Answer : The rate constant at 785.0 K is, 
Explanation :
According to the Arrhenius equation,

or,
![\log (\frac{K_2}{K_1})=\frac{Ea}{2.303\times R}[\frac{1}{T_1}-\frac{1}{T_2}]](https://tex.z-dn.net/?f=%5Clog%20%28%5Cfrac%7BK_2%7D%7BK_1%7D%29%3D%5Cfrac%7BEa%7D%7B2.303%5Ctimes%20R%7D%5B%5Cfrac%7B1%7D%7BT_1%7D-%5Cfrac%7B1%7D%7BT_2%7D%5D)
where,
= rate constant at
= 
= rate constant at
= ?
= activation energy for the reaction = 262 kJ/mole = 262000 J/mole
R = gas constant = 8.314 J/mole.K
= initial temperature = 
= final temperature = 
Now put all the given values in this formula, we get:
![\log (\frac{K_2}{6.1\times 10^{-8}s^{-1}})=\frac{262000J/mole}{2.303\times 8.314J/mole.K}[\frac{1}{600.0K}-\frac{1}{785.0K}]](https://tex.z-dn.net/?f=%5Clog%20%28%5Cfrac%7BK_2%7D%7B6.1%5Ctimes%2010%5E%7B-8%7Ds%5E%7B-1%7D%7D%29%3D%5Cfrac%7B262000J%2Fmole%7D%7B2.303%5Ctimes%208.314J%2Fmole.K%7D%5B%5Cfrac%7B1%7D%7B600.0K%7D-%5Cfrac%7B1%7D%7B785.0K%7D%5D)

Therefore, the rate constant at 785.0 K is, 
It is avogrado number. One molecue of magnesium has 6.023 x 10^23 atoms
Answer:
Final temperature: 659.8ºC
Expansion work: 3*75=225 kJ
Internal energy change: 275 kJ
Explanation:
First, considering both initial and final states, write the energy balance:
Q is the only variable known. To determine the work, it is possible to consider the reversible process; the work done on a expansion reversible process may be calculated as:
The pressure is constant, so:
(There is a multiplication by 100 due to the conversion of bar to kPa)
So, the internal energy change may be calculated from the energy balance (don't forget to multiply by the mass):
On the other hand, due to the low pressure the ideal gas law may be appropriate. The ideal gas law is written for both states:
Subtracting the first from the second:

Isolating
:

Assuming that it is water steam, n=0.1666 kmol

ºC