Question

Predict the spontaneity of a reaction (and the temperature dependence of the spontaneity) for each possible combination of signs for \(\Delta H\) and \(\Delta S\) (for the system). a. \(\Delta H\) negative, \(\Delta S\) positive b. \(\Delta H\) positive, \(\Delta S\) negative c. \(\Delta H\) negative, \(\Delta S\) negative d. \(\Delta H\) positive, \(\Delta S\) positive

Short answer

a. Spontaneous at all temperatures. b. Non-spontaneous at all temperatures. c. Spontaneous at low temperatures. d. Spontaneous at high temperatures.

Step-by-step solution

Understanding Gibbs Free Energy

The spontaneity of a reaction can be determined using Gibbs free energy (ΔG). The formula for Gibbs free energy is ΔG = ΔH - TΔS where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A reaction is spontaneous if ΔG is negative.

Case a: ΔH negative and ΔS positive

For ΔH < 0 and ΔS > 0, the reaction is spontaneously favorable at all temperatures because the negative ΔH lowers ΔG and the positive TΔS term also lowers ΔG as temperature increases.

Case b: ΔH positive and ΔS negative

For ΔH > 0 and ΔS < 0, the reaction is never spontaneous because the positive ΔH increases ΔG and the negative TΔS term, which increases with temperature, further increases ΔG.

Case c: ΔH negative and ΔS negative

For ΔH < 0 and ΔS < 0, the reaction may be spontaneous at low temperatures, where the negative ΔH dominates, but non-spontaneous at high temperatures, where the negative TΔS term, which becomes more significant with temperature, increases ΔG.

Case d: ΔH positive and ΔS positive

For ΔH > 0 and ΔS > 0, the reaction may be non-spontaneous at low temperatures, where the positive ΔH dominates, but spontaneous at high temperatures, where the positive TΔS term is larger and has a greater effect in lowering ΔG.

Key concepts

Chemical Spontaneity

Chemical spontaneity refers to whether a chemical reaction will occur without additional input of energy. It's a central concept in thermodynamics, which is the field of physics studying how energy moves and changes form. A spontaneous reaction is one that proceeds on its own, under a given set of conditions, usually resulting in products that are more stable than the reactants.

To predict spontaneity, we look at the Gibbs free energy, represented by the symbol ΔG. If ΔG is negative, the process is spontaneous; if ΔG is positive, the process is non-spontaneous; and at equilibrium (when ΔG is zero), the rates of forward and reverse reactions are equal, so there's no net change in the system.

Enthalpy (ΔH)

Enthalpy, symbolized as ΔH, represents the total heat content of a system. It's an essential part of understanding chemical reactions because it tells us whether the reaction releases heat energy (exothermic, ΔH < 0) or absorbs it (endothermic, ΔH > 0).

These changes in heat can affect the surroundings, like when an exothermic reaction warms up the environment. It's important to note that a negative ΔH, indicating an exothermic process, often contributes to spontaneity because systems naturally progress towards lower energy states. However, enthalpy is just one piece of the puzzle when predicting whether a reaction will occur spontaneously.

Entropy (ΔS)

Entropy is a measure of the disorder or randomness in a system, denoted as ΔS. The second law of thermodynamics states that the total entropy of an isolated system can only increase over time.

In chemical processes, we can see changes in entropy when substances mix or change phase. For example, gases have higher entropy than liquids or solids, reflecting their greater disorder. A positive ΔS indicates an increase in disorder as the reaction proceeds, which tends to favor spontaneity, as nature tends toward states of higher entropy. On the other hand, a negative ΔS indicates a decrease in disorder, which generally does not favor spontaneity. Yet, the overall spontaneity of a reaction depends on both entropy and enthalpy changes combined.

Reaction Temperature Dependence

The temperature of a reaction significantly influences its spontaneity. Let's consider the Gibbs free energy equation: ΔG = ΔH - TΔS. Temperature (T) acts as a multiplier of the entropy change (ΔS), so it can either intensify or mitigate the effects of entropy on the free energy.

For reactions where ΔH and ΔS are both negative, an increase in temperature could tip the balance from spontaneous to non-spontaneous as the TΔS term becomes more prominent. Conversely, for reactions where ΔH and ΔS are both positive, higher temperatures might make a non-spontaneous reaction spontaneous due to the greater influence of the TΔS term. Thus, temperature doesn't just speed up or slow down reactions (as often taught in kinetics) but can also be the deciding factor in whether a reaction is favorable to begin with.