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(a)
Interpretation:
The expression for the change in molar Gibbs energy has to be derived.
Concept Introduction:
The van der Waals equation of state can be expressed as
Where,
Ideal gas equation can also be represented as
Molar Gibbs energy can be mathematically represented in terms of T and P,
At constant T,
The change in molar Gibbs energy for an ideal gas is,
Where,
(a)
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Explanation of Solution
The van der Waals equation of state can be expressed as
According to the give question, we can neglect attractive effects. Then the equation becomes,
Solving for
Where,
By taking integration from limit initial value to final value,
The expression in the above box represents the change in molar Gibbs energy for a real gas.
(b)
Interpretation:
Whether the change in molar Gibbs energy is greater or smaller than for a perfect gas has to be decided.
Concept Introduction:
The change in molar Gibbs energy for an ideal gas is,
The change in molar Gibbs energy for a perfect gas is,
(b)
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Answer to Problem 4.2PR
The change in molar Gibbs energy for a perfect gas is greater than the change in molar Gibbs energy for an ideal gas by a factor
Explanation of Solution
The change in molar Gibbs energy for an ideal gas is,
The change in molar Gibbs energy for a perfect gas is,
The change,
Therefore, the change in molar Gibbs energy for a perfect gas is greater than the change in molar Gibbs energy for an ideal gas by a factor
(c)
Interpretation:
The percentage difference between van der Walls and perfect gas for carbon dioxide has to be calculated.
Concept Introduction:
The change in molar Gibbs energy for a perfect gas is greater than the change in molar Gibbs energy for an ideal gas by a factor
Percentage increase
(c)
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Answer to Problem 4.2PR
The percentage difference has been calculated to be
Explanation of Solution
Given data:
Calculation of percentage difference:
Percentage difference:
Therefore, the calculated percentage difference is
(d)
Interpretation:
The critical constants for the given gas in terms of the parameters ‘a’ and ‘b’ has to be derived.
(d)
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Explanation of Solution
A gas described by the equation of state
If we plot a graph between P and V which is called an isotherm, we will get a flat inflexion where
Calculation of critical constants:
Critical Volume
Taking the first and second derivative and equalizing it to zero, we can get two equations,
Consider equation (1). We can express T in terms of V as below,
Now substituting the value of T in equation (2) and solving for
Critical Temperature
By substituting the value of
By substituting the value of
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Chapter 4 Solutions
Elements Of Physical Chemistry
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