Value of R in SI units is 

Options

A. `8.315 xx 10^(7) erg K^(-1) "mole"^(-1)`
B. `8.315 JK^(-1)"mole"^(-1)`
C. `0.0823` lit.Atm.`K^(-1) "mole"^(-1)`
D. `2 cal K^(-1)"mole"^(-1)`

Answer

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

### Step 1: Understand the Ideal Gas Law
The ideal gas law is represented by the equation:
\[ PV = nRT \]
where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = gas constant
- \( T \) = temperature

### Step 2: Identify the SI Units
In SI units, the variables in the ideal gas law are expressed as follows:
- Pressure \( P \) is measured in Pascals (Pa)
- Volume \( V \) is measured in cubic meters (m³)
- Temperature \( T \) is measured in Kelvin (K)
- Number of moles \( n \) is measured in moles (mol)

### Step 3: Rearrange the Ideal Gas Law to Solve for R
To find the value of R, we can rearrange the ideal gas law:
\[ R = \frac{PV}{nT} \]

### Step 4: Substitute the SI Units into the Equation
Substituting the SI units into the equation gives:
\[ R = \frac{(Pa)(m^3)}{(mol)(K)} \]

### Step 5: Calculate the Value of R
The value of R in SI units is calculated as:
\[ R = 8.3145 \, \text{J/(mol·K)} \]
where 1 Joule (J) is equivalent to 1 Pascal meter cubed (Pa·m³).

### Conclusion
Thus, the value of R in SI units is:
\[ R = 8.3145 \, \text{J/(mol·K)} \]