JEE Advance - Chemistry (2009 - Paper 1 Offline - No. 3)

The term that corrects for the attractive forces present in a real gas in the van der Waals equation is
$$nb$$
$${{a{n^2}} \over {{V^2}}}$$
$$ - {{a{n^2}} \over {{V^2}}}$$
$$ - nb$$

Explanation

The van der Waals equation is a modified version of the ideal gas law which accounts for the non-ideal behavior of real gases. This adjustment is done through two correction terms, each addressing a specific factor where real gases deviate from ideal behavior:

  • Intermolecular attraction
  • Volume occupied by the gas particles themselves

The van der Waals equation is given by:

$$\left(P + \frac{{a n^2}}{{V^2}}\right) \left(V - nb\right) = nRT$$

Let's break down the components:

  1. $$\left(P + \frac{{a n^2}}{{V^2}}\right)$$: This term adds a correction to the pressure (P) of the gas. The parameter $$a$$ provides a correction for the intermolecular forces. As these forces are attractive, they effectively reduce the pressure exerted by the gas. Thus, $$\frac{{a n^2}}{{V^2}}$$ is added to the actual pressure to account for this decrease due to attraction.
  2. $$\left(V - nb\right)$$: The corrected volume term where $$b$$ accounts for the volume occupied by the gas particles themselves, which is otherwise not considered in the ideal gas law. The subtraction by $$nb$$ (where $$n$$ is the number of moles of the gas and $$b$$ is a constant related to the volume occupied by one mole of gas particles) corrects for the volume unavailable to the gas particles for movement.

From the options provided:

  • Option A ($$nb$$) and Option D ($$-nb$$) relate to the volume correction for the space that the gas molecules occupy.
  • Option B ($$\frac{{a n^2}}{{V^2}}$$) and Option C ($$- \frac{{a n^2}}{{V^2}}$$) relate to the intermolecular forces.

The enhancement factor $$\frac{{a n^2}}{{V^2}}$$ is added to the pressure to counteract the lowering effect of the attractions on the measured pressure, thus the term correcting for the attractive forces and increasing the effective pressure would be positively stated, not negatively. Therefore:

Option B ($$\frac{{a n^2}}{{V^2}}$$) is the correct answer, as it accounts for the attractive forces in the modification of the ideal gas law in the van der Waals equation.

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