@octopus well if the the water is the solvent, there is no solute, and it is 0 M/kg if water is the solute, there is no solvent and the molality is undefined. you can take the reciprocal of the molar mass to get something with the same units a molality, but there's no solution, is there?
@confusedcharlot it might not be a solution in a strict definitional sense of "solution = solute + solvent, where solute not= solvent not= 0" but it still works if you think of water as being both the solute and the solvent, or at least of being both the solute and total solution (remember molarity is mol solute per L of solution, not per L of solvent)
chemical reaction speeds & equilibria depend a lot on a "molecules per unit volume" density/concentration measure, or molarity, so the "molarity of water" is a meaningful quantity when calculating equilibria where water is a reactant
eg Kw (dissociation constant of water) = [H+] * [OH-] / [H2O], where [X] means "mols of X per liter of solution"
in pure or approximately pure water (from the perspective of water; a liter of water with 0.1 mol HCl is pH 1 but still almost all water!), this works out to [H+] * [OH-] = 10^-14 (ie pH + pOH = 14)
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@confusedcharlot it might not be a solution in a strict definitional sense of "solution = solute + solvent, where solute not= solvent not= 0" but it still works if you think of water as being both the solute and the solvent, or at least of being both the solute and total solution (remember molarity is mol solute per L of solution, not per L of solvent)
chemical reaction speeds & equilibria depend a lot on a "molecules per unit volume" density/concentration measure, or molarity, so the "molarity of water" is a meaningful quantity when calculating equilibria where water is a reactant
eg Kw (dissociation constant of water) = [H+] * [OH-] / [H2O], where [X] means "mols of X per liter of solution"
in pure or approximately pure water (from the perspective of water; a liter of water with 0.1 mol HCl is pH 1 but still almost all water!), this works out to
[H+] * [OH-] = 10^-14
(ie pH + pOH = 14)