Gibbs Free Energy

The correct answer is 983


= - 0.34 - 0.14
= 0.48 V

= - 0.48 - 0.0295 log 10
= - 0.5095 V

= -2 × 96500 × 0.5095 J / mol
= 98333.5 × 10^-3 kJ / mol
= 983.3 × 10^-1 kJ / mol
= 983 × 10^-1 kJ / mol

Analysis of Statements on Electrochemical Reactions:

1. Statement 1: The first statement is correct because, under constant pressure and temperature, the electrical work of a reaction equals the Gibbs free energy ( ).
2. Statement 2: The second statement is incorrect. The standard cell potential ( ) is defined under standard conditions (1 atm pressure, 298 K), so it is not dependent on pressure.
3. Statement 3: The third statement is correct, as the relationship between and temperature involves entropy ( ):
4. Statement 4: The fourth statement is correct, as a cell operates reversibly when its potential is perfectly balanced by an opposing source of potential difference.

Conclusion:

There is 1 incorrect statement (Statement 2).

Step 1: Evaluate Each Statement

• (1): A black body emits or absorbs energy in the form of electromagnetic radiation. Correct—This is a fundamental principle of black body radiation.
• (2): The frequency distribution of the emitted radiation depends on temperature. Correct—Planck’s law explains this dependency.
• (3): At a given temperature, the intensity vs. frequency curve passes through a maximum value. Correct—This is a key observation of black body radiation.
• (4): The maximum of the intensity vs. frequency curve shifts to a higher frequency at higher temperatures. Correct—This is explained by Wien’s displacement law.

Step 2: Count the Incorrect Statements

All the given statements are correct.

Number of Incorrect Statements: 0

Conclusion:

Final Answer: The number of incorrect statements is 0.

Analysis of Gibbs Free Energy (G) vs Extent of Reaction

Key Concepts:

• The graph of vs. extent of reaction ( ) typically has a minimum point.
• The slope of the curve indicates spontaneity:
  • If , the reaction is spontaneous.
  • If , the reaction is at equilibrium.
  • If , the reaction is non-spontaneous.

Explanation of Points on the Graph:

1. Point (a):
   • At point (a), (negative slope).
   • The reaction is spontaneous.
2. Point (b):
   • At point (b), (slope = 0).
   • The reaction is at equilibrium.
3. Point (c):
   • At point (c), (positive slope).
   • The reaction is non-spontaneous.

Given Statements:

• A: Reaction is spontaneous at (a) and (b) → False (it is not spontaneous at (b), as (b) is equilibrium).
• B: Reaction is at equilibrium at point (b) and non-spontaneous at point (c) → True.
• C: Reaction is spontaneous at (a) and non-spontaneous at (c) → True.
• D: Reaction is non-spontaneous at (a) and (b) → False.

Conclusion:

The number of true statements is 2 (Statements B and C).

To solve this problem, we need to analyze the thermodynamic parameters of the given chemical reaction: the enthalpy change ( ) and the entropy change ( ). The Gibbs free energy change ( ) determines the spontaneity of a reaction:

• A reaction is spontaneous if .
• The given reaction is endothermic, meaning .

Let's consider the conditions under which the reaction is non-spontaneous at the freezing point of water (0°C or 273 K) and spontaneous at the boiling point of water (100°C or 373 K).

1. At the freezing point (273 K): The reaction is non-spontaneous, indicating:
   • which implies .
   • This inequality suggests that the value is greater than , given that enthalpy is positive.
2. At the boiling point (373 K): The reaction is spontaneous, indicating:
   • which implies .
   • This indicates that value is less than .

Between these two temperatures, as the reaction transitions from non-spontaneous to spontaneous, it suggests that:

• : The increase in entropy helps the reaction become spontaneous at higher temperatures.

Given that both and are positive, the correct option is:

Both and are (+ve).

Concept: At the transition temperature between two phases:
Step 1:Apply condition
Step 2:Solve for
Step 3:Convert to Celsius