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Chapter 8: Problem 100

The atomic radius of \(\mathrm{K}\) is \(227 \mathrm{pm}\) and that of \(\mathrm{K}^{+}\) is \(133 \mathrm{pm} .\) Calculate the percent decrease in volume that occurs when \(\mathrm{K}(g)\) is converted to \(\mathrm{K}^{+}(g) .\) [The volume of a sphere is \(\left(\frac{4}{3}\right) \pi r^{3},\) where \(r\) is the radius of the sphere.]

Short Answer

Expert verified
The percent decrease in volume when \(\mathrm{K}(g)\) is converted to \(\mathrm{K}^{+}(g)\) is calculated using the formula for percent decrease and the volumes of the initial and final states. We calculate these volumes using the given atomic radii and the formula for the volume of a sphere.

Step by step solution

01

Calculate the Initial Volume

First, let's calculate the volume of the \(\mathrm{K}(g)\) atom using the formula for the volume of a sphere, which is \(\left(\frac{4}{3}\right) \pi r^{3}\). Here, the radius \(r\) is given as \(227 \mathrm{pm}\). So, the volume \(V_1\) of \(\mathrm{K}(g)\) is \(\left(\frac{4}{3}\right) \pi (227 ^{3})\).
02

Calculate the Final Volume

Next, we calculate the volume \(V_2\) of the \(\mathrm{K}^{+}(g)\) ion in a similar manner. Its radius is \(133 \mathrm{pm}\), so the volume is \(\left(\frac{4}{3}\right) \pi (133 ^{3})\).
03

Calculate the Percent Decrease

The percent decrease can be calculated using the formula \(\frac{(V_1- V_2)}{V_1} \times 100\), where \(V_1\) is the initial volume, \(V_2\) is the final volume.\nSubstitute \(V_1\) and \(V_2\) into the formula to obtain the percent decrease.

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Most popular questions from this chapter

Based on your knowledge of the chemistry of the alkali metals, predict some of the chemical properties of francium, the last member of the group.

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