Table 10.3 shows that the van der Waals b parameter has units of L / mol. This implies that we c

step 1 Here in this problem I can write the value of volume of xe is equal to 4 by 3 pi r cube. So it c

Table 10.3 shows that the van der Waals b parameter has...

Table 10.3 shows that the van der Waals $b$ parameter has units of $\mathrm{L} / \mathrm{mol}$. This implies that we can calculate the size of atoms or molecules from $b$. Using the value of $b$ for Xe, calculate the radius of a Xe atom and compare it to the value found in Figure 7.6, $1.30 \AA$ A. Recall that the volume of a sphere is $(4 / 3) \pi r^{3}$.

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Key Concepts

van der Waals Equation

The van der Waals equation is an adjusted form of the ideal gas law that accounts for intermolecular interactions and the finite size of gas molecules. It introduces correction factors to address the effects of attractive forces between particles and the volume occupied by molecules, providing a more accurate description of real gases under various conditions.

van der Waals b Parameter and Molecular Size

The b parameter in the van der Waals equation represents the excluded volume per mole, which is the effective volume occupied by the gas particles themselves. This parameter allows us to estimate the size of atoms or molecules by correlating the excluded volume with the physical dimensions of the particles, serving as a bridge between macroscopic measurements and microscopic particle properties.

Volume of a Sphere and Atomic Radius Calculation

The calculation of an atomic or molecular radius from the excluded volume is based on assuming the particles are spherical. The formula for the volume of a sphere, V = (4/3)?r³, is used to relate the excluded volume to the radius of a particle. By setting the spherical volume equal to the volume per particle derived from the b parameter, one can solve for the radius and compare it with experimentally determined or literature values.

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