Question

Which statement is true? a. A reaction in which the entropy of the system increases can be spontaneous only if it is exothermic. b. A reaction in which the entropy of the system increases can be spontaneous only if it is endothermic. c. A reaction in which the entropy of the system decreases can be spontaneous only if it is exothermic.

Short answer

The correct statement is (c): A reaction in which the entropy of the system decreases can be spontaneous only if it is exothermic, as this can help to make the free energy change negative which is required for spontaneity.

Step-by-step solution

Understanding Spontaneity

Determine the criteria for spontaneity. A reaction is spontaneous if it results in an overall increase in entropy of the universe, which is the sum of the entropy changes of the system and surroundings. The spontaneity of a reaction is described by the Gibbs free energy equation: \( \Delta G = \Delta H - T\Delta S \), where \( \Delta G \) is the change in free energy, \( \Delta H \) is the change in enthalpy, \( T \) is the temperature in Kelvin, and \( \Delta S \) is the change in entropy. A reaction is spontaneous when \( \Delta G < 0 \) at constant temperature and pressure.

Evaluating Option A

Assess the situation where the system's entropy increases (\( \Delta S > 0 \) for the system), which can contribute positively to the spontaneity of the reaction. However, whether the reaction is exothermic or endothermic also affects \( \Delta G \). For a reaction where \( \Delta S \) is positive, being exothermic (\(\Delta H < 0\)) will increase the likelihood a reaction is spontaneous but is not the only condition since an increase in temperature can make endothermic reactions with increased entropy spontaneous as well.

Evaluating Option B

If the entropy of the system increases (\( \Delta S > 0 \)), the reaction can be spontaneous regardless of it being endothermic (\(\Delta H > 0\)) or exothermic, depending largely on the temperature. High temperatures can turn an endothermic reaction spontaneous if the entropy increase is significant enough.

Evaluating Option C

Now consider a reaction where the entropy of the system decreases (\( \Delta S < 0 \) for the system). In this case, one of the possible ways for the reaction to be spontaneous is if it releases heat, meaning it's exothermic (\( \Delta H < 0 \) ), which contributes negatively to \( \Delta G \) and could result in \( \Delta G < 0 \) and thus a spontaneous reaction.

Key concepts

Entropy and Its Role in Spontaneous Reactions

Entropy, often symbolized as \( S \), is a fundamental concept in thermodynamics that represents the degree of disorder or randomness in a system. Simply put, it's a measure of how spread out or how dispersed a system's energy is among its particles. In the universe, processes tend to favor the direction that increases the overall entropy. When trying to understand whether a chemical reaction will occur spontaneously, we look at the entropy change of both the system and its surroundings.

For a reaction to be spontaneous, the total entropy of the universe should increase. This doesn't always mean that the entropy within the system must go up; the surroundings' entropy change can sometimes compensate. For example, when water freezes, the entropy within the system decreases because the molecules become more ordered. However, the process can still be spontaneous at lower temperatures because the entropy of the surroundings increases by a greater amount due to the release of heat energy.

So while a reaction where the entropy of the system increases has a higher chance of being spontaneous because it contributes to the overall entropy of the universe, this isn't the only factor. Temperature, pressure, and changes in enthalpy (\( \Delta H \)) also play a crucial role, as we will see with Gibbs free energy.

Understanding Gibbs Free Energy

Gibbs free energy, denoted as \( \Delta G \), is a thermodynamic function that combines entropy (\( S \) ) and enthalpy (\( H \) ) to predict the spontaneity of a reaction at constant temperature and pressure. The relationship is expressed in the formula \( \Delta G = \Delta H - T\Delta S \), where \( T \) is the temperature in Kelvin. If the value of \( \Delta G \) is negative, then the reaction is considered spontaneous. In other words, the system has the potential to do work without an input of energy from the outside.

A decline in Gibbs free energy indicates that a system has become more stable after a reaction. The concept is powerful because it takes into account both the heat content (\( \Delta H \)) and the disorder (\( \Delta S \) ) of a system, relating them through temperature—a variable we can often control. It's also worth noting that while a reaction might be spontaneous under one set of conditions, changing the temperature could alter \( \Delta G \) and shift the balance in favor of non-spontaneity, or vice versa.

Exothermic and Endothermic Reactions Explained

Reactions can absorb or release heat, which classifies them as endothermic or exothermic, respectively. Endothermic reactions require an input of energy (\( \Delta H > 0 \) ) and are typically associated with a cooling of the surroundings. Photosynthesis in plants is a perfect example of an endothermic process, as it consumes energy from sunlight to synthesize sugars from carbon dioxide and water.

On the other hand, exothermic reactions release energy (\( \Delta H < 0 \) ) and result in a warming of the surroundings. Combustion of fuels, like the burning of natural gas in a stove, is an example of an exothermic reaction. Whether a reaction is exothermic or endothermic can significantly affect its spontaneity. Exothermic reactions often lead to an increase in the entropy of the surroundings due to heat release, promoting spontaneity. Conversely, endothermic reactions must typically rely on a significant increase in the system's entropy to drive them towards spontaneity, especially at higher temperatures where the \( T\Delta S \) term can overcome a positive \( \Delta H \) value.