The van der Waals equation for a real gas is given by $\left(P+\frac{a}{V^2}\right)(V-b)=R T$. What ...

The van der Waals equation for a real gas is:$ \left(P + \frac{a}{V^2}\right)(V-b) = RT $To determine the dimension of $\left(\frac{a}{b}\right)$, we start with the principle of homogeneity. This principle asserts that the dimensions of each term in a dimensional equation must be consistent on both sides of the equation. For terms to be added, their dimensions must match.First, consider the dimensions of the given variables:Pressure, $ P $, has dimensions $[P] = M^1 L^{-1} T^{-2}$.Volume, $ V $, has dimensions $[V] = M^0 L^3 T^0$.From the equation, $\left(P + \frac{a}{V^2}\right)$, we deduce that:$ \left[\frac{a}{V^2}\right] = [P] $Thus, the dimension of $ a $ is:$ [a] = [P V^2] $Since $ V $ has dimensions $[V] = L^3$:$ [P V^2] = \left[M^1 L^{-1} T^{-2}\right] \times \left[L^3\right]^2 = M^1 L^5 T^{-2} $Next, determine the dimension of $ b $:$ [b] = [V] = L^3 $Finally, compute the dimension of $\left(\frac{a}{b}\right)$:$ \left[\frac{a}{b}\right] = \left[\frac{P V^2}{V}\right] = [P V] $Given:$ [P V] = [M^1 L^{-1} T^{-2}] \times [L^3] = M^1 L^2 T^{-2} $Thus, the dimension of $\left(\frac{a}{b}\right)$ is $M L^2 T^{-2}$.

States Of Matter - IAT-IISER Chemistry PYQs

Q: Why is it harder to compress liquids and solids relative to gases?...

In solids and liquids, the molecules are much closer together compared to gases. This proximity leaves little available space between the molecules, making it challenging to further compress them. In contrast, gases have molecules that are far apart and move freely, allowing for easier compression due to the significant empty space present between them. As a result, compressing solids and liquids requires substantially more force than compressing gases.Other options are incorrect for the following reasons:Electron-nuclear attraction, mentioned in options (b) and (c), is a fundamental force found in all states of matter and does not specifically impact compression.While solids and liquids do have definite volumes (option a), this characteristic is not the primary reason for the difficulty in compression. The closeness of the molecules is the key factor.

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PYQ 2022

easy

chemistry ID: iat-iise

The van der Waals equation for a real gas is given by . What is the dimension of ?

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PYQ 2023

easy

chemistry ID: iat-iise

Why is it harder to compress liquids and solids relative to gases?

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Solids and liquids have definite volume.

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Due to the presence of electron-nuclear attraction in solids and liquids.

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Due to the absence of electron-nuclear attraction in solids and liquids

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Molecules are closer to each other in solids and liquids.

03

PYQ 2025

easy

chemistry ID: iat-iise

The work done when one mole of an ideal gas expands at constant temperature from volume to (in two equal steps of volume in a linear fashion) is . How much more work would be done by the gas if it expands in three equal steps?[is the universal gas constant]

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States Of Matter

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Questions
3 MCQs

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Official Solution

States Of Matter

High-Yield Trend

Questions 3 MCQs

Official Solution

Official Solution

Official Solution

Questions
3 MCQs