Problem 46 - Chemistry Matter and Change

Question

Determine whether each of the following reactions is spontaneous. a. \(\Delta H_{\text { system }}=-75.9 \mathrm{kJ}, T=273 \mathrm{K}, \Delta S_{\text { system }}=138 \mathrm{J} / \mathrm{K}\) b. \(\Delta \mathrm{H}_{\text { system }}=-27.6 \mathrm{kJ}, T=535 \mathrm{K}, \Delta S_{\text { system }}=-55.2 \mathrm{J} / \mathrm{K}\) c. \(\Delta H_{\text { system }}=365 \mathrm{kJ}, T=388 \mathrm{K}, \Delta S_{\mathrm{system}}=-55.2 \mathrm{J} / \mathrm{K}\) d. \(\Delta H_{\mathrm{system}}=452 \mathrm{kJ}, T=165 \mathrm{K}, \Delta S_{\mathrm{system}}=55.7 \mathrm{J} / \mathrm{K}\)

Step-by-Step Solution

Answer

Reaction a is spontaneous; reactions b, c, and d are non-spontaneous.

Step 1: Understanding Spontaneity and Gibb's Free Energy

To determine if a reaction is spontaneous, we can use Gibbs free energy equation: \( \Delta G = \Delta H - T \Delta S \). A reaction is spontaneous if \( \Delta G < 0 \).

Step 1: Identify the Values

For each reaction, identify \( \Delta H \), \( T \), and \( \Delta S \). Remember to convert \( \Delta S \) from \( \mathrm{J/K} \) to \( \mathrm{kJ/K} \) by dividing by 1000.

Step 2: Calculate ΔG for Reaction a

Given \( \Delta H = -75.9 \, \mathrm{kJ} \), \( T = 273 \, \mathrm{K} \), \( \Delta S = 138 \, \mathrm{J/K} = 0.138 \, \mathrm{kJ/K} \). Compute \( \Delta G = \Delta H - T \Delta S = -75.9 - 273 \times 0.138 \). Calculate \( \Delta G \).

Step 3: Calculate the Result for Reaction a

Perform the calculation: \( \Delta G = -75.9 - 273 \times 0.138 = -75.9 - 37.674 = -113.574 \, \mathrm{kJ} \). Since \( \Delta G < 0 \), the reaction is spontaneous.

Step 4: Calculate ΔG for Reaction b

Given \( \Delta H = -27.6 \, \mathrm{kJ} \), \( T = 535 \, \mathrm{K} \), \( \Delta S = -55.2 \, \mathrm{J/K} = -0.0552 \, \mathrm{kJ/K} \). Calculate \( \Delta G = -27.6 - 535 \times (-0.0552) \).

Step 5: Calculate the Result for Reaction b

Calculate \( \Delta G = -27.6 - 535 \times (-0.0552) = -27.6 + 29.532 = 1.932 \, \mathrm{kJ} \). Since \( \Delta G > 0 \), the reaction is non-spontaneous.

Step 6: Calculate ΔG for Reaction c

Given \( \Delta H = 365 \, \mathrm{kJ} \), \( T = 388 \, \mathrm{K} \), \( \Delta S = -55.2 \, \mathrm{J/K} = -0.0552 \, \mathrm{kJ/K} \). Calculate \( \Delta G = 365 - 388 \times (-0.0552) \).

Step 7: Calculate the Result for Reaction c

Calculate \( \Delta G = 365 - 388 \times (-0.0552) = 365 + 21.4176 = 386.4176 \, \mathrm{kJ} \). Since \( \Delta G > 0 \), the reaction is non-spontaneous.

Step 8: Calculate ΔG for Reaction d

Given \( \Delta H = 452 \, \mathrm{kJ} \), \( T = 165 \, \mathrm{K} \), \( \Delta S = 55.7 \, \mathrm{J/K} = 0.0557 \, \mathrm{kJ/K} \). Calculate \( \Delta G = 452 - 165 \times 0.0557 \).

Step 9: Calculate the Result for Reaction d

Calculate \( \Delta G = 452 - 165 \times 0.0557 = 452 - 9.1905 = 442.8095 \, \mathrm{kJ} \). Since \( \Delta G > 0 \), the reaction is non-spontaneous.

Key Concepts

Spontaneity

In chemistry, the spontaneity of a reaction refers to whether a chemical process can occur without any external energy input. This concept is crucial, as it helps understand why some reactions happen naturally while others do not. To evaluate spontaneity, the Gibbs Free Energy (9G) is utilized, which combines enthalpy (9H), temperature (T), and entropy (9S) in the formula:

• \( \Delta G = \Delta H - T \Delta S \)

\(\)Calculation Steps:

• If \( \Delta G < 0 \), the reaction is spontaneous (it can proceed without input energy).
• If \( \Delta G > 0 \), the reaction is non-spontaneous (it requires energy input to proceed).
• If \( \Delta G = 0 \), the system is at equilibrium.

Evaluating Gibbs Free Energy not only predicts spontaneity, but also provides insights into the directionality of a reaction under constant temperature and pressure. It bridges the thermodynamic properties of entropy and enthalpy with the feasibility of reactions.

Thermodynamics

Thermodynamics stands as the foundation for understanding the energy changes in chemical reactions. It examines the laws governing energy transformation and exchange, crucial for predicting reaction behaviors. In thermodynamics, three primary quantities are often involved:

• Enthalpy (9H): Represents heat content change in reactions. Negative 9H (9H < 0) suggests heat release.
• Entropy (9S): Measures disorder or randomness within a system. Positive 9S (9S > 0) indicates increased randomness.
• Temperature (9T): Influences reactions' direction and extent by affecting entropy.

Understanding these components through thermodynamic laws helps in anticipating the favorability and extent of chemical reactions. For example, the second law predicts that any spontaneous process increases the total entropy of a system and its surroundings, often in the form of increased randomness or dispersal of energy.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products, which can be driven naturally or require energy. There are various types of reactions, including:

• Synthesis
• Decomposition
• Combustion
• Redox

These reactions are guided by the principles of Gibbs Free Energy which determines if they will occur without external energy. The impact of enthalpy, entropy, and temperature on reactions can be observed in the spontaneity of the reactions. Considerations like energy release (exothermic) or absorption (endothermic) and increased disorder can hint at a reaction's course, whether needing balance or forcibly driven by conditions to proceed. Through the study of chemical thermodynamics, conditions under which reactions process and their effectiveness can be analyzed efficiently.