Answer 1:
One mole of a substance is defined as having exactly 6.02214076*10^{23} (*see note below) constitutive particles of that substance. Those particles can be atoms, ions, molecules, etc.
To determine the number of moles for some given number of molecules, one can use a simple but powerful technique known as dimensional analysis.
Dimensional analysis is essentially a method of converting units, involving multiplying given units by conversion factors and "canceling" like units that appear in both the numerator and denominator to reach the desired measure. Since this method works for any units, it is applicable for a wide range of problems. [Assuming the starting and ending units are of a consistent "type". For example, distances can only be measured in length units; trying to convert to 3 miles to pounds is nonsensical and impossible.]
For the present case, the given units are molecules of water and the desired units aremoles of water. The conversion factor is the definition of the mole, i.e., 1 mol H_{2}O / 6.022...*10^{23} molecules H_{2}O. Thus,
6.022*10^{22} molecules H_{2}O * (1 mol H_{2}O / 6.022...*10^{23} molecules H_{2}O) ≈ 0.1 mol H_{2}O.
*The mole used to be defined as the amount of a substance containing as many constitutive particles as the number of atoms of carbon12 in 12 grams of carbon 12. The definition was changed in 2018/2019 to be
1 mole = 6.02214076*10^{23} (exact) particles. The US standards institute (NIST) has a fascinating (lengthy) article on this redefinition. Because the change is so recent, many articles/sites/textbooks will likely have the earlier definition still.
The responses to this question on ScienceLine and this chemistry page contain more information on using the mole/Avogadro's Number.
