There are two adjustable parameters,
𝑎
and
𝑏
that appear in the Van der Waals gas equation of state. Based on what you understand their roles to be, how would they compare between
C
F
4
and
C
F
2
C
l
2
? (The carbon atom is central in each compound.)

Question

There are two adjustable parameters, 
𝑎
 and 
𝑏
 that appear in the Van der Waals gas equation of state.  Based on what you understand their roles to be, how would they compare between 
C
F
4
 and 
C
F
2
C
l
2
?  (The carbon atom is central in each compound.)

BlackTom AI · Accepted Answer

To approach this, recall what the Van der Waals constants mean and how molecular size and polarizability influence them.
Option 1: 'Both a and b would be smaller for CF4Cl2.' This would imply that the larger molecule has weaker intermolecular attractions and a smaller excluded volume, which contradicts the general trend that bigger, more polarizable molecules exhibit stronger dispersion forces and occupy more space. So this is unlikely to be correct.
Option 2: 'Probably a would be smaller for CF4Cl2 but b would be larger.' Here, the statement splits the effects: it claims weaker attractions but a larger molecular volume. While b (excluded volume) tends to increase with molecular size, the assertion that a decreases with a larger, more polarizable molecule contradicts the well-established relationship that heavier, more polarizable species have stronger London dispersion (attractive) interactions, making this option questionable.
Option 3: 'None of the others.' If Option 4 is true, then this option would be incorrect. Since there is a plausible reason for both parameters to increase with a larger molecule, this option would not hold.
Option 4: 'Both a and b would be larger for CF4Cl2.' This aligns with the physical interpretation: a scales with attractive dispersion forces, which grow with molecular size, polarizability, and contact area; a increases as molecules become larger and more polarizable, reflecting stronger van der Waals attractions. Meanwhile, b represents the excluded volume (the finite size of the molecule); larger molecules simply take up more space, so b increases as well. Therefore, for CF4Cl2 compared to CF2Cl2, where CF4Cl2 is a larger, more bulky species, both constants are expected to be larger, consistent with the idea that bigger, more polarizable molecules experience stronger dispersion and occupy more volume.
Option 5: 'Probably a would be larger for CF4Cl2 but b would be smaller.' This proposes opposite trends for the two constants, which is inconsistent with the general correlation between molecular size and both parameters: larger molecules tend to have both stronger dispersion attractions (larger a) and larger excluded volumes (larger b). Thus this choice is not well supported by the underlying chemistry.
In summary, the only option that coherently reflects how a and b should scale with increasing molecular size and polarizability of CF4Cl2 relative to CF2Cl2 is that both parameters increase, making Option 4 the correct interpretation based on the physical roles of a and b.

There are two adjustable parameters, 𝑎 and 𝑏 that appear in the Van der Waals gas equation of state. Based on what you understand their roles to be, how would they compare between C F 4 and C F 2 C l 2 ? (The carbon atom is central in each compound.)

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