Question

Which of the following statements are incorrect for thermodynamic properties? (A) Both \(E_{\text{cell}}\) and \(\Delta_r G\) of reaction are extensive properties. (B) Both \(E_{\text{cell}}\) and \(\Delta_r G\) of reaction are intensive properties. (C) \(E_{\text{cell}}\) is an intensive property while \(\Delta_r G\) of reaction is an extensive property. (D) \(E_{\text{cell}}\) is an extensive property while \(\Delta_r G\) of reaction is an intensive property. Choose the answer from the options given below:

• A. (A), (B) and (D) only
• B. (A), (B) and (C) only
• C. (B), (C) and (D) only
• D. (A), (C) and (D) only

Hint:

Remember: \[ \Delta G=-nFE_{\text{cell}} \] Here \(E_{\text{cell}}\) is intensive, whereas \(\Delta G\) depends on the number of moles and is therefore extensive.

Answer 1

The Correct Option is A

Step 1: Classify \(E_{\text{cell}}\).
Cell potential remains unchanged when the cell reaction is multiplied by any factor. Therefore, \[ E_{\text{cell}} \] is an intensive property. \[ {E_{\text{cell}}\ \text{is intensive}} \]

Step 2: Classify \(\Delta_r G\).
Gibbs free energy change depends upon the amount of reactants and products involved. When a reaction is multiplied by a factor \(n\), \[ \Delta_r G \] also becomes \(n\) times larger. Hence it is an extensive property. \[ {\Delta_r G\ \text{is extensive}} \]

Step 3: Check each statement.
Statement (A): Both extensive \(\Rightarrow\) Incorrect. Statement (B): Both intensive \(\Rightarrow\) Incorrect. Statement (C): \(E_{\text{cell}}\) intensive and \(\Delta_r G\) extensive \(\Rightarrow\) Correct. Statement (D): \(E_{\text{cell}}\) extensive and \(\Delta_r G\) intensive \(\Rightarrow\) Incorrect.

Step 4: Identify incorrect statements.
Incorrect statements are: \[ (A),\ (B),\ (D) \] Hence the correct answer is: \[ {(A),\ (B)\ \text{and}\ (D)\ \text{only}} \]