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

step 1 Given Wendell's constant B for Zenon is 0 .051 and 4 mole. So the volume of 1 mole of Xeatem can

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 $\mathrm{Xe},$ calculate the radius of a Xe atom and compare it to the value found in Figure 7.7 , that is, 1.40$\hat{\mathrm{A}}$ . Recall that the volume of a sphere is $(4 / 3) \pi r^{3}$ .

Key Concepts

Spherical Volume Formula

The volume of a sphere is given by the formula (4/3)?r³, where r is the radius. This mathematical relationship allows us to solve for the radius if the volume of an atom or molecule is known, facilitating the comparison between calculated and observed sizes.

Atomic/Molecular Volume Calculation

By dividing the b parameter by Avogadro's number, we obtain an estimate of the volume occupied by a single molecule or atom. This calculation bridges macroscopic measurements (like molar volume) with microscopic properties (like particle size).

Unit Conversion

Converting units accurately is essential when relating macroscopic parameters to microscopic dimensions. This involves converting the molar volume from liters to cubic meters or cubic centimeters and ensuring consistency when calculating the radius in units such as angstroms.

Van der Waals Equation

The van der Waals equation is a modified version of the ideal gas law that accounts for the finite size of particles and the intermolecular forces between them. It introduces two parameters, a and b, which correct for the attractive forces and the volume excluded by the particles, respectively.

Excluded Volume (b Parameter)

The parameter b represents the effective volume excluded by one mole of particles due to their finite size. Its units of L/mol or cm³/mol suggest that it can be directly related to the physical volume occupied by the particles, allowing us to estimate their size.

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