Before You Begin

Question #44525

Difficulty: 8/10 | 🟢 Free

The Question

A concentration cell is constructed at 298 K as follows:

$\ce{Ag(s) | AgCl(s) | NaCl(aq, m_1) || NaCl(aq, m_2), Na2SO4(aq, m_3) | AgCl(s) | Ag(s)}$

The two half-cell solutions are separated by a salt bridge. It is given that the two solutions are perfectly isotonic. Assume ideal van't Hoff factors for osmotic pressure ( $i_{\ce{NaCl}} = 2$ , $i_{\ce{Na2SO4}} = 3$ ) and that the Debye-Hückel limiting law is valid for calculating the activity coefficients of individual ions.

If $m_3 > 0$ , which of the following statements correctly describes the cell potential ( $E_{\text{cell}}$ ) and the relationship between the single-ion activity coefficients of chloride ( $\gamma_{\ce{Cl^-}, 1}$ and $\gamma_{\ce{Cl^-}, 2}$ ) in the two half-cells?

Options

A.
$E_{\text{cell}} > 0$ and $\gamma_{\ce{Cl^-}, 1} > \gamma_{\ce{Cl^-}, 2}$
B.
$E_{\text{cell}} < 0$ and $\gamma_{\ce{Cl^-}, 1} < \gamma_{\ce{Cl^-}, 2}$
C.
$E_{\text{cell}} = 0$ and $\gamma_{\ce{Cl^-}, 1} = \gamma_{\ce{Cl^-}, 2}$
D.
$E_{\text{cell}} > 0$ and $\gamma_{\ce{Cl^-}, 1} < \gamma_{\ce{Cl^-}, 2}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

Don't get tricked by the process! Learn the mechanical traps used in competitive exam questions.

Concepts Behind This Question

Colligative Property Definition|Isotonic, Hypertonic, Hypotonic|Concentration Cells

Why This Question Is Tricky

Common Mistakes

This problem tests the critical distinction between osmotic equilibrium (isotonicity) and electrochemical equilibrium ( $E_{\text{cell}} = 0$ ).

A common 'Textbook Rule' failure occurs when students assume that isotonic solutions have no driving force for any process, falsely concluding $E_{\text{cell}} = 0$ .

However, osmotic pressure is a colligative property dependent on the total particle concentration, whereas cell potential depends on the specific thermodynamic activity of the electroactive ion.

By introducing a secondary electrolyte ( $\ce{Na2SO4}$ ), the ionic strength is decoupled from the chloride concentration.

This forces the application of the Debye-Hückel limiting law, revealing that non-ideal behavior (activity coefficients) further drives the cell potential away from zero.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Solutions - Class 12
Concept	Colligative Property Definition
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free