Which one of the following indicates the value of the gas constant R?

Options

A. `1.987 " cal " deg^(-1) mol^(-1)`
B. `8.3 " cal " deg^(-1) mol^(-1)`
C. `0.0821 " lit " deg^(-1) mol^(-1)`
D. `1.987 " J " deg^(-1) mol^(-1)`

Explanation

To find the value of the gas constant \( R \), we can follow these steps:

### Step 1: Understand the Universal Gas Constant
The universal gas constant \( R \) is a fundamental constant in the ideal gas law and has different values depending on the units used.

### Step 2: List the Common Values of \( R \)
The common values of \( R \) in different units are:
- \( R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \)
- \( R = 1.987 \, \text{cal K}^{-1} \text{mol}^{-1} \)
- \( R = 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \)
- \( R = 8.314 \times 10^7 \, \text{erg K}^{-1} \text{mol}^{-1} \)

### Step 3: Identify the Correct Value from Options
Given the options, we need to identify which one corresponds to the values listed above. The option \( 1.987 \, \text{cal K}^{-1} \text{mol}^{-1} \) matches one of the standard values of \( R \).

### Step 4: Conclusion
Thus, the correct value of the gas constant \( R \) from the options provided is:
\[ R = 1.987 \, \text{cal K}^{-1} \text{mol}^{-1} \]