It is desired to enrich the partial pressure of hydrogen in a hydrogennitrogen gas mixture for which the partial pressures of both gases are 0.1013 MPa (1 atm). It has been proposed to accomplish this by passing both gases through a thin sheet of some metal at an elevated temperature; inasmuch as hydrogen diffuses through the plate at a higher rate than does nitrogen, the partial pressure of hydrogen will be higher on the exit side of the sheet. The design calls for partial pressures of 0.051 MPa (0.5 atm) and 0.01013 MPa (0.1 atm), respectively, for hydrogen and nitrogen. The concentrations of hydrogen and nitrogen (CH and CN, in mol/m3 ) in this metal are functions of gas partial pressures (pH2 and pN2 , in MPa) and absolute temperature and are given by the followingexpressions:CH = 2.5 * 1031pH2 expa -27,800 J>molRT b (5.16a)CN = 2.75 * 1031pN2 expa -37,600 J>molRT b (5.16b) Furthermore, the diffusion coefficients for the diffusionof these gases in this metal are functions ofthe absolute temperature, as follows:DH(m2>s) = 1.4 * 10-7 expa -13,400 J>molRT b (5.17a)DN(m2>s) = 3.0 * 10-7 expa -76,150 J>molRT b (5.17b) Is it possible to purify hydrogen gas in this manner?If so, specify a temperature at which the processmay be carried out, and also the thickness of metalsheet that would be required. If this procedure isnot possible, then state the reason(s) why

Definition 1.1. Given two integers a and d with d non-zero, we say that d divides a (written d | a) if there is an integer c with a = cd. If no such integer exists, so d does not divide a, we write d - a. If d divides a, we say that d is a divisor of a. Proposition 1.2.1: Assume that a, b, and c are integers. If a | b and b | c, then a | c. Proposition 1.3. Assume that a, b, d, x, and y are integers. If d | a and d | b, then d | ax + by. Corollary 1.4. Assume that a, b, and d are integers. If d | a and d | b, then d | a + b and d | a − b. Proposition 1.4. Let a, b, c ∈ Z be integers. a) If a | b and b | c, then a | c. b) If a | b and b | a, then a = ±b. c) If a | b and a | c, then a | (b + c) and a | (b − c). Prime: A prime number is an integer p ≥ 2 whose only divisors are