Question

Which of the following is the correct relationship between fugacity (\( f \)) and chemical potential (\( \mu \))?

• A. \( \mu = \mu_0 + RT \ln(f) \)
• B. \( f = \mu_0 + RT \ln(\mu) \)
• C. \( \mu_0 = f + RT \ln(\mu) \)
• D. \( f = \mu + RT \ln(\mu_0) \)

Hint:

The relationship \( \mu = \mu_0 + RT \ln(f) \) is used to calculate chemical potential in non-ideal gases, where the ideal gas law is no longer valid.

Answer 1

The Correct Option is A

The correct relationship between fugacity \( f \) and chemical potential \( \mu \) is given by: \[ \mu = \mu_0 + RT \ln(f) \] where:
- \( \mu \) is the chemical potential at a given temperature and pressure,
- \( \mu_0 \) is the standard chemical potential (at the reference state),
- \( R \) is the universal gas constant,
- \( T \) is the temperature, and
- \( f \) is the fugacity of the substance.
This equation shows how the chemical potential is related to fugacity, which is a corrected pressure used in place of ideal gas pressure to account for non-ideal behavior in real gases.
The other options are incorrect:
- Option (2) reverses the relationship between \( f \) and \( \mu \).
- Option (3) incorrectly defines \( \mu_0 \) in terms of \( f \) and \( \mu \).
- Option (4) mistakenly interchanges the variables for \( f \) and \( \mu \).
Thus, the correct answer is \( \mu = \mu_0 + RT \ln(f) \).