Question

Which of these processes are spontaneous? (a) A satellite falls to Earth. (b) Water decomposes to \(\mathrm{H}_{2}\) and \(\mathrm{O}_{2}\) at \(298 \mathrm{~K}\) and 1 atm. (c) Average car prices increase.

Short answer

Only process (a) is spontaneous.

Step-by-step solution

Understanding spontaneity

A process is spontaneous if it occurs without needing to be driven by an external force. Thermodynamically, a spontaneous process often involves a decrease in free energy (negative \(\Delta G\)).

Analyze process (a) A satellite falls to Earth

Gravity naturally pulls objects towards the Earth, making this process spontaneous as it happens without external influence.

Analyze process (b) Water decomposes to \( \mathrm{H}_{2} \) and \( \mathrm{O}_{2} \) at \( 298 \mathrm{K} \)

The decomposition of water into hydrogen and oxygen is not spontaneous under standard conditions (1 atm and 298K), because it requires energy input (positive \(\Delta G\)).

Analyze process (c) Average car prices increase

An increase in average car prices isn’t governed by thermodynamic principles but by economic factors, so spontaneity in a thermodynamic sense does not apply.

Key concepts

thermodynamics

Thermodynamics is the study of energy, entropy, and the laws governing them. It helps us understand how energy changes during physical and chemical processes.
There are four laws in thermodynamics:

• The Zeroth Law defines temperature.
• The First Law is the law of energy conservation. It states that energy cannot be created or destroyed, only transformed or transferred.
• The Second Law states that entropy, a measure of disorder, always increases in an isolated system. This law also implies that energy naturally flows from hot to cold objects.
• The Third Law states that as temperature approaches absolute zero, entropy approaches a minimum value.

These laws are essential for predicting whether a process will be spontaneous. For instance, in the analysis of a satellite falling to Earth, gravity plays a role in the spontaneous decrease of potential energy, which aligns with these principles.

Gibbs free energy

Gibbs free energy (G) is a thermodynamic property used to predict the spontaneity of a process.
It combines enthalpy (H), entropy (S), and temperature (T) into a single value: \[ \Delta G = \Delta H - T \Delta S \]
If \(\Delta G\) is negative, the process is spontaneous; if positive, the process is non-spontaneous. For instance, when water decomposes into hydrogen and oxygen at standard conditions (298 K and 1 atm), \(\Delta G\) is positive, indicating that the reaction requires energy input to proceed and is therefore not spontaneous. Gibbs free energy effectively balances the enthalpy change and the entropy change to determine overall spontaneity.

chemical reactions

Chemical reactions involve the transformation of reactants into products, following the conservation of mass and energy.
They can be classified based on their spontaneity, which is determined by thermodynamic principles.

• Spontaneous reactions occur without external input. An example is the rusting of iron.
• Non-spontaneous reactions require external energy, such as electrolysis of water.

Understanding the conditions under which reactions occur is key in predicting their spontaneity using concepts like Gibbs free energy and the laws of thermodynamics. For example, economic factors govern the increase in car prices, not thermodynamic principles. This underscores the importance of context when analyzing whether processes are spontaneous.