the molar ionic conductance at infinite dilution of Ag+ is 61.92x10-4 S mol-1 m2 at 25C.The ionic mobility of Ag+ is

To determine the ionic mobility of Ag⁺, we can use the relationship between ionic conductance, ionic mobility, and the concentration of the solution. The ionic conductance (\( \Lambda \)) at infinite dilution gives us a direct way to find the ionic mobility (\( \mu \)). The formula we need is:

Understanding Ionic Mobility

Ionic mobility is defined as the velocity of an ion per unit electric field strength. It is a crucial concept in electrochemistry, as it explains how easily ions move through a solution under the influence of an electric field. The mobility is expressed in units of \( m²/(V \cdot s) \).

Key Relationships

The relationship between molar ionic conductance (\( \Lambda \)) and ionic mobility (\( \mu \)) can be represented as:

• \( \Lambda = z \cdot F \cdot \mu \)

In this equation:

• \( \Lambda \) is the molar ionic conductance at infinite dilution,
• \( z \) is the charge of the ion (for Ag⁺, \( z = +1 \)),
• \( F \) is Faraday's constant, approximately \( 96485 \, C/mol \),
• \( \mu \) is the ionic mobility.

Calculation Steps

We're given that \( \Lambda = 61.92 \times 10^{-4} \, S \, mol^{-1} \, m^{2} \) at 25°C. Using this information, we can rearrange the formula to find \( \mu \):

• First, substitute the known values:
• \( \mu = \frac{\Lambda}{z \cdot F} \)
• Substituting \( z = 1 \):
• \( \mu = \frac{61.92 \times 10^{-4} \, S \, mol^{-1} \, m^{2}}{1 \cdot 96485 \, C/mol} \)

Now, let's perform the calculation:

• Calculate \( \mu \):
• \( \mu = \frac{61.92 \times 10^{-4}}{96485} \approx 6.42 \times 10^{-9} \, m^{2}/(V \cdot s) \)

Final Result

Thus, the ionic mobility of Ag⁺ is approximately \( 6.42 \times 10^{-9} \, m^{2}/(V \cdot s) \). This indicates how effectively the Ag⁺ ions can move through the solution when an electric field is applied.

Understanding ionic mobility is essential in fields like electrochemistry, as it impacts processes like conductivity and the efficiency of electrochemical cells. The higher the mobility, the more efficiently ions can transport charge, which is crucial for various applications.