Question

At what temperatures will the following processes be spontaneous? a. $\mathrm{\Delta }H=-18\mathrm{kJ}$ and $\mathrm{\Delta }S=-60.\mathrm{J}/\mathrm{K}$ b. $\mathrm{\Delta }H=+18\mathrm{kJ}$ and $\mathrm{\Delta }S=+60.\mathrm{J}/\mathrm{K}$ c. $\mathrm{\Delta }H=+18\mathrm{kJ}$ and $\mathrm{\Delta }S=-60.\mathrm{J}/\mathrm{K}$ d. $\mathrm{\Delta }H=-18\mathrm{kJ}$ and $\mathrm{\Delta }S=+60.\mathrm{J}/\mathrm{K}$

Short answer

a. $T>300K$ b. $T<300K$ c. No spontaneous temperature range d. Always spontaneous

Step-by-step solution

Convert units

Make sure all the units match. In this case, we'll convert ΔH from kJ to J: ΔH = -18 kJ × (1000 J/1 kJ) = -18,000 J Now we have ΔH = -18,000 J and ΔS = -60 J/K.

Solve for T

Use the Gibbs free energy equation and solve for T: ΔG < 0 ⇒ -18,000 - T(-60) < 0 Solve for T to find the temperature range. b. ΔH = +18 kJ and ΔS = +60 J/K Repeat Step 1 and Step 2 with given values. c. ΔH = +18 kJ and ΔS = -60 J/K Repeat Step 1 and Step 2 with given values. d. ΔH = -18 kJ and ΔS = +60 J/K Repeat Step 1 and Step 2 with given values.

Summary:

By solving for T in each case using the Gibbs free energy equation and the given values of ΔH and ΔS, we can determine the temperature ranges when each process will be spontaneous.

Key concepts

Spontaneity of Reactions

In chemistry, the spontaneity of a reaction indicates whether a reaction can occur without any external input. A spontaneous reaction naturally proceeds forward under certain conditions.
The spontaneity of a reaction is determined by the change in Gibbs free energy ($\mathrm{\Delta }G$). If $\mathrm{\Delta }G<0$, the reaction is spontaneous. Conversely, if $\mathrm{\Delta }G>0$, the reaction is non-spontaneous and requires additional energy to proceed.
It's important to understand that spontaneity does not necessarily mean that a reaction happens quickly. Instead, it refers to the thermodynamically favorable nature of the reaction.

• A spontaneous reaction has negative $\mathrm{\Delta }G$
• It releases free energy
• Does not require external energy input

This concept helps us predict whether reactions will occur naturally and under what conditions, particularly regarding temperature and other influencing factors.

Thermodynamics

Thermodynamics is the branch of physical science that deals with the relations between heat and other forms of energy. It describes how energy moves and changes in different systems.
The main laws of thermodynamics are crucial for understanding how these processes work in chemistry. The first law, known as the law of energy conservation, states that energy cannot be created or destroyed—only transformed from one form to another.
Another critical aspect is the idea of equilibrium and how energy is distributed. Reactions occur because systems tend to move towards lower energy states. Thermodynamics helps us calculate these changes to determine if a reaction is feasible.

• Relates to energy transfer and transformation
• First law deals with energy conservation
• Pivotal in understanding reaction potential
  Thermodynamics is a guiding principle in predicting whether chemical reactions occur, how they release or absorb energy, and their efficiency under specific conditions.
  Understanding this field provides a foundation for much of our knowledge of natural phenomena and aids in industrial applications where energy transformations are crucial.

Entropy

Entropy ($S$) refers to the measure of a system's disorder or randomness. In any process, entropy tends to increase, reflecting the universe's overall trend towards disorder.
In chemical reactions, changes in entropy ($\mathrm{\Delta }S$) can indicate whether a process will be spontaneous. Generally, reactions that increase entropy are more likely to be spontaneous.
Entropy is central to the second law of thermodynamics, which tells us that for any spontaneous process, the total entropy of the system and its surroundings increases.

• Entropy measures disorder
• An increase often indicates feasible reactions
• Key to understanding the direction of energy transfer

Considering entropy provides insights into the probability of reactions occurring and helps us grasp the greater tendency of systems toward equilibrium with higher disorder.

Enthalpy

Enthalpy ($H$) is a concept used to understand the energy changes in a system, particularly during chemical reactions. It relates to heat exchange at constant pressure.
When reactions occur, changes in enthalpy ($\mathrm{\Delta }H$) are crucial to determine whether they release or absorb heat. Exothermic reactions, which release heat, have negative enthalpy changes ($\mathrm{\Delta }H<0$). On the other hand, endothermic reactions absorb heat, resulting in positive enthalpy changes ($\mathrm{\Delta }H>0$).
Enthalpy tells us about the heat content of a system and its changes when reactions are performed.

• Measures heat content
• Negative $\mathrm{\Delta }H$: Exothermic, heat released
• Positive $\mathrm{\Delta }H$: Endothermic, heat absorbed
  Understanding enthalpy changes allows chemists to predict how reactions respond to different conditions, such as temperature fluctuations. It provides a detailed perspective on energy requirements and dynamics of reactions.