Question

Calculate the volumetric size of a water molecule in water vapor at normal conditions, assuming 1 mole of the vapor occupies 22.4 l, as if the vapor were an ideal gas. Give answer in angstroms, two significant digits. Do not write down units in your answer.Calculate the volumetric size of a water molecule in water vapor at normal conditions, assuming 1 mole of the vapor occupies 22.4 l, as if the vapor were an ideal gas. Give answer in angstroms, two significant digits. Do not write down units in your answer.

Answer 1

Let volumetric size of a water molecule = v

Since, 1 mole of water consists of
`6.023* 10^(23)` molecules of water.

Thus, total volume of 1 mole of water =
`volumetric size * 6.023* 10^(23)`

Substitute the value of total volume of 1 mole of water i.e. 22.4 L in above formula.

`22.4 L = v* 6.023* 10^(23)`

`v= (22.4 L)/(6.023* 10^(23))`

Convert the unit litre to angstrom

`v=(22.4 L)/(6.023* 10^(23))* (1dm^(3))/(1L)* ((10^(9))^(3)(A^(o))^(3))/(1 dm^(3))`

=
`3.7* 10^(-23)* 10^(27) (A^(o))^(3)`

=
`3.7 * 10^(4)(A^(o))^(3)`

Therefore, the volumetric size of the water molecule is
`3.7 * 10^(4)(A^(o))^(3)`