Value of gas constant R in the ideal gas equation PV = nRT depends upon

Options

A. temperature of the gas
B. pressure of the gas
C. units in which P , V and T are measured
D. nature of the gas .

Answer

To determine the value of the gas constant \( R \) in the ideal gas equation \( PV = nRT \), we need to analyze the equation and the units involved. Here’s a step-by-step solution:

### Step 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 gas
- \( R \) = Universal gas constant
- \( T \) = Temperature of the gas

### Step 2: Rearranging the Equation
We can express the gas constant \( R \) in terms of the other variables:
\[ R = \frac{PV}{nT} \]

### Step 3: Analyzing the Units
The value of \( R \) depends on the units used for pressure, volume, and temperature. Different combinations of these units will yield different values for \( R \):
- For example:
- If pressure is in atmospheres (atm) and volume is in liters (L), then \( R = 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \).
- If pressure is in pascals (Pa) and volume is in cubic meters (m³), then \( R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \).

### Step 4: Conclusion
From the analysis, we can conclude that the value of the gas constant \( R \) depends on the units in which pressure, volume, and temperature are measured. Therefore, the correct answer is that the value of \( R \) depends on the units in which \( PV \), \( T \) is measured.

### Final Answer
The value of the gas constant \( R \) in the ideal gas equation \( PV = nRT \) depends on the **units in which \( PV \) and \( T \) are measured**.

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