The correct value of the gas contant R is close to

Options

A. 0.082 litre- atmosphere K
B. 0 . 082 litre - atmosphere `K^(-1) mol^(-1)`
C. `0.082 " litre - atmosphere"^(-1) K mol^(-1)`
D. `0 .082" litre"^(-1) "atmosphere"^(-1)` K mol.

Answer

To find the correct value of the gas constant \( R \), we can use the ideal gas equation, which is given by:

\[ PV = nRT \]

### Step-by-Step Solution:

1. **Identify the Variables**:
- Pressure (\( P \)) = 1 atmosphere
- Volume (\( V \)) = 22.4 liters (at STP for 1 mole of gas)
- Number of moles (\( n \)) = 1 mole
- Temperature (\( T \)) = 273 Kelvin

2. **Rearrange the Ideal Gas Equation**:
We need to isolate \( R \) in the equation. Rearranging gives us:
\[ R = \frac{PV}{nT} \]

3. **Substitute the Values into the Equation**:
Now we substitute the known values into the equation:
\[ R = \frac{(1 \, \text{atm}) \times (22.4 \, \text{L})}{(1 \, \text{mol}) \times (273 \, \text{K})} \]

4. **Calculate \( R \)**:
Performing the calculation:
\[ R = \frac{22.4}{273} \approx 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \]

5. **Check the Units**:
The units of \( R \) can be broken down as follows:
- Pressure in atmospheres (atm)
- Volume in liters (L)
- Temperature in Kelvin (K)
- Number of moles (mol)

Thus, the units of \( R \) are:
\[ R \, \text{units} = \frac{\text{L} \cdot \text{atm}}{\text{K} \cdot \text{mol}} \]

6. **Final Answer**:
The correct value of the gas constant \( R \) is approximately:
\[ R \approx 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \]