Question
Describe and explain how each of the following factors affects the rate of diffusion. 1. Concentration gradient 2. Temperature 3. Particle size/molecular weight 4. Nature of media through which the diffusion occurs.
Answers
GPT-5 mini
Briefly, the rate of diffusion is controlled by how big the driving force is (concentration gradient), how fast particles move (temperature, particle size/mass), and how easily they can move through the surrounding medium (viscosity, phase, porosity, interactions). Below are the effects and the reasons:
1) Concentration gradient
- Effect: The larger the concentration gradient (difference in concentration over distance), the larger the net flux of particles. If the gradient is zero there is no net diffusion.
- Why: Fick’s first law: J = −D (dC/dx). Flux J (amount per unit area per time) is proportional to the slope dC/dx. A larger slope ⇒ larger net movement toward equilibrium.
- Note: Gradient sets the direction and magnitude of net flux but does not change the molecular mobility D itself.
2) Temperature
- Effect: Higher temperature increases the diffusion rate (larger D and faster spreading); lower temperature slows diffusion.
- Why: Thermal energy increases particle kinetic energy and frequency of collisions, so particles move faster and explore space more quickly. For small spherical particles in a liquid the Stokes–Einstein relation gives D = kT / (6π η r) (k = Boltzmann constant, T = absolute temperature, η = fluid viscosity, r = particle radius). So D increases roughly with T and decreases with viscosity. In gases D also increases with temperature (and typically decreases with pressure).
- Consequence: Diffusion length scales as √(Dt), so raising T shortens the time to equilibrate over a given distance.
3) Particle size / molecular weight
- Effect: Larger particles (or higher molecular weight molecules) diffuse more slowly than smaller ones.
- Why: Larger particles have larger hydrodynamic radius r and therefore a smaller diffusion coefficient (see Stokes–Einstein: D ∝ 1/r). For molecules of similar shape/density, r scales roughly as M^(1/3), so D ≈ M^(−1/3) (approximate). Bigger particles also experience more drag and collide differently with the medium, lowering mobility.
- Additional point: Very large particles may experience hindered or collective transport (sedimentation, aggregation) that further reduces effective diffusion.
4) Nature of the medium through which diffusion occurs
- Effect: Diffusion is fastest in gases, slower in liquids, and very slow in solids. Within the same phase, higher viscosity, greater crowding, binding interactions, tortuosity and smaller effective pore size reduce diffusion rates.
- Why and examples:
- Phase: Gas molecules are far apart and move quickly → high D. Liquids have closer contacts and more friction → lower D. Solids restrict atomic/molecular motion → very low D (often via defects or vacancies).
- Viscosity: Higher viscosity η lowers D (Stokes–Einstein). Temperature often changes η strongly, so media can amplify temperature effects.
- Porous/gel media: Porosity ε, tortuosity τ and partitioning reduce the effective diffusion coefficient: D_eff ≈ D_free · (ε/τ) · K (K is partition coefficient). Narrow pores or a convoluted path (high τ) slow apparent diffusion.
- Chemical interactions: Adsorption, binding, charge interactions, hydrophobic partitioning into membranes, or specific transport pathways can slow or in some cases selectively speed net transport (facilitated diffusion).
- Concentration-dependent viscosity or crowding: High solute concentrations can reduce D by increasing local friction.
Short summary equations/relations:
- Fick’s first law: J = −D (dC/dx) (flux ∝ concentration gradient)
- Time/length scaling: diffusion distance x ~ √(D t)
- Stokes–Einstein (spheres in liquid): D = kT / (6π η r) (D ↑ with T, ↓ with η and r)
These points explain why steep gradients, high temperature, small particle size, and a low-viscosity/open medium give the fastest diffusion.
1) Concentration gradient
- Effect: The larger the concentration gradient (difference in concentration over distance), the larger the net flux of particles. If the gradient is zero there is no net diffusion.
- Why: Fick’s first law: J = −D (dC/dx). Flux J (amount per unit area per time) is proportional to the slope dC/dx. A larger slope ⇒ larger net movement toward equilibrium.
- Note: Gradient sets the direction and magnitude of net flux but does not change the molecular mobility D itself.
2) Temperature
- Effect: Higher temperature increases the diffusion rate (larger D and faster spreading); lower temperature slows diffusion.
- Why: Thermal energy increases particle kinetic energy and frequency of collisions, so particles move faster and explore space more quickly. For small spherical particles in a liquid the Stokes–Einstein relation gives D = kT / (6π η r) (k = Boltzmann constant, T = absolute temperature, η = fluid viscosity, r = particle radius). So D increases roughly with T and decreases with viscosity. In gases D also increases with temperature (and typically decreases with pressure).
- Consequence: Diffusion length scales as √(Dt), so raising T shortens the time to equilibrate over a given distance.
3) Particle size / molecular weight
- Effect: Larger particles (or higher molecular weight molecules) diffuse more slowly than smaller ones.
- Why: Larger particles have larger hydrodynamic radius r and therefore a smaller diffusion coefficient (see Stokes–Einstein: D ∝ 1/r). For molecules of similar shape/density, r scales roughly as M^(1/3), so D ≈ M^(−1/3) (approximate). Bigger particles also experience more drag and collide differently with the medium, lowering mobility.
- Additional point: Very large particles may experience hindered or collective transport (sedimentation, aggregation) that further reduces effective diffusion.
4) Nature of the medium through which diffusion occurs
- Effect: Diffusion is fastest in gases, slower in liquids, and very slow in solids. Within the same phase, higher viscosity, greater crowding, binding interactions, tortuosity and smaller effective pore size reduce diffusion rates.
- Why and examples:
- Phase: Gas molecules are far apart and move quickly → high D. Liquids have closer contacts and more friction → lower D. Solids restrict atomic/molecular motion → very low D (often via defects or vacancies).
- Viscosity: Higher viscosity η lowers D (Stokes–Einstein). Temperature often changes η strongly, so media can amplify temperature effects.
- Porous/gel media: Porosity ε, tortuosity τ and partitioning reduce the effective diffusion coefficient: D_eff ≈ D_free · (ε/τ) · K (K is partition coefficient). Narrow pores or a convoluted path (high τ) slow apparent diffusion.
- Chemical interactions: Adsorption, binding, charge interactions, hydrophobic partitioning into membranes, or specific transport pathways can slow or in some cases selectively speed net transport (facilitated diffusion).
- Concentration-dependent viscosity or crowding: High solute concentrations can reduce D by increasing local friction.
Short summary equations/relations:
- Fick’s first law: J = −D (dC/dx) (flux ∝ concentration gradient)
- Time/length scaling: diffusion distance x ~ √(D t)
- Stokes–Einstein (spheres in liquid): D = kT / (6π η r) (D ↑ with T, ↓ with η and r)
These points explain why steep gradients, high temperature, small particle size, and a low-viscosity/open medium give the fastest diffusion.