Value of gas constant R is

Options

A. 0.082 litre atm
B. `1.987 "cal" mol^(-1) K^(-1)`
C. 8.3 J mol^(-1) K^(-1)`
D. 83 erg mol^(-1) K^(-1)`

Answer

To determine the value 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:
- \( P \) = pressure of the gas
- \( V \) = volume of the gas
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

2. **Rearranging the Ideal Gas Law**: We can rearrange the ideal gas law to solve for \( R \):
\[ R = \frac{PV}{nT} \]

3. **Units of \( R \)**: The gas constant \( R \) can be expressed in various units. Some common values are:
- \( 8.314 \, \text{J/(mol·K)} \) (Joules per mole per Kelvin)
- \( 0.0821 \, \text{L·atm/(mol·K)} \) (liters atmosphere per mole per Kelvin)
- \( 1.987 \, \text{cal/(mol·K)} \) (calories per mole per Kelvin)

4. **Identifying the Correct Option**: From the options provided:
- \( 0.082 \, \text{L·atm/(mol·K)} \)
- \( 1.987 \, \text{cal/(mol·K)} \)
- \( 8.314 \, \text{J/(mol·K)} \)
- \( 83 \, \text{ARG/(mol·K)} \)

The correct value of the gas constant \( R \) is:
\[ R = 8.314 \, \text{J/(mol·K)} \]

5. **Conclusion**: Therefore, the value of the gas constant \( R \) is \( 8.314 \, \text{J/(mol·K)} \).

### Final Answer:
The value of gas constant \( R \) is \( 8.314 \, \text{J/(mol·K)} \).

---