The Question is from neet-chemistry chemical-thermodynamics , and it was created by the author P SRAVAN KUMAR

Question

In the van der Waals&rsquo; equation, the constant $'a'$ and $'b'$ with temperature shows which trend:

P SRAVAN KUMAR · Accepted Answer

## CORE INFORMATION
✓ **Answer**: D
## CONCEPT FRAMEWORK
	**Primary Concept**: Van der Waals Equation
	**Related Topics**: Real Gases, Ideal Gas Law, Intermolecular Forces
	**Prerequisites**: Understanding of ideal gas limitations and the van der Waals equation.
## SOLUTION PATHWAY
**Given Information**:
	We are analyzing the temperature dependence of 'a' and 'b' in the van der Waals equation.
**Method & Steps**:
	1. **Van der Waals Equation**: $(P + \frac{an^2}{V^2})(V - nb) = nRT$
	Reasoning: This equation corrects the ideal gas law for real gas behavior.
	2. **'a' Constant**: Accounts for intermolecular attractions.
	Working: 'a' is empirically determined and depends on the specific gas.  It generally decreases slightly with increasing temperature because at higher temperatures, the kinetic energy of molecules overcomes attractive forces more effectively.
	3. **'b' Constant**: Accounts for the finite volume occupied by gas molecules.
	Working: 'b' is also empirically determined. It is related to the size of the gas molecules and is generally considered independent of temperature because molecular size doesn't significantly change with temperature.
	Key Point: While 'b' is often treated as constant, high-precision measurements show it can have a slight temperature dependence. However, this variation is often negligible compared to the change in 'a'.
	4. **Overall Trend**: Both 'a' and 'b' can vary with temperature, but the variation in 'a' is more pronounced.
	Result: Both 'a' and 'b' can vary, but 'a' shows a more noticeable decrease with increasing temperature.
	Verification: This aligns with experimental observations and the theoretical understanding of intermolecular forces and molecular size.
## OPTION ANALYSIS
[A] :x: Incorrect. 'a' generally decreases with increasing temperature.
[B] :x: Incorrect. Both 'a' and 'b' can vary, though 'b'’s variation is usually less significant.
[C] :x: Incorrect. 'b' can also vary with temperature, though the change is often minor.
[D] ✓: Correct. Both constants can change with temperature.
## LEARNING AIDS
	**Common Mistakes**:
		1. Assuming 'b' is strictly constant: While the temperature dependence of 'b' is small, it exists.
		2. Neglecting the temperature dependence of 'a': The decrease in 'a' with increasing temperature is a key aspect of real gas behavior.
	**Quick Tips**:
		1. Remember 'a' for attraction and 'b' for size/volume.
		2.  Visualize how higher temperatures reduce the influence of attractive forces, leading to a decrease in 'a'.

P SRAVAN KUMAR · Answer

Both remains same

P SRAVAN KUMAR · Answer

$'a'$ remains same, $b$ varies

P SRAVAN KUMAR · Answer

$'a'$ varies, $b$ remains same

P SRAVAN KUMAR · Answer

The correct Option is "Both varies"

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