Question

Identify the correct statement regarding a spontaneous process. (a) Endothermic processes are never spontaneous (b) Exothermic process are always spontaneous (c) Lowering of energy in the reaction process is the only criterion for spontaneity (d) For a spontaneous process in an isolated system, the change in entropy is positive.

Short answer

Statement (d) is correct: For a spontaneous process in an isolated system, the change in entropy is positive.

Step-by-step solution

Understanding Spontaneity

To determine which statement is correct about spontaneous processes, we first need to understand the basic concepts relating to spontaneity in thermodynamics. A spontaneous process occurs naturally without needing to input external energy once it has started.

Evaluating Endothermic Processes

Statement (a) asserts that endothermic processes are never spontaneous. While endothermic processes absorb energy, they can be spontaneous if the change in entropy is large enough to drive the process. Thus, this statement is false.

Assessing Exothermic Processes

Statement (b) claims that exothermic processes are always spontaneous. While many exothermic processes are spontaneous because they release energy, spontaneity also depends on entropy changes; hence, this statement is incorrect.

Evaluating Energy and Spontaneity

Statement (c) suggests that lowering energy is the sole criterion for spontaneity. This is incorrect because spontaneity depends on both energy change and entropy change as described by the Gibbs free energy equation, \( \Delta G = \Delta H - T \Delta S \), where \( \Delta G\) must be negative for spontaneity.

Analyzing Entropy in Isolated Systems

Finally, statement (d) indicates that for a spontaneous process in an isolated system, the entropy change is positive, aligning with the second law of thermodynamics. This statement accurately describes that \( \Delta S_{\text{total}} > 0 \), confirming the process's spontaneity.

Key concepts

Endothermic Processes

An endothermic process is a type of chemical reaction or physical change that absorbs heat from its surroundings. When these reactions occur, the system gains energy, and it might seem like they can't happen without continuous energy input. However, these processes can still be spontaneous under certain conditions due to the role of entropy.
Endothermic processes are often contrasted with exothermic ones, where heat is released. While it is true that endothermic reactions need energy input to proceed, they become spontaneous when the increase in entropy compensates for the energy absorbed.
To better understand, let's look at the Gibbs free energy equation, which states: \[ \Delta G = \Delta H - T \Delta S \] Where:

• \( \Delta G \) is the change in Gibbs free energy (negative for spontaneous reactions).
• \( \Delta H \) is the change in enthalpy (positive for endothermic reactions).
• \( T \) is the temperature in Kelvin.
• \( \Delta S \) is the change in entropy.

Even though \( \Delta H \) is positive in endothermic processes, if \( T \Delta S \) is high enough, it can lead to a negative \( \Delta G \), making the process spontaneous.

Exothermic Processes

Exothermic processes are famously known for releasing energy in the form of heat. They often proceed spontaneously because they lower the energy state of the system by releasing warmth to the surroundings. But, not every exothermic reaction is naturally spontaneous.
The spontaneity of exothermic reactions doesn't just rely on the heat released. It also depends significantly on the entropy change involved. The idea is that, along with decreasing energy, a process that increases the disorder (entropy) of the universe will more likely be spontaneous.
According to the Gibbs free energy equation \( \Delta G = \Delta H - T \Delta S \), the spontaneity is determined by both the enthalpy change \( \Delta H \) and the entropy change \( \Delta S \). For an exothermic reaction where \( \Delta H \) is negative, a positive \( \Delta S \) or a high temperature \( T \) makes \( \Delta G \) negative, promoting spontaneity. However, under particular conditions, like very low temperatures or negative entropy changes, exothermic processes might not spontaneously occur.

Entropy Change

Entropy is a key player in dictating whether a process is spontaneous. It measures the degree of disorder or randomness within a system. A higher entropy usually means more disorder, which can drive a process forward spontaneously.
The second law of thermodynamics states that in an isolated system, the total entropy should always increase or at least stay the same for a spontaneous process. This principle explains why certain reactions proceed on their own while others do not.
Entropy change, \( \Delta S \), gets determined by the variation in the states of reactants and products. Consider gas molecules in a container: when allowed space to spread, their entropy increases due to greater random movement and distribution. In practical terms, an increase in the number of microstates available to a system usually signifies entropy growth.
Thus, for any process being spontaneous, the change in entropy combined with the heat exchange in the process determines the feasibility, following the Gibbs free energy condition: \[ \Delta G = \Delta H - T \Delta S \] Hence, understanding entropy is crucial as it reflects on the system's tendency to shift toward a state of maximal dispersion and disorder.