = 1439\,\text{kJ/mol} - 1214\,\text{kJ/mol} = 225\,\text{kJ/mol} \]
05

Relate positive ∆G to the formation of NO

Since the ∆G calculated for the formation of NO has a positive value of 225 kJ/mol, it indicates that energy must be supplied to form NO from its elements in the given reaction. This is why many oxides of nitrogen, such as NO, have positive values for the standard free energy of formation, making their formation non-spontaneous under standard conditions.

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Most popular questions from this chapter

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