Interpretation:
The chemical processes for each step of the given process are to be stated. The change in entropy for the complete process is to be determined.
Concept introduction:
The term entropy is used to represent the randomness in a system. When a system moves from an ordered arrangement to a less order arrangement, then the entropy of the system increases. The entropy of mixing of gases is given as,
Answer to Problem 3.32E
The first process is the mixing of gas and the second process is the expansion of mixture. The entropy of mixing for the given mixture is
Explanation of Solution
The initial volume of the
The initial volume of the
The temperature is
The pressure is
The ideal gas equation is given as,
Where,
•
•
•
•
•
Rearrange the above equation for the value of
Substitute the values of the volume of argon gas
Therefore, the number of moles of the
Substitute the values of the volume of helium gas
Therefore, the number of moles of the
The mole fraction of a substance present in the two-component system is given as,
Where,
•
•
Substitute the number of moles of argon gas and helium gas to calculate the mole fraction of argon gas in the equation (3).
Substitute the number of moles of argon gas and helium gas to calculate the mole fraction of helium gas in the equation (3).
The entropy of mixing of gases to form given mixture is given as,
Where,
•
•
•
•
•
Substitute the value of
Therefore, the entropy of mixing for the given mixture is
The total volume of the given mixture is given as,
Where,
•
•
Substitute the value of the volume of argon and the volume of helium in the above equation.
Therefore, the initial volume of the given mixture is
The final volume of thegiven mixture is
The change entropy bythe expansion of the given system is given as,
Where,
•
•
Substitute the value of
Therefore, the change entropy by the volume change of the given system is
The total entropy change of the given mixture is given as,
Where,
•
•
Substitute the value of the entropy change by mixingand the entropy change by expansionin the above equation.
Therefore, the change in entropy for the complete process is
The first process is the mixing of gas and the second process is the expansion of mixture. The entropy of mixing for the given mixture is
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Chapter 3 Solutions
Physical Chemistry
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