Question

what is the volume of water at 1 ATM evaporated from 0.1 ml of water?

Answer 1

You mean volume of water vapour ?

Considering that water vapours will behave like ideal gas, we can apply ideal gas law to them.

PV = nRT
P = 1 atm =1.013 * 10^5 N/m2
R = 8.314 J/K/mol
To find n, number of moles , we notice n=mass of gas(m) / molar mass of gas(M)
the volume of water is 0.1ml
density of water is 1g/ml
so m = 0.1g
M = 18 g
Hence we can get the no of moles
Your question does not provide value of temperature at which it evaporates. It may be room temperature (298K)

V is the volume of water vapour which we can get from the above eqn.