The quantity(pV)/(kt) represents

Options

A. (a)mass of the gas
B. (b)kinetic energy of the gas
C. ( c)number of moles of a the gas
D. (d)number of molecules in the gas.

Answer

To solve the question regarding the quantity \(\frac{pV}{kT}\), let's break it down step by step.

### 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 of the gas,
- \(n\) = number of moles of the gas,
- \(R\) = universal gas constant,
- \(T\) = temperature in Kelvin.

### Step 2: Relate Boltzmann's Constant to the Ideal Gas Law
Boltzmann's constant \(k\) is related to the universal gas constant \(R\) by the equation:
\[ R = kN_A \]
where \(N_A\) is Avogadro's number (the number of molecules in one mole of a substance).

### Step 3: Substitute \(R\) in the Ideal Gas Law
We can express \(R\) in terms of \(k\) and \(N_A\):
\[ PV = n(kN_A)T \]
This simplifies to:
\[ PV = nkNT \]

### Step 4: Rearranging the Equation
Now, we can rearrange this equation to find \(\frac{PV}{kT}\):
\[ \frac{PV}{kT} = nN_A \]
where \(n\) is the number of moles and \(N_A\) is Avogadro's number.

### Step 5: Interpret the Result
The product \(nN_A\) gives the total number of molecules \(N\) in the gas:
\[ N = nN_A \]
Thus, we conclude that:
\[ \frac{PV}{kT} = N \]

### Final Answer
The quantity \(\frac{pV}{kT}\) represents the total number of molecules in the gas.