# Understanding the Partition Function of a Mixture in Statistical Mechanics

**In statistical mechanics, the partition function plays a crucial role in determining the thermodynamic properties of a system. Let's explore how the partition function of a mixture can be expressed in terms of the single-particle partition functions of its components.**

## Expressing the Partition Function Z of the Mixture

The partition function of a mixture is expressed as **Z = NA * qA * NB * qB**, where:

**Z**is the total partition function of the mixture.**NA**is the number of particles of type A in the mixture.**qA**is the single-particle partition function for particles of type A.**NB**is the number of particles of type B in the mixture.**qB**is the single-particle partition function for particles of type B.

## Explanation of the Expression

The expression **Z = NA * qA * NB * qB** signifies the total partition function for a system containing NA particles of type A and NB particles of type B. Each individual particle contributes multiplicatively to the total partition function, considering all possible states accessible to them.

Here, **qA** and **qB** represent the sum of the statistical weights of all states accessible to a single particle of type A and B, respectively, weighted by the Boltzmann factor.

Express the partition function Z of the mixture in terms of the single-particle partition functions of A and B.

Final answer: The partition function of a mixture is expressed as Z = NA * qA * NB * qB in statistical mechanics, where qA and qB are the single-particle partition functions for particles A and B respectively. Therefore, the correct option is A.

Explanation: The partition function Z of the mixture can be expressed in terms of the single-particle partition functions of A and B. In statistical mechanics, each individual particle contributes multiplicatively to the total partition function (also known as summation over states). In this case, the correct expression would be Z = NA * qA * NB * qB.

Here, qA and qB are the single-particle partition functions for particles A and B respectively. They represent the sum of the statistical weights of all states accessible to a single particle, weighted by the Boltzmann factor.

To summarize, the correct answer is option A: Z = NA * qA * NB * qB.