Question

: A suspension of colloids at room temperature (25°C) contains CaS0₄ in (a) 3 mM and (b) 30 mM concentration. Find the Debye length (in nm) for both the cases. Use relevant data given in lecture 12-13. (c) Why do you suppose the Debye length changes with change in salt concentration? Provide reasoning from colloidal science to support your answer. (d) If NaCI was used instead of CaS0₄, how would the Debye length values change for cases (a) and (b)? (No calculation necessary for part (d))

Answer 1

Above equation 1/k is called debye length.

IS= Ionic strength =0.5 (summation of c_iz_i²).

where ci is the concentration of each ion and zi is the respective valency.

it has units of concentration and corrects for the greater effect of polyvalent ions.

1. the potential decays exponentially with distance from the surface .

2. Every Debye‐length, the potential will decrease by 1/e.

3. The Debye Length diminishes as the square root of the ionic strength

by 1/e.

Ionic strength	debye length
10mM	3nm
100mM	1nm
1M	0.3nm

• more ions take the place of the counter ions and thus the potential decays more rapidly with distance from the charged surface.
• the more dilute, the longer the Debye Length.
• The chemical potential of the cations does not change with distance from the membrane.  The concentration of the cation changes.  Similarly for all mobile ions.  At equilibrium there cannot be any change in energy with distance.