Question

Hydrogen is diffusing through solid nickel. At a temperature of 358 K, the diffusivity is 1.16 x 10-8 cm2/s. At a temperature of 438 K, the diffusivity is 1.05 x 10-7 cm2/s. What is the activation energy in J/mol?

Answer 1

Q_d=35881 J/mol

So the activation energy is 35881 J/mol.

Step-by-step explanation:

Consider the following equations:

`lnD_(1) =lnD_(o) -(Q_(d) )/(R*T_(1) )`

`lnD_(2) =lnD_(o) -(Q_(d) )/(R*T_(2) )`

Solving the above two equation to find the Q_d in term of diffusivity and temperature we will get:

`Q_(d)=-R*(lnD_(1) -lnD_(2) )/((1)/(T_(1) )-(1)/(T_(2) )  )`

where:

Q_d is the activation energy

D_1 is the diffusivity at T_1

D_2 is the diffusivity at T_2

`Q_(d)=-8.31*(ln1.16*10^-12 -ln1.05*10^-11 )/((1)/(358 )-(1)/(438 )  )`

Q_d=35881 J/mol

So the activation energy is 35881 J/mol.