Determine the excluded volume per mole and the volume actually occupied by a mole for a gas consisting of molecules with radius 167 pm. [Note: To obtain the volume in liters, we must express the radius in decimeters (dm).] Enter your answers in scientific notation.

Explanation:

Volume of one mole of a gas = 22.4 litre.

No of molecules in one mole of gas = 6.02 x 10²³ .

Volume of one molecule = 4/3 π R³

= 4/3 x 3.14 x ( 167 x 10⁻¹² m )³

= 19.5 x 10⁶ x 10⁻³⁶ m³

=19.5 x 10⁻³⁰ m³

= 19.5 x 10⁻³⁰ x 10³ litre .

=  19.5 x 10⁻²⁷ litre .

So volume occupied by molecules in one mole of gas

= 19.5 x 10⁻²⁷ x 6.02 x 10²³  litre

117.4 x 10⁻⁴ litre

= .01174 litre.

Excluded volume

= ( 22.4 -  .01174  ) litre .

= 22.388 litre.

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