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Assertion : At law pressure, van der Waa...

Assertion : At law pressure, van der Waals equation may be expressed as
`pV=RT-(a)/(V)`
Reason : At low pressure, b can be neglected in comparision to V.

A

Assertion and reason both are correct statements and reason is correct explanation for assertion.

B

Assertion and reason both are correct statements but reason is not correct explanation for assertion.

C

Assertion is correct statement but reason is wrong statement.

D

Assertion is wrong statement but reason is correct statement.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion and reason provided regarding the van der Waals equation at low pressure. ### Step-by-Step Solution: 1. **Understand the Van der Waals Equation**: The van der Waals equation for one mole of a gas is given by: \[ \left( P + \frac{a}{V^2} \right)(V - b) = RT \] where \( P \) is the pressure, \( V \) is the volume, \( T \) is the temperature, \( R \) is the universal gas constant, \( a \) accounts for the attraction between particles, and \( b \) accounts for the volume occupied by the gas particles. 2. **Consider Low Pressure**: At low pressure, the volume \( V \) of the gas is large. This means that the term \( b \) (which represents the volume occupied by gas molecules) becomes negligible compared to \( V \). Thus, we can simplify the equation. 3. **Neglect the \( b \) Term**: Under low pressure conditions, we can approximate the equation as: \[ P + \frac{a}{V^2} \approx \frac{RT}{V} \] Therefore, we can rearrange it to: \[ P \approx \frac{RT}{V} - \frac{a}{V^2} \] 4. **Rearranging the Equation**: We can multiply both sides by \( V \) to eliminate the fraction: \[ PV \approx RT - \frac{a}{V} \] This leads us to the assertion: \[ PV = RT - \frac{a}{V} \] 5. **Conclusion on Assertion and Reason**: - **Assertion**: The assertion states that at low pressure, the van der Waals equation can be expressed as \( PV = RT - \frac{a}{V} \). This is correct based on our derivation. - **Reason**: The reason states that at low pressure, \( b \) can be neglected in comparison to \( V \). This is also correct since \( V \) is large, making \( b \) negligible. Thus, both the assertion and reason are correct. ### Final Answer: Both the assertion and reason are correct.
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