Diffusion coefficient $$ln D = ln D_0 - \frac{Q_d}{R}(\frac{1}{T})$$ not dependent on T stays constant with change in T increases with increasing T decreases with increasing T
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Derive an explicit relation between the diffusion coefficient (D) and temperature and pressure for an ideal gas. Use the relation to calculate the percentage of change in D for a given ideal gas if temperature is increased by 20% in a constant volume process.
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At constant volume and temperature conditions the rates of diffusion $\mathrm{D}_{\mathrm{A}}$ and $\mathrm{D}_{\mathrm{B}}$ of gases $\mathrm{A}$ and B having densities $\rho_{A}$ and $\rho_{B}$ are related by the expression a. $\mathrm{D}_{A}=\left[\mathrm{D}_{\mathrm{B}} \rho_{\mathrm{A}} / \rho_{\mathrm{B}}\right]^{1 / 2}$ b. $\mathrm{D}_{\mathrm{A}}=\left[\mathrm{D}_{\mathrm{B}} \rho_{\mathrm{B}} / \rho_{\mathrm{A}}\right]^{1 / 2}$ c. $\mathrm{D}_{\mathrm{A}}=\mathrm{D}_{\mathrm{B}}\left[\rho_{A} / \rho_{\mathrm{B}}\right]^{1 / 2}$ d. $\mathrm{D}_{\mathrm{A}}=\mathrm{D}_{\mathrm{B}}\left[\rho_{\mathrm{B}} / \rho_{A}\right]^{1 / 2}$
Use the Stokes-Einstein equation and Einstein's diffusion equation to relate variables described below. (hint: you can combine the two equations to relate time or distance to temperature, viscosity, and size.) How will doubling the diffusion coefficient affect the time that it takes for a substance to reach its new position? How will doubling the distance that a substance has to diffuse affect the time for it to reach its new position? How will doubling the viscosity affect the value of the diffusion coefficient? 1. Increase by a factor of 2, i.e. twice as big. How will doubling the radius of a molecule affect the time for it to reach its new position? 3. Increase by a factor of 4, i.e. 4 times as large. How will doubling the temperature affect the time for a substance to reach its new position? How will doubling the temperature affect the value of the diffusion coefficient? 4. Decrease by a factor of 4, i.e. 1/4 as large.
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