Give the values of gas constant is different units.

Answer

To find the values of the gas constant (R) in different units, we start with the ideal gas equation:

1. **Ideal Gas Equation**:
\[ PV = nRT \]
Where:
- \( P \) = Pressure
- \( V \) = Volume
- \( n \) = Number of moles
- \( R \) = Universal gas constant
- \( T \) = Temperature (in Kelvin)

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

3. **Units of R**:
The units of \( R \) can be derived from the units of \( P \), \( V \), \( n \), and \( T \).

4. **Different Units of R**:
- **In CGS (Centimeter-Gram-Second) System**:
- Pressure (P) in dynes/cm²
- Volume (V) in cm³
- Moles (n) in moles
- Temperature (T) in Kelvin
- The value of \( R \) in CGS is:
\[ R = 8.314 \times 10^7 \, \text{erg} \cdot \text{mole}^{-1} \cdot \text{K}^{-1} \]

- **In SI (International System of Units)**:
- Pressure (P) in pascals (Pa)
- Volume (V) in cubic meters (m³)
- Moles (n) in moles
- Temperature (T) in Kelvin
- The value of \( R \) in SI is:
\[ R = 8.314 \, \text{J} \cdot \text{mole}^{-1} \cdot \text{K}^{-1} \]

- **In Calorie Units**:
- The value of \( R \) in calories is:
\[ R = 2.0 \, \text{cal} \cdot \text{mole}^{-1} \cdot \text{K}^{-1} \]

- **In Liter-Atmosphere Units**:
- The value of \( R \) in liter-atmosphere is:
\[ R = 0.0821 \, \text{L} \cdot \text{atm} \cdot \text{mole}^{-1} \cdot \text{K}^{-1} \]

5. **Summary**:
Thus, the values of the gas constant \( R \) in different units are:
- CGS: \( 8.314 \times 10^7 \, \text{erg} \cdot \text{mole}^{-1} \cdot \text{K}^{-1} \)
- SI: \( 8.314 \, \text{J} \cdot \text{mole}^{-1} \cdot \text{K}^{-1} \)
- Calories: \( 2.0 \, \text{cal} \cdot \text{mole}^{-1} \cdot \text{K}^{-1} \)
- Liter-Atmosphere: \( 0.0821 \, \text{L} \cdot \text{atm} \cdot \text{mole}^{-1} \cdot \text{K}^{-1} \)