Question

To derive the ideal-gas equation, we assume that the volume of the gas atoms/molecules can be neglected.

Given the atomic radius of krypton, 1.1 Å, and knowing that a sphere has a volume of 4πr3/3, calculate the fraction of space that Kr atoms occupy in a sample of krypton at STP. Express your answer using two significant figures.

Answer 1

Sol :-

Given the atomic radius of krypton (r) =  1.1 Å = 1.1 x 10^-10 m

Because, 1 Å = 10^-10 m

As,

Sphere has a Volume (V) = 4 r³ / 3

So, Substitute the value of r =1.1 x 10^-10 m and = 3.14   in this equation

Volume (V) = 4 x 3.14 x (1.1 x 10^-10 m )³ / 3

= 5.572 x 10^-30 m³

= 5.572 x 10^-27 L

Because, 1 m³ = 10³ L

Now,

1 mole of krypton = 6.022 x 10²³ /mole

So,

1 mole of krypton contains volume = 5.572 x 10^-27 L x 6.022 x 10²³ /mole

= 3.355 x 10^-3 L

As,

At STP, 1 mole of gas contains = 22.4 L of volume

So,

Fraction of space that Kr atoms occupy in a sample of krypton at STP = 3.355 x 10^-3 L / 22.4 L

= 0.00015

= 1.5 x 10^-4(upto two significant figures)

Hence, Fraction of space that Kr atoms occupy in a sample of krypton at STP = 1.5 x 10-4