In the equation `PV = nRT`, the gas constant R is not equal to

Options

A. `8.31 xx 10^(7) erg K^(-1) mol^(-1)`
B. `8.31 xx 10^(7) "dyne" cm K^(-1) mol^(-1)`
C. `8.31 JK^(-1) mol^(-1)`
D. `8.31 L atm K^(-1) mol^(-1)`

Explanation

To solve the question regarding the gas constant \( R \) in the equation \( PV = nRT \), we will follow these steps:

### Step 1: Understand the equation
The equation \( PV = nRT \) is the ideal gas law, 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: Identify the value of \( R \)
The gas constant \( R \) can be expressed in different units. The most common values of \( R \) are:
1. \( R = 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \)
2. \( R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \)

### Step 3: Analyze the options
The question asks for which value \( R \) is not equal to. We need to compare the provided options with the known values of \( R \).

### Step 4: Evaluate the provided options
Assuming the options include:
1. \( 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \)
2. \( 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \)
3. \( 8.31 \, \text{J K}^{-1} \text{mol}^{-1} \)
4. Some incorrect value (e.g., \( 5.0 \, \text{L atm K}^{-1} \text{mol}^{-1} \))

From the known values of \( R \), we see that:
- \( 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \) is correct.
- \( 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \) is also correct.
- \( 8.31 \, \text{J K}^{-1} \text{mol}^{-1} \) is approximately equal to \( 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \) and can be considered correct in a rounded context.

### Step 5: Determine the incorrect value
If an option like \( 5.0 \, \text{L atm K}^{-1} \text{mol}^{-1} \) is provided, it is not equal to the known values of \( R \). Hence, this would be the answer to the question.

### Conclusion
The gas constant \( R \) is not equal to \( 5.0 \, \text{L atm K}^{-1} \text{mol}^{-1} \) (or any other incorrect value provided in the options).

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