Which of the following are not the units of gas constant (R) ?

Options

A. dynes `K^(-1) mol^(-1)`
B. ergs `"degree"^(-1) mol^(-1)`
C. `"cm"^(3) K^(-1) mol^(-1)`
D. `Pa dm^(3) K^(-1) mol^(-1)`

Explanation

To determine which of the following are not the units of the gas constant (R), we need to analyze the units of R and compare them with the options provided.

### Step-by-Step Solution:

1. **Understand the Gas Constant (R)**:
The gas constant (R) is defined in the context of the ideal gas law and has the units of energy per mole per Kelvin. The standard unit of R is:
\[ R = \frac{J}{mol \cdot K} \]
where J (Joules) is the unit of energy, mol is the unit of amount of substance, and K is the unit of temperature in Kelvin.

2. **Analyze the Options**:
We need to check each option to see if it corresponds to the units of R.

- **Option A: Dine**:
- Dine is a unit of force, not energy. Since R requires energy in its units, this cannot be a unit of R.
- **Conclusion**: This is NOT a unit of R.

- **Option B: Arg**:
- Arg is a unit of energy (1 arg = 10^7 joules). It also involves temperature (degree) and can be related to Kelvin. Therefore, this is a valid unit for R.
- **Conclusion**: This IS a unit of R.

- **Option C: Centimeter cube**:
- Centimeter cube (cm³) is a unit of volume, not energy. Since R requires energy in its units, this cannot be a unit of R.
- **Conclusion**: This is NOT a unit of R.

- **Option D: Pascal decimeter cube**:
- Pascal (Pa) is a unit of pressure, and decimeter cube (dm³) is a unit of volume. The product of pressure and volume (P × V) gives energy (work done), which is consistent with the units of R.
- **Conclusion**: This IS a unit of R.

3. **Final Answer**:
The options that are NOT units of the gas constant (R) are:
- Option A: Dine
- Option C: Centimeter cube