1. What is Relative Permittivity of Solvent given Zeta Potential?

Definition: This calculator determines the relative permittivity (dielectric constant) of a solvent based on its dynamic viscosity, ionic mobility, and zeta potential.

Purpose: It's used in electrochemistry and colloid science to understand solvent properties in relation to charged particles.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \epsilon_r \) — Relative permittivity of solvent (dimensionless)
• \( \mu_{liquid} \) — Dynamic viscosity of liquid (Pa·s)
• \( \mu \) — Ionic mobility (m²/V·s)
• \( \zeta \) — Zeta potential (V)
• \( \pi \) — Archimedes' constant (~3.14159)

Explanation: The formula relates the dielectric properties of the solvent to the mobility of ions and the electrical potential at the slipping plane.

3. Importance of Relative Permittivity Calculation

Details: The relative permittivity affects ion transport, colloidal stability, and electrochemical processes in solutions.

4. Using the Calculator

Tips: Enter the dynamic viscosity in Pa·s, ionic mobility in m²/V·s, and zeta potential in volts. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is typical relative permittivity for water?
A: Pure water has a relative permittivity of about 78.5 at 25°C.

Q2: How does temperature affect the calculation?
A: Both viscosity and ionic mobility are temperature-dependent, so measurements should be at consistent temperatures.

Q3: What range of zeta potential is typical?
A: Zeta potential typically ranges from -100 mV to +100 mV for most colloidal systems.

Q4: Can this be used for non-aqueous solvents?
A: Yes, the formula applies to any solvent, though ionic mobility values may be much lower in organic solvents.

Q5: How accurate is this calculation?
A: It provides a good estimate but actual values may vary due to factors like ion pairing or solvent structure effects.