Text 8.7 Using the virial equation of state for hydrogen at 298 K given in problem 7 (text 8.6), calculate a. The fugacity of hydrogen at 500 atm and 298 K b. The pressure at which they fugacity is twice the pressure c. The change in Gibbs free energy caused by a compression of 1 mole of hydrogen from 1 to 500 atm. What is the magnitude of the contribution to (c) caused by the non ideality of hydrogen

a). P = 688 atm

b). P = 1083.04 atm

c).Δ G = 16.188 J/mol    

Explanation:

a). Fugacity 'f' can be calculated from the following equations :

where, P = pressure ,  Z = compressibility

Now, the virial equation is :

 ........(1)

Also, PV=ZRT for real gases .......(2)

∴

So from the fugacity equation ,

Putting the value of P = 500 atm in the above equation, we get,

f = 688 atm

b). Given f = 2P

  ∴  P = 1083.04 atm

c). dG = Vdp -S dt  at constant temperature, dT = 0

Therefore, dG = V dp

Δ G = 16.188 J/mol  

answer is: nuclear fusion produces elements that are heavier than helium.

nuclei combine to form a heavier nucleus, releasing energy.  

for example, fusion of hydrogen atoms at the sun.  

this fusion nuclear reaction is in the inner core of the sun and hydrogen (atomic number 1) is conveted into helium (atomic number 2).  

the inner core is the central region of the sun and all solar energy is produced in the core by nuclear fusion.