The quantity `(PV)/(k_(B)T)` represents the (` k_(B):`Boltzmann constant)

Options

A. number of particles of the gas
B. mass of the gas
C. number of moles of the gas
D. translation energy of the gas

Explanation

To solve the question regarding the quantity \((PV)/(k_B T)\), where \(k_B\) is the Boltzmann constant, we can follow these steps:

### Step 1: Understand the Ideal Gas Law
The ideal gas law is given by the equation:
\[ PV = nRT \]
where:
- \(P\) = Pressure of the gas
- \(V\) = Volume occupied by the gas
- \(n\) = Number of moles of the gas
- \(R\) = Universal gas constant
- \(T\) = Temperature in Kelvin

### Step 2: Rearranging the Ideal Gas Law
From the ideal gas law, we can express the number of moles \(n\) as:
\[ n = \frac{PV}{RT} \]

### Step 3: Relate Moles to Molecules
To convert the number of moles to the number of molecules, we multiply \(n\) by Avogadro's number \(N_A\):
\[ \text{Number of molecules} = n \times N_A = \frac{PV}{RT} \times N_A \]

### Step 4: Substitute for \(R\)
We know that the Boltzmann constant \(k_B\) is related to the gas constant \(R\) by the equation:
\[ k_B = \frac{R}{N_A} \]
Substituting this into our equation gives:
\[ PV = nRT = n(k_B N_A) = \frac{PV}{RT} \times (k_B N_A) \]

### Step 5: Express \(PV/(k_B T)\)
Now, we can express \(\frac{PV}{k_B T}\):
\[ \frac{PV}{k_B T} = \frac{PV}{\left(\frac{R}{N_A}\right)T} = \frac{PV \cdot N_A}{RT} \]
From our earlier steps, we have:
\[ \frac{PV}{k_B T} = \text{Number of molecules} \]

### Conclusion
Thus, the quantity \(\frac{PV}{k_B T}\) represents the number of molecules (or particles) of the gas.

### Final Answer
The quantity \(\frac{PV}{k_B T}\) represents the number of molecules of the gas.

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