If the mole fraction of water in a HCl solution is 0.78 . calculate the molality of the solution? I don't understand how to relate mole fraction to molality.
2026-03-25 07:41:10.1774424470
relating mole fraction to molality
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The mole fraction is the ratio of moles of solute to moles of solvent. A mole fraction of $.78$ means that for every mole of HCl, there are $.78$ moles of water. Molality is the number of moles of solute per mass of solvant. Since HCl has a molar mass of 36.5 g/mol, we would use dimensional analysis to calculate the molality: $$\frac{0.78 \text{ molH$_2$O}}{1\text{ mol HCl}}\cdot\frac{1 \text{ mol HCl}}{36.5\text{ g HCl}}=.021 \frac{\text{mol H$_2$O}}{\text{g HCl}}.$$ Usually, molality is given in mol/kg, so this is $21$ mol/kg.