Assertion : Gas constant R = lite atmosphere `"deg"^(-1) mol^(-1)`
Reason : Total pressure of a mixture of non-reacting gases = sum of the partial pressures of all the component gases of the mixture

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not a correct explanation of A
C. A is true but R is false
D. A is false but R is true

Answer

To analyze the given assertion and reason, we will break down the concepts step by step.

### Step 1: Understanding the Assertion
The assertion states that the gas constant \( R \) is equal to \( \text{liter} \cdot \text{atmosphere} \cdot \text{degree}^{-1} \cdot \text{mol}^{-1} \).

- The gas constant \( R \) is used in the ideal gas equation \( PV = nRT \).
- Rearranging this gives \( R = \frac{PV}{nT} \).
- Here, \( P \) (pressure) is measured in atmospheres, \( V \) (volume) in liters, \( n \) (number of moles) is in moles, and \( T \) (temperature) is in degrees Kelvin (or Celsius, but typically Kelvin is used in calculations).

### Step 2: Confirming the Unit of R
To confirm the unit of \( R \):
- Pressure \( P \) in atmospheres (atm)
- Volume \( V \) in liters (L)
- Temperature \( T \) in Kelvin (K)
- Number of moles \( n \) in moles (mol)

Thus, the unit of \( R \) can be expressed as:
\[ R = \frac{(L \cdot atm)}{(mol \cdot K)} \]
This confirms that the assertion is correct.

### Step 3: Understanding the Reason
The reason states that the total pressure of a mixture of non-reacting gases is equal to the sum of the partial pressures of all the component gases of the mixture.

- This statement is a reflection of Dalton's Law of Partial Pressures, which states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of each gas.
- For example, if we have gases A and B, the total pressure \( P_{total} = P_A + P_B \).

### Step 4: Evaluating the Relationship Between Assertion and Reason
Both the assertion and the reason are true statements in the context of gas laws:
- The assertion correctly describes the unit of the gas constant \( R \).
- The reason correctly describes Dalton's Law of Partial Pressures.

However, the reason does not explain why the gas constant \( R \) has the unit given in the assertion. Therefore, while both statements are true, the reason is not the correct explanation for the assertion.

### Conclusion
- **Assertion**: True
- **Reason**: True
- **Conclusion**: The reason is not the correct explanation for the assertion.

### Final Answer
Both the assertion and the reason are true, but the reason is not the correct explanation of the assertion.

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