In the equation of state of an ideal gas `PV = nRT, the value of universal gas constant would depend only on :

Options

A. the nature of the gas
B. the units of measurement
C. the pressure of the gas
D. None of these

Answer

To solve the question regarding what the value of the universal gas constant \( R \) depends on in the ideal gas equation \( PV = nRT \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ideal Gas Equation**: The ideal gas equation is given by \( PV = nRT \), where:
- \( P \) = Pressure of the gas
- \( V \) = Volume of the gas
- \( n \) = Number of moles of the gas
- \( R \) = Universal gas constant
- \( T \) = Temperature of the gas (in Kelvin)

2. **Identify the Universal Gas Constant \( R \)**: The universal gas constant \( R \) is a proportionality constant that relates the energy scale to the temperature scale in the context of the ideal gas law.

3. **Recognize the Dependence on Units**: The value of \( R \) is not a fixed number but depends on the units used for pressure, volume, and temperature. Different sets of units will yield different numerical values for \( R \).

4. **Examples of \( R \) in Different Units**:
- In SI units (Joules), \( R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \)
- In calorie units, \( R = 2 \, \text{cal K}^{-1} \text{mol}^{-1} \)

5. **Conclusion**: Therefore, the value of the universal gas constant \( R \) depends only on the units of measurement used for pressure, volume, and temperature.

### Final Answer:
The value of the universal gas constant \( R \) depends only on the units of measurement used for pressure, volume, and temperature.

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