Given the atomic radius of argon, 0.97 Å, and knowing that a sphere has a volume of 4πr3/3, calculate the fraction of space that Ar atoms occupy in a sample of argon at STP. Express your answer using two significant figures.

Question

Physics

Ashes

16 March, 17:31

Given the atomic radius of argon, 0.97 Å, and knowing that a sphere has a volume of 4πr3/3, calculate the fraction of space that Ar atoms occupy in a sample of argon at STP. Express your answer using two significant figures.

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Answers (1)

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Marilyn Potts · Answer 1

1.0x10^-4

Explanation:

First, in order to do this, we need to calculate the volume of 1 simple atom of Ar. Using the formula of the volume of a sphere we have the following

Converting A to cm:

0.97 * 1x10^-8 = 9.7x10^-9 cm

Now the volume:

V = 4/3π (9.7x10^-9) ³

V = 3.82x10^-24 cm³

We know that 1 cm³ is 1 mL, and 1 L is 1000 mL so:

V = 3.82x10^-24 mL / 1000 = 3.82x10^-27 L

Now, using avogadro's number, we should get the total volume of all atoms of Ar so:

3.82x10^-27 * 6.02x10^23 = 2.3x10^-3 L

Finally, at STP the volume of an ideal gas is 22.4 L so:

2.3x10^-3 / 22.4 = 1.03x10^-4

With two significant figure, it would be 1.0x10^-4