Andrew H.

asked • 11/21/24

How to get ion size using Debye-Huckle question

Given the activity coefficients for an ion with z = 2 in solution as a function of the ionic strength. Find the ion size, α, of this species. ie Given data is Ionic Strength and Activity Coefficient

J.R. S.

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There clearly isn't sufficient information provided for us to help answer this question. We would at least need activity coefficients and ionic strength values.
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11/21/24

Andrew H.

thanks, this is activity ActivityCoefficient,γ 0.010 0.668 0.015 0.628 0.020 0.595 0.025 0.567 0.030 0.544 0.035 0.530 0.040 0.507 0.045 0.494 0.050 0.488 0.055 0.475 0.060 0.462 0.065 0.443 0.070 0.442 0.075 0.438 0.080 0.423 0.085 0.420 0.090 0.404 0.095 0.406 0.100 0.401
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11/21/24

Andrew H.

ie ActivityCoefficient is 0.010, 0.015, 0.020, 0.025, 0.030, 0.035, 0.040, 0.045, 0.050, 0.055, 0.060, 0.065, 0.070, 0.075, 0.080, 0.085, 0.090, 0.095, 0.100 Y: 0.668, 0.628, 0.595, 0.567, 0.544, 0.530, 0.507, 0.494, 0.488, 0.475, 0.462, 0.443, 0.442, 0.438, 0.423, 0.420, 0.404, 0.406, 0.401
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11/21/24

Andrew H.

sorry I misplaced them this is data for Ionic Strength: 0.010, 0.015, 0.020, 0.025, 0.030, 0.035, 0.040, 0.045, 0.050, 0.055, 0.060, 0.065, 0.070, 0.075, 0.080, 0.085, 0.090, 0.095, 0.100
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11/21/24

Andrew H.

This is data for Activity Coefficient Y: 0.668, 0.628, 0.595, 0.567, 0.544, 0.530, 0.507, 0.494, 0.488, 0.475, 0.462, 0.443, 0.442, 0.438, 0.423, 0.420, 0.404, 0.406, 0.401
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11/21/24

1 Expert Answer

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Sebastian A. answered • 11/24/24

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To find the ion size (α) from ionic strength (I) and activity coefficient (γ), use the modified Debye-Hückel equation:

log(γ) = - (A * z²) / (α * √I)

Rearrange to solve for α:

α = - (A * z²) / (log(γ) * √I)

Where:

  1. A ≈ 0.509 L¹/₂ mol⁻¹/₂ (at 25°C),
  2. z is the ion's charge,
  3. I is the ionic strength in mol/L,
  4. γ is the activity coefficient.

Steps:

  1. Use the given values for I (ionic strength) and γ (activity coefficient).
  2. Plug them into the formula to calculate α (ion size).

Example: For I = 0.01 mol/L and γ = 0.85, the ion size α will be approximately 2.88 nm.

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