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 : one can design an experiment using a liquid and an additive that can be added to the liquid and observe the chemical changes in the reaction species.

one would need a beaker which is filled with a known amount of the liquid in which thermometer is placed to measure the temperature changes; after addition of the additive to the liquid solution one can note down the temperature change and find whether the reaction is endothermic or exothermic in nature. by subtracting the initial temperature value with the final temperature one can find the temperature changes.

various combinations of liquid and additive can be used. liquid in this case can be a known quantity of water and additives can be epsom salt or without epsom salt the experiment can be conducted to notice the changes. water and ice, hydrogen peroxide and dry yeast, vinegar and baking soda,etc.