Electrochemical Cells And Gibbs Free Energy

Given the cell: with and equilibrium condition:
Steps: 1.
Half-reactions: \begin{itemize} \item Anode: \quad ( ) \item Cathode: \end{itemize} 2.
Nernst equations: \begin{itemize} \item Anode: \item Cathode: \end{itemize} 3.
Cell potential ( ): \subsection{Answer:} The required pH is .

Concept: Electrochemical cell reactions follow electron transfer balance and thermodynamic relations. Step 1: {Check option (A)} To balance electrons: Adding both reactions: Thus statement (A) is correct. Step 2: {Check option (B)} Electrons cancel when half reactions are added, hence they do not appear in overall reaction. Thus (B) is correct. Step 3: {Check option (C)} Nernst equation: Thus slope of the graph between and is proportional to . Thus (C) is correct. Step 4: {Check option (D)} Electrical work done: Work equals product of charge and potential difference, not their ratio. Thus statement (D) is incorrect.

Step 1: Understanding the Concept:
We use the Nernst equation to find the cell potential. First, we identify the cathode and anode based on standard reduction potentials, then determine the overall cell reaction and standard EMF.
: Key Formula or Approach:
Standard Cell EMF: .
Nernst Equation: .
Step 2: Detailed Explanation:
1. Identifying Electrodes:
Since , Silver acts as the cathode and Zinc acts as the anode.
Anode (Oxidation):
Cathode (Reduction):
Overall reaction: .
Here, .

2. Calculating Standard EMF:
.

3. Applying Nernst Equation:




.
Step 3: Final Answer:
The value of is .

The given reaction is of the form , and we are provided with the rate constant at 30°C. The relationship between the rate of the reaction and the concentration of will depend on the order of the reaction. For a second-order reaction: where is the rate constant. - (A) True: For a second-order reaction, if the concentration of is increased by a factor of 4, the rate will increase by , as per the rate law. - (B) True: The reaction is second order, as indicated by the rate law being proportional to . - (C) False: The half-life period for a second-order reaction is inversely proportional to the concentration of , so it is dependent on the concentration. - (D) Not necessarily true: The decomposition of could be an example of a second-order reaction, but more information is needed. - (E) True: The equation is valid for a first-order reaction, not second-order.
Final Answer: A and B Only

Step 1: Understanding the Concept:
Statement I involves the Arrhenius equation relating rate constants at two temperatures. Statement II involves the rate law for first-order kinetics.
Step 2: Detailed Explanation:
Statement I: Using . Given , , , . Since , the rate constant doubles. (True)
Statement II: For a first-order reaction, Rate . This is an equation of the form , which represents a straight line passing through the origin. (True)
Step 3: Final Answer:
Both statements are true.

Concept: In an electrochemical cell:

• Reduction occurs at the cathode (higher reduction potential).
• Oxidation occurs at the anode.
• .

Step 1:Identify cathode and anode} Reduction potentials: Thus
Step 2:Balance electrons} Multiply silver reaction by :
Step 3:Add the reactions} Thus option (A) is correct.
Step 4:Cell potential} Hence option (B) is incorrect.
Step 5:Other statements}

• Fe undergoes oxidation, not reduction.
• is an intensive property.

Thus