To determine the value of gas constant R, which is given as 8.314 X, we need to identify what X represents in terms of units.
### Step-by-Step Solution:
1. **Understand the Ideal Gas Law**:
The ideal gas equation is given by:
\[
PV = nRT
\]
where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = universal gas constant
- \( T \) = temperature
2. **Rearranging the Ideal Gas Law**:
We can rearrange this equation to solve for R:
\[
R = \frac{PV}{nT}
\]
3. **Substituting Standard Conditions**:
At standard conditions, we can use:
- \( P = 1 \, \text{atm} \)
- \( V = 22.4 \, \text{L} \)
- \( n = 1 \, \text{mol} \)
- \( T = 273 \, \text{K} \)
Substituting these values into the equation for R:
\[
R = \frac{(1 \, \text{atm})(22.4 \, \text{L})}{(1 \, \text{mol})(273 \, \text{K})}
\]
4. **Calculating R**:
Performing the calculation:
\[
R = \frac{22.4}{273} \approx 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1}
\]
However, we need the value in joules.
5. **Converting to Joules**:
We know that:
\[
1 \, \text{atm} \cdot \text{L} = 101.325 \, \text{J}
\]
Therefore:
\[
R = 0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1} \times 101.325 \, \text{J/L atm} \approx 8.314 \, \text{J K}^{-1} \text{mol}^{-1}
\]
6. **Identifying X**:
From our calculation, we find that:
\[
R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1}
\]
Thus, \( X \) represents the unit "J K\(^{-1}\) mol\(^{-1}\)".
### Conclusion:
The value of gas constant R is 8.314 X, where X represents "J K\(^{-1}\) mol\(^{-1}\)".
