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Chapter 20: Problem 51

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

Short Answer

Expert verified
Many oxides of nitrogen, such as NO, have positive values for the standard free energy of formation (ΔG°f) because the enthalpy (ΔH°) and entropy (ΔS°) changes during the formation of these compounds from their constituent elements are both positive. The positive ΔG°f suggests that the formation of these oxides is non-spontaneous under standard conditions and their stability may be lower compared to their constituent elements, such as N2 and O2. However, the value of ΔG°f depends on temperature, and the formation of these compounds may become more favorable at higher temperatures.

Step by step solution

01

Introduction to Standard Free Energy of Formation

Standard free energy of formation, denoted by ΔG°f, is the change in Gibbs free energy when one mole of a substance is formed from its constituent elements in their standard states. Mathematically, it is given by ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature, and ΔS is the change in entropy. A positive ΔG°f means that the process of forming the compound from its elements is non-spontaneous under standard conditions, indicating that the compound may be less stable compared to its constituent elements. On the other hand, a negative ΔG°f indicates a spontaneous formation and greater stability of the compound compared to its constituent elements.
02

Formation of NO and its ΔH° and ΔS° values

Let's consider the formation of nitric oxide (NO) from its constituent elements, nitrogen (N2) and oxygen (O2). The balanced chemical equation for this reaction is: \( \frac{1}{2} N_2 + \frac{1}{2} O_2 \rightarrow NO \) The standard enthalpy change, ΔH°, for this reaction is positive, since the reaction requires energy to break the strong triple bond in the nitrogen molecule. The standard entropy change, ΔS°, is also positive for this reaction because one mole of gas is produced while one mole of gas is consumed, which leads to a net increase in the number of gas molecules and thus an increase in entropy.
03

Calculating ΔG°f for the formation of NO

Now, we can use the equation ΔG = ΔH - TΔS to calculate the standard free energy of formation for NO. Since both ΔH° and ΔS° are positive, the value of ΔG°f will depend on the temperature. At lower temperatures, the term "TΔS" will be smaller, making ΔG°f more likely to be positive. At higher temperatures, the term "TΔS" will increase, and the value of ΔG°f may become negative, indicating that the formation of NO becomes more favorable.
04

Explanation for the positive ΔG°f of NO

In summary, many oxides of nitrogen, such as NO, have positive values for the standard free energy of formation because the enthalpy and entropy changes during the formation of these compounds from their constituent elements are both positive. The positive ΔG°f suggests that the formation of these oxides is non-spontaneous under standard conditions, and their stability may be lower compared to their constituent elements such as N2 and O2. However, it's important to note that the value of ΔG°f depends on temperature, and the formation of these compounds may become more favorable at higher temperatures.

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