Please Solve all parts with a detailed explanation.

1. Fick's First Law says: 2. Steady State Diffusion: A latex balloon is filled with helium. The balloon is 0.1mm thick. The concentration of he gas inside the balloon is 0.04462M and outside the balloon is 2.3107M. The moles inside and outside remain constant. a. If the diffusivity of helium through latex is 7.0109m2/s at room temperature, what is the flux of He through the balloon? b. You are surprised to discover that the He is diffusing through the balloon faster than you thought. What concentration of He would you need outside the balloon to halve the flux? c. At what temperature would you have to store the balloon to halve the flux? Room temperature is 298K. The activation energy for He diffusion is 1.441020J. d. Is there another way to halve the flux of helium through the balloon? What is it? 1L=0.001m3;1Moleofgas=22.4L;MolarmassofHe=4.003g/mole 3. Temperature Dependence: Consider a material that has intrinsic (e.g., vacancy) and extrinsic (e.g., grain boundary) mechanisms for diffusion. The activation barrier for the intrinsic mechanism is 1.4eV, and the activation barrier for the extrinsic mechanism is 0.95eV. The pre-exponential factor for the intrinsic mechanism is 1012m2/s, and the pre-exponential factor for the extrinsic mechanism is 1014m2/s. a. Make an appropriate plot (using excel, origin or other plotting program) showing the temperature dependence of diffusivity for both the intrinsic and extrinsic values of the diffusion coefficient, from room temperature to 2000K. Be sure to label your axes and use at least 5 values for each set of data (plot should have data points). Your x-axis should start at 0 . b. At what temperature do the intrinsic and extrinsic values coincide? c. Using the information above, write an equation to solve for the temperature where the values coincide. d. Keeping the values for pre-exponential factor the same as above, how would this intersection temperature change if the values for activation barrier were switched between intrinsic and extrinsic? e. Keeping the values for activation barrier the same as above, how would this intersection temperature change if the values for the pre-exponential factor were switched between intrinsic and extrinsic? f. In general, intrinsic behavior is seen at high temperatures, while extrinsic behavior is seen at low temperatures. Does this generalization describe what you see in your data? Explain. g. What does it mean that diffusion is an activated process? 4. Non-steady State Diffusion: To determine its diffusion coefficient, gallium (Ga) was coated between two samples of a metal-ceramic composite (aluminum-silicon carbide). Ga wets both Al and SiC, and it has a lower melting point than either Al or SiC. The composite was heat treated at 400C for 24 hours. The Ga diffused into the Al. The behavior followed a thin film solution to the diffusion equation. c(x,t)=4Dtexp4Dtx2 a. Show that this function is a solution to Fick's second Law. In other words, take dc/dx,d2c/dx2 and dc/dt, and obtain an equality. The following chemical data were collected as the Ga penetrated into the Al: Al, and the Al sample represents positive values of x, what is the boundary condition, C(x=+,t>0)= ? c. Fill in the table above with values for natural log of the Ga concentration ( kGa ) and position (x) squared. d. Plotting the values with hGa on the y axis and x2 on the x axis will give you a trend that should be a straight line of negative slope. The reciprocal of the slope is equal to 4Dt. In other words, you have linearized this equation in order to solve for D. Now solve for D : e. Describe how would you solve for 4Dt, the pre-exponential. f. Do you think the Ga diffused into the SiC? Explain