Value of gas constant R is

Options

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

Answer

To find the value of the gas constant R, we can follow these steps:

### Step 1: Understand the Ideal Gas Equation
The Ideal Gas Law is expressed as:
\[ PV = nRT \]
where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = universal gas constant
- \( T \) = temperature

### Step 2: Identify the Standard Value of R
The standard value of the gas constant \( R \) is:
\[ R = 8.314 \, \text{J/(K·mol)} \]
This is the most commonly used value in calculations involving gases.

### Step 3: Check Different Units of R
The value of \( R \) can be expressed in different units:
1. In joules: \( R = 8.314 \, \text{J/(K·mol)} \)
2. In calories: To convert joules to calories, use the conversion \( 1 \, \text{cal} = 4.18 \, \text{J} \):
\[ R = \frac{8.314 \, \text{J/(K·mol)}}{4.18 \, \text{J/cal}} \approx 1.987 \, \text{cal/(K·mol)} \]
3. In liters and atmospheres: Another common value is:
\[ R = 0.0821 \, \text{L·atm/(K·mol)} \]

### Step 4: Evaluate the Options
If given multiple-choice options, evaluate each based on the magnitude and units:
- Check if the magnitude matches the standard value.
- Ensure the units are correct.

### Step 5: Identify the Correct Answer
From the calculations and evaluations, the correct value of the gas constant \( R \) in calories is approximately:
\[ R \approx 1.987 \, \text{cal/(K·mol)} \]
This matches with option B if it is provided in the question.

### Final Answer
The value of the gas constant \( R \) is approximately \( 8.314 \, \text{J/(K·mol)} \) or \( 1.987 \, \text{cal/(K·mol)} \).

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