Problem 6 - Chemistry in 30 days

Question

Spontaneous adsorption of a gas on a solid surface is an exothermic process because (a) \(\Delta H\) for the system increases (b) \(\triangle S\) for the gas increases (c) \(\triangle S\) for the gas decreases (d) \(\Delta G\) for the gas incrao

Step-by-Step Solution

Answer

(c) \(\triangle S\) for the gas decreases.

Step 1: Understanding the Process

Spontaneous adsorption of a gas on a solid surface is an exothermic process. This means that heat is released during adsorption.

Step 2: Assessing Entropy Change

When a gas is adsorbed onto a solid surface, its mobility decreases, leading to a decrease in the entropy (94S) of the gas. This implies 94S for the gas is negative.

Step 3: Evaluating Gibbs Free Energy

Spontaneity of a process is determined by the Gibbs free energy change (94G), which should be negative for a spontaneous process. 94G can be calculated using the formula: 94G = 94H - T94S.

Step 4: Applying the Gibbs Free Energy Equation

Since the process is exothermic, 94H is negative (heat-releasing). As established, 94S is negative. A negative 94H and 94S still result in a negative 94G if the magnitude of 94H is greater than T94S.

Step 5: Choosing the Correct Option

Considering the spontaneous and exothermic nature of adsorption, and the fact that 94S for the gas decreases, option (c) 94S for the gas decreases, correctly explains why adsorption is exothermic.

Key Concepts

Spontaneous Exothermic Process

When we talk about spontaneous processes, we're referring to changes that occur naturally, without external input once started. A spontaneous exothermic process releases energy in the form of heat. In the case of adsorption, when a gas molecule comes in contact with a solid surface, it adheres to it, releasing energy as it forms intermolecular bonds. This heat release signifies an exothermic reaction.

A fascinating fact about exothermic processes is that they help in stabilizing a system by lowering its overall energy. For adsorption, this means that after the process, the system has less energy than it started with. This release of energy is a driving force for the spontaneity of the process.

• The spontaneity here is driven by the decrease in energy.
• A process being exothermic indicates immediate heat release.
• This spontaneous release is favorable and naturally occurs once initiated.

Entropy Change

Entropy, a measure of randomness or disorder, plays a pivotal role in determining whether a process will be spontaneous. In the context of gas adsorption onto a solid, the entropy of the system changes significantly. Here, the gas molecules move freely in the gaseous state, implying high entropy. However, when these molecules adsorb onto a solid surface, their movement becomes restricted, leading to a decrease in entropy for the gas.

It's crucial to note that:

• As the gas molecules become less mobile, the system's disorder reduces.
• This reduction signifies a negative change in entropy (9S).

Despite this decrease in entropy, gas adsorption is spontaneous due to the favorable energy release discussed earlier.

Gibbs Free Energy

Gibbs free energy (9G) determines if a process is spontaneous. For adsorption, 9G must be negative, reflecting that the process occurs naturally without added work.The formula linking Gibbs free energy, enthalpy, and entropy is:\[9G = 9H - T9S\]Where:

• 9H is the enthalpy change (negative for exothermic processes).
• 9S is the entropy change (negative for gas adsorption).
• T is the absolute temperature in Kelvin.

For the process to be spontaneous:

• 9H (energy released) must outweigh T9S (temperature times change in entropy).
• This balance results in a negative 9G, ensuring spontaneity.