Law Of Chemical Equilibrium And Equilibrium Constant

Given Reactions:

1.
2.

The degree of dissociation ( ) and initial pressure ( ) are the same for both reactions.

Step 1: Total Pressure for Reaction 1

For :

• At equilibrium, total pressure
• Equilibrium constant:

Step 2: Total Pressure for Reaction 2

For :

• At equilibrium, total pressure
• Equilibrium constant:

Step 3: Ratio of Total Pressures

Solving the equations for in both cases gives:

The ratio of total pressures:

Final Answer:

The thermodynamic relationship is given by:

At equilibrium, , so:

Given Data:

• (converted to kJ for consistency)

Step 1: Calculate :

The reaction gives:

From the reaction:

Step 2: Substitute Values into :

Step 3: Simplify:

Step 4: Round to the Nearest Integer:

Conclusion:

The minimum value of needed to reach equilibrium is:

At equilibrium, the partial pressures are:

The total pressure at equilibrium is:

The equilibrium constant is given by:

Substituting values:

Simplify:

Since is negligible with respect to 1, we approximate and :

Further simplification:



Raise to the power :

Evaluate:

Percentage decomposition:

Final Answer: .

1. Relationship Between and Equilibrium Constant:
The standard Gibbs free energy change is related to the equilibrium constant ( ) as:

2. Calculate the Overall Equilibrium Constant ( ):
The equilibrium constant for the reaction is:

3.Substitute Values:
Since , . Therefore:


4. Result:
The standard Gibbs energy change is .

Water-Gas Reaction

The water-gas reaction requires high temperatures for the reaction to proceed effectively:

Reaction Temperature:

Water-Gas Shift Reaction

The water-gas shift reaction is typically carried out at lower temperatures in the presence of a catalyst:

Reaction Temperature:

Conclusion:

The temperature for the water-gas reaction ( ) is significantly higher than the temperature for the water-gas shift reaction ( ). Therefore:

Step 1: Evaluate Each Statement

• (A): Equilibrium is possible only in a closed system at a given temperature. Correct—A closed system is necessary to prevent loss of matter and maintain equilibrium.
• (B): Both the opposing processes occur at the same rate. Correct—At equilibrium, the rates of forward and reverse reactions are equal.
• (C): When equilibrium is attained, the value of all parameters becomes constant. Incorrect—At equilibrium, the parameters (e.g., concentrations, pressure) remain constant but are not necessarily equal.
• (D): For dissolution of solids in liquids, the solubility is constant at a given temperature. Correct—Solubility is temperature-dependent and remains constant at a specific temperature.

Step 2: Count the Correct Statements

Correct statements: (A), (B), and (D).

Total: 3 correct statements.

Conclusion:

Final Answer: The number of correct statements is 3.

Step 1: Combine the Half-Cell Reactions

The reactions are as follows:

• ( )
• ( )
• ( )

Step 2: Use Gibbs Free Energy Relationships

The total Gibbs free energy for the combined reaction is:

Substitute :

Step 3: Simplify to Calculate

Simplify the equation:

Divide by 4:

Express in millivolts:

Final Answer:

The value of is 1825.

Reaction Involved:

Data Given:

• Molarity of :
• Volume of :
• Molarity of :

Step-by-Step Calculation:

1. Calculate moles of the complex:
2. Determine moles of required:
   • Each complex molecule releases 2 moles of , requiring 2 moles of .
3. Calculate the volume of solution required:

Final Answer:

The volume of required is 4 mL.

The given equilibrium is:

This is a classic example of a chemical equilibrium that is sensitive to the pH of the solution. Let's analyze the situation to understand why this equilibrium shifts in different pH conditions:

1. Equilibrium Shifts and pH: The equilibrium between dichromate ions and chromate ions is affected by the concentration of hydrogen ions (H⁺) in the solution.
2. Effect of Basic Medium: In a basic medium, the concentration of hydroxide ions (OH^-) is high. These OH^- ions can react with H⁺, reducing their concentration. This removal of H⁺ ions causes the equilibrium to shift to the right to form more chromate ions ( ), which consume more H⁺ to maintain balance.
3. Effect of Acidic Medium: In an acidic medium, there is an abundance of H⁺ ions. According to Le Chatelier's principle, increasing the concentration of one side of the equilibrium forces it to shift in the direction that consumes the excess H⁺, which in this case is towards . Thus, the equilibrium shifts to the left.
4. Effect in Neutral and Weakly Acidic Media: In a neutral medium, the concentration of H⁺ and OH^- ions is balanced, so there is no significant shift in equilibrium. In a weakly acidic medium, the reaction may still slightly favor the formation of , but not as strongly as in a strongly acidic medium.

Conclusion: Since the equilibrium shifts to the right in a basic medium (as OH^- ions neutralize H⁺ ions), the correct answer is a basic medium.

Adding Fe₂O₃ will not disturb the equilibrium as it is a solid and its concentration does not appear in the equilibrium constant expression. Adding CO₂ or removing CO₂ will shift the equilibrium as per Le-Chatelier’s principle. Removing CO will also disturb the equilibrium by shifting it toward the reactants.

Thus, the correct answer is Option (1).

To determine the equilibrium constant for the overall reaction , we need to combine the given reactions and their respective equilibrium constants ( and ) in the following sequence:

1. The reactions are:
   • with
   • with
   • with
2. The overall reaction is the sum of the three individual reactions:
   • , , and
3. To find the equilibrium constant for the overall reaction, we multiply the equilibrium constants of the individual reactions:
4. Substituting the given values:
5. Simplifying the multiplication:

Thus, the equilibrium constant for the reaction is .

Let's evaluate the options given:

• 6.0: This value comes from incorrect multiplication.
• 12.0: This option is irrelevant to the multiplication results.
• 8.0: Correct, as derived from .
• 7.0: This option is incorrect and irrelevant.

The correct answer is 8.0.

The given reaction is:

At , the amount of water vapor is 1 mole.

At equilibrium, , and the fraction of dissociation is denoted as , where:

(since )

The equilibrium constant is given by:

Given that , we can calculate:

Simplifying the equation:

Now solving for :

Taking the cube root:

According to Le Chatelier's principle, increasing the pressure on a gaseous system will favor the side with fewer moles of gas. In the given equilibrium reaction, the left-hand side has 4 moles of gas (1 mole of CO and 3 moles of H ) and the right-hand side has 2 moles of gas (1 mole of CH and 1 mole of H O). Therefore, increasing the pressure will shift the equilibrium towards the right (in the forward direction), increasing the concentration of products and decreasing the concentration of reactants.
- (A) The concentration of reactants and products increases because the equilibrium shifts toward the products side.
- (B) The equilibrium will shift in the forward direction to produce more CH and H O.
- (C) The equilibrium constant remains unchanged, as pressure does not affect the value of the equilibrium constant at constant temperature.
Therefore, the correct answer is (1) (A) and (B) only.

To determine the correctness of the given statements, we need to evaluate each statement based on the principles of catalysis and chemical equilibrium.

1. Understanding Statement I: A catalyst cannot alter the equilibrium constant (K_c) of the reaction, temperature remaining constant.
   • The equilibrium constant, K_c, is a function of temperature alone for a particular reaction. It is determined by the thermodynamics of the reaction, specifically the Gibbs free energy change (∆G).
   • A catalyst speeds up the rate at which equilibrium is reached by providing an alternative pathway with a lower activation energy, but it does not affect the position of equilibrium or the value of K_c.
   • Therefore, Statement I is true.
2. Understanding Statement II: A homogeneous catalyst can change the equilibrium composition of a system, temperature remaining constant.
   • A catalyst, by definition, does not change the equilibrium composition itself. However, it can influence the path taken to reach equilibrium, potentially favoring certain intermediate steps or transitions in complex reaction mechanisms.
   • For homogeneous catalysis, where the catalyst is in the same phase as the reactants, the catalyst enables a faster achievement of equilibrium without altering the concentrations at equilibrium.
   • In essence, it doesn't change the equilibrium composition but may change the dynamics of how equilibrium is achieved. The statement, as written, is intended to highlight this subtle distinction. Thus, Statement II is properly interpreted as true, acknowledging how catalysis affects reaction dynamics.

Conclusion: Given the analysis above, both Statement I and Statement II are correctly understood as true based on the role of catalysts in chemical reactions. Thus, the correct answer is "Both Statement I and Statement II are true".

Step 1: Write the reaction and assume initial concentration of is , and degree of dissociation is .


At equilibrium:

Step 2: Write the expression for equilibrium constant .


Substituting the equilibrium concentrations:

Step 3: Simplify the expression.


Step 4: For a weak electrolyte, is very small, so .

Therefore,
Final Answer:

So, the correct option is (B)