Question

Consider the reaction $$ 2 \mathrm{O}(g) \longrightarrow \mathrm{O}_{2}(g) $$ a. Predict the signs of \(\Delta H\) and \(\Delta S\). b. Would the reaction be more spontaneous at high or low temperatures?

Short answer

a. For the given reaction, ΔH < 0 (exothermic) and ΔS < 0 (decrease in disorder). b. The reaction would be more spontaneous at low temperatures, as ΔG would be more negative in this case.

Step-by-step solution

a. Predict the signs of ΔH and ΔS

In this reaction, we have two oxygen atoms combining to form an oxygen molecule. We can make predictions about ΔH and ΔS based on the characteristics of the reactants and products. ΔH: The formation of chemical bonds typically releases heat, making the reaction exothermic. As the oxygen atoms form an oxygen molecule, they are forming a bond, so we would expect the enthalpy change to be negative (exothermic). Therefore, ΔH < 0. ΔS: Entropy is a measure of the randomness or disorder of a system. As two oxygen atoms combine to form a single molecule, the system becomes more ordered and less random. As a result, the entropy change would be negative. Therefore, ΔS < 0.

b. Spontaneity at High or Low Temperatures

To determine whether the reaction is more spontaneous at high or low temperatures, we will consider the Gibbs free energy change equation: ΔG = ΔH - TΔS Where ΔG is the Gibbs free energy change, T is the temperature in Kelvin, and we have already determined that ΔH < 0 and ΔS < 0. When ΔG is negative, the reaction is spontaneous. Since both ΔH and ΔS are negative, the equation becomes: ΔG = Negative - T(Negative) At low temperatures, the TΔS term will be smaller in magnitude, making the overall ΔG more negative. When the temperature is increased, the TΔS term will become larger in magnitude, making ΔG less negative or even positive. Thus, the reaction would be more spontaneous at low temperatures.

Key concepts

Enthalpy Change

In chemical reactions, the enthalpy change (\( \Delta H \)) indicates the heat absorbed or released. It helps us understand the nature of a reaction in terms of energy. If a reaction releases heat, it is known as exothermic and the enthalpy change will be negative (\( \Delta H < 0 \)). This typically occurs when bonds form, as energy is released during this process.

Considering the given reaction where two oxygen atoms form an oxygen molecule, it is exothermic because a chemical bond is formed. Thus, energy is released, making \( \Delta H \) negative. Understanding enthalpy change gives insight into why some reactions might feel warm (exothermic) or require heat input (endothermic).

Entropy Change

Entropy (\( \Delta S \)) quantifies the disorder or randomness in a system. When evaluating a chemical reaction, entropy change indicates whether the system becomes more ordered or disordered. A positive entropy change (\( \Delta S > 0 \)) suggests increased randomness, while a negative one (\( \Delta S < 0 \)) indicates increased order.

In our reaction example, two oxygen atoms come together to form one oxygen molecule. This decreases the randomness or disorder since two separate entities become one. Thus, the entropy change is negative. Recognizing entropy change is crucial in chemistry as it helps predict how the structure of the molecular arrangement might shift due to a reaction.

Gibbs Free Energy

Gibbs free energy (\( \Delta G \)) is a term used to determine the spontaneity of a chemical reaction. It combines both enthalpy and entropy changes into a single value using the formula:

• \( \Delta G = \Delta H - T\Delta S \)

Here, T is the absolute temperature in Kelvin. A negative \( \Delta G \) indicates a spontaneous reaction, while a positive one suggests non-spontaneity.

In our context, since both \( \Delta H \) and \( \Delta S \) are negative, the balance between these terms at different temperatures determines the spontaneity. This is why it's vital to consider all components—enthalpy, entropy, and temperature—in tandem to predict reaction outcomes accurately.

Reaction Spontaneity

Reaction spontaneity determines whether a reaction will occur naturally under certain conditions without external energy input. The sign of the Gibbs free energy change (\( \Delta G \)) primarily governs whether a reaction is spontaneous or not.

For our specific reaction: \( 2 \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{O}_{2}(\mathrm{g}) \), with both a negative \( \Delta H \) and \( \Delta S \), it will be more spontaneous at lower temperatures. This is because the negative \( T\Delta S \) term in the Gibbs free energy equation is minimized at low temperatures, making \( \Delta G \) more negative.

Thus, understanding reaction spontaneity allows chemists to predict under what conditions certain reactions will progress quickly or need more input to occur.