Ion Velocity Calculator:
Enter the values of valence of the ion, Z, elementary charge, e(c), electric field strength, E(V/m), viscosity of the medium, n(Pa.s) and radius of the ion, r(m) to determine the value of ion velocity, Vi(m/s).
Ion Velocity Formula:
Ion velocity refers to the speed at which an ion moves in a fluid or electromagnetic field. It is a fundamental concept in fields such as electrochemistry, physics, and environmental science, particularly relevant in processes like electrophoresis and ion transport in cells.
Ion velocity depends on several factors including the electric field strength, the charge of the ion, the viscosity of the medium, and the radius of the ion.
Ion velocity, Vi(m/s) in metres per seconds is calculated by dividing the product of valence of the ion, Z, elementary charge, e(c) (1.602 * 10-19 ) in coulombs and electric field strength, E(V/m) in volts per metre by 18.84, viscosity of the medium, n(Pa.s) in Pascal seconds and radius of the ion, r(m) in metres.
Ion velocity, Vi(m/s) = Z * e(c) * E(V/m) / 18.84 * n(Pa.s) * r(m)
Vi(m/s) = ion velocity in metres per seconds, m/s.
Z = valence of the ion.
e(c) = elementary charge in coulombs, C.
E(V/m) = electric field strength in volts per metre, V/m.
n(Pa.s) = viscosity of the medium in Pascal seconds, Pa.s.
r(m) = radius of the ion in metres, m.
Ion Velocity Calculation:
1.Calculate the velocity of a sodium ion (Na+) with a charge of +1, in a medium with viscosity 0.89 mPa.s, under an electric field of 1000 V/m, assuming the radius of the ion is 0.0001 mm.
Given: Z = +1, e(c) = 1.602 * 10-19, E(V/m) = 1000V/m, n(Pa.s) = 0.89 * 10-3, r(m) = 0.0001m.
Ion velocity, Vi(m/s) = Z * e(c) * E(V/m) / 18.84 * n(Pa.s) * r(m)
Vi(m/s) = 1 * 1.602 * 10-19 * 1000 / 18.84 * 0.89 * 10-3 * 0.0001
Vi(m/s) = 9.554m/s.
2.Determine the radius of a chloride ion (Cl-) with a charge of -1, in a water medium with viscosity 1Pa·s, subject to an electric field of 500 V/m and the ion velocity of -0.024m/s.
Given: Z = -1, e(c) = 1.602 * 10-19, E(V/m) = 500V/m, n(Pa.s) = 1 * 10-3, Vi(m/s) = 0.024m/s.
Ion velocity, Vi(m/s) = Z * e(c) * E(V/m) / 18.84 * n(Pa.s) * r(m)
r(m) = Z * e(c) * E(V/m) / 18.84 * n(Pa.s) * Vi(m/s)
r(m) = -1 * 1.602 * 10-19 * 500 / 18.84 * 1 * 10-3 * 0.024
r(m) = 0.00018m.
Applications and Considerations:
- Electrophoresis: Understanding ion velocity is crucial for analyzing substances in laboratories using electrophoretic techniques.
- Biological Systems: Ion transport across cell membranes involves mechanisms where ion velocity is key to cellular functions.
- Environmental Science: Movement of ions in soils and waters can be predicted using ion velocity, important for pollution control and management.
- Industrial Processes: Ion exchange systems and electroplating technologies utilize controlled ion velocities to ensure efficiency and quality.