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$(35$ points$)$ Consider a $1-mm$ thick $-$iron $(BCC$ membrane subjected to a temperature of $250C.$ The membrane is also subjected to pressure sides as shown below. Compute the diffusion flux through this membrane if the hydrogen pressure on one side of the membrane is $0\mathrm{.}15$MPa$(1\mathrm{.}48$atm$),$ and on the other side $7\mathrm{.}5$MPa$(74$atm$).$ When a small enough $-$iron $($BCC$)$ plate is subjected to an atmosphere of hydrogen gas, the concentration and mass quantities of hydrogen in sides A and $B$ are given below

Low$-$pressure side A

$C_H(A)=7\mathrm{.}02{10}^{-5}wt\%$

$m_H(A)=7\mathrm{.}02{10}^{-5}Kgin100gof-Fe$

$P_A=7\mathrm{.}5$MPa

High$-$pressure side B

Pure $-$Fe

$C_H(B)=9\mathrm{.}93{10}^{-6}wt\%$

$m_H(B)=9\mathrm{.}93{10}^{-6}Kgin100gof-Fe$

$P_B=0\mathrm{.}15$MPa

${}_{Fe}=7\mathrm{.}87\frac{g}{c}{m}^3$

$-Fe$ in a hydrogen atmosphere

$2\mathrm{.}1$ The volume of $Fe$ in gas $A$ in $100g$ is

a$.V_{Fe(A)}=4\mathrm{.}27{10}^{-5}m$

b$.V_{Fe(A)}=3\mathrm{.}27{10}^{-5}{m}^3$

c$.V_{Fe(A)}=5\mathrm{.}27{10}^{-5}{m}^3$

d$.$ None of the above

$2\mathrm{.}2$ The volume of $Fe$ in gas $B$ in $100g$ is

a$.V_{Fe(B)}=1\mathrm{.}27{10}^{-5}{m}^3$

b$.V_{Fe(B)}=3\mathrm{.}27{10}^{-5}{m}^3$

c$.V_{Fe(B)}=5\mathrm{.}27{10}^{-5}{m}^3$

d$.$ None of the above

$2\mathrm{.}3$ The concentration of hydrogen at the A face in kilograms of $H$ per cubic meter of alloy is

a$.C_{H(A)}^{\text{'}}=5\mathrm{.}53{10}^{-3}K\frac{g}{m^3}$

b$.$ C$"\text{'}$H$($A$)=3\mathrm{.}51{10}^{-4}K\frac{g}{m^3}$

c$.C_{H(A)}^9=5\mathrm{.}27{10}^{-5}K\frac{g}{m^3}$

d$.$ None of the above

$2\mathrm{.}4$ The concentration of hydrogen at the A face in kilograms of $H$ per cubic meter of alloy is

a$.C_{H(B)}^{\text{'}\text{'}}=4\mathrm{.}87{10}^{-5}K\frac{g}{m^3}$

b$.C_{H(B)}^{\text{'}\text{'}}=7\mathrm{.}82{10}^{-4}{m}^3$

c$.C_{H(B)}^{\text{'}\text{'}}=6\mathrm{.}65{10}^{-3}K\frac{g}{m^3}$

d$.$ None of the above

$2\mathrm{.}5$ The hydrogen concentration gradient is

a$.\frac{C}{}x=6\mathrm{.}63K\frac{g}{m^4}$

b$.\frac{C}{}x=4\mathrm{.}75k\frac{g}{m^4}$

c$.\frac{C}{}x=8\mathrm{.}12K\frac{g}{m^4}$

d$.$ None of the above

$2\mathrm{.}6$ The hydrogen diffusion coefficient is

a$.D=8\mathrm{.}23{10}^{-10}\frac{m^2}{s}$

b$.D=6\mathrm{.}41{10}^{-9}\frac{m^2}{s}$

c$.D=8\mathrm{.}23{10}^{-8}\frac{m^2}{s}$

d$.$ None of the above

$2\mathrm{.}7$ The hydrogen diffusion flux is

a$.J=5\mathrm{.}21{10}^{-10}\frac{m^2}{s}$

b$.J=3\mathrm{.}05{10}^{-8}\frac{m^2}{s}$

c$.J=3\mathrm{.}85{10}^{-9}\frac{m^2}{s}$

d$.$ None of the above