Question

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The atomic radius of K is 216 pm, and that of K+ is 133 pm. Calculate the percent decrease in volume that occurs when K(g) is converted to K+(g).

[The volume of a sphere is (4/3)πr3, there r is the radius of the sphere.]



ANSWER IS 76.66%

Answer 1

To calculate the percent decrease in volume when a potassium atom becomes a potassium ion, use the volume of a sphere formula and then find the percent change. The respective volumes are calculated using the given radii, and the decrease is approximately 76.66%.

Step-by-step explanation:

The student is asking how to calculate the percent decrease in volume when a potassium atom (K) becomes a potassium ion (K+). To find the percent decrease in volume, you must first calculate the volumes of both the atom and the ion using the formula for the volume of a sphere, V = (4/3)πr3, where r is the radius.

The volume of the K atom: VK = (4/3)π(216 pm)3
The volume of the K+ ion: VK+ = (4/3)π(133 pm)3

To find the percent decrease, subtract the final volume from the initial volume, divide by the initial volume, and multiply by 100.

Percent decrease in volume (%) = ((VK - VK+) / VK) × 100

Substituting the values and calculating gives a percent decrease of approximately 76.66%.