S.I. unit of gas constant R is

Options

A. 0.0821 litre atm `K^(-1) "mole"^(-1)`
B. 2 calories `K^(-1) "mole"^(-1)`
C. 8.31 joule `K^(-1) "mole"^(-1)`
D. None

Answer

To determine the SI unit of the gas constant \( R \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**: The ideal gas law is given by the equation:
\[ PV = nRT \]
where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is the temperature.

2. **Rearranging the Equation**: To find the gas constant \( R \), we can rearrange the equation:
\[ R = \frac{PV}{nT} \]

3. **Identify the Units**:
- **Pressure (P)**: The SI unit of pressure is Pascal (Pa), which is equivalent to \( \text{N/m}^2 \) or \( \text{kg/(m \cdot s}^2) \).
- **Volume (V)**: The SI unit of volume is cubic meter (m³).
- **Number of moles (n)**: The SI unit for the amount of substance is mole (mol).
- **Temperature (T)**: The SI unit of temperature is Kelvin (K).

4. **Substituting the Units into the Equation**:
- Substitute the units into the rearranged equation for \( R \):
\[ R = \frac{(Pa)(m^3)}{(mol)(K)} \]
- Since \( 1 \, \text{Pa} = 1 \, \text{N/m}^2 = 1 \, \text{kg/(m \cdot s}^2) \), we can express \( R \) in terms of base SI units:
\[ R = \frac{(kg/(m \cdot s^2))(m^3)}{mol \cdot K} \]
- Simplifying this gives:
\[ R = \frac{kg \cdot m^2}{s^2 \cdot mol \cdot K} \]

5. **Final SI Unit of R**: Therefore, the SI unit of the gas constant \( R \) is:
\[ R = \frac{J}{mol \cdot K} \]
where \( J \) (Joule) is the unit of energy.

### Conclusion:
The SI unit of the gas constant \( R \) is \( \text{J/(mol} \cdot \text{K)} \).