Which of the following equations represents the compressibility factor for 1 mol of gas.

Options

A. `Z = (PV)/(R )`
B. `Z = (PV)/(T)`
C. `Z= (RT)/(PV)`
D. `Z = (PV)/(RT)`

Explanation

To determine which equation represents the compressibility factor for 1 mole of gas, we will follow these steps:

### Step 1: Understand the Definition of Compressibility Factor
The compressibility factor (Z) is a measure of how much a real gas deviates from ideal gas behavior. It is defined as the ratio of the product of pressure (P) and molar volume (V) to the product of the universal gas constant (R) and temperature (T).

### Step 2: Write the Formula for Compressibility Factor
The formula for the compressibility factor is given by:
\[ Z = \frac{PV}{RT} \]
Where:
- \( P \) = Pressure of the gas
- \( V \) = Molar volume of the gas
- \( R \) = Universal gas constant
- \( T \) = Temperature in Kelvin

### Step 3: Identify the Correct Option
We need to find which of the provided options matches the formula \( Z = \frac{PV}{RT} \).

- Option 1: \( \frac{PV}{R} \) - Incorrect
- Option 2: \( \frac{PV}{T} \) - Incorrect
- Option 3: \( \frac{RT}{PV} \) - Incorrect
- Option 4: \( \frac{PV}{RT} \) - Correct

### Step 4: Conclusion
The equation that represents the compressibility factor for 1 mole of gas is:
\[ Z = \frac{PV}{RT} \]
Thus, the correct answer is Option 4.

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