Question

What is the molality of pure water at $273$ K?

Answer 1

Hint : We know that the molarity and molality are concentration terms which mean that we can measure the concentration of a solution. Molarity of a solution is equal to the total number of moles of solute per litre of a solution.

Complete Step By Step Answer:
As we know that the molarity of the solution is defined as the number of moles of the solute which is present in one L volume of the solution. We can represent it by the symbol, M. The molarity of the solution is the ratio of the number of moles to the volume of the solution. The number of moles can be calculated by dividing the given mass to the molar mass of the compound.
Both molarity and molality are related to the concentration of the solution. Pure water shows abnormal behaviour at certain temperatures which can be related to concentration. The volume of the solution must be taken in liters only. If the concentration or density of the solute is given in kg or any other unit, it has to be converted into grams because these are the standard units taken for the calculation of Molarity. The concentration of the solution tells the strength of the solution. There are many factors that can be used for calculating the strength of the solution like molarity, molality, normality, mole fraction, ppm, etc. We know that pure water freezes at $273$ K. At $273$ K the molality of pure water is equivalent to the molarity. Let us calculate the molality of pure water at $273$ K here.
$Molarity=\dfrac{Moles}{Weight\text{ }of\text{ }pure\text{ }water}.$
Molar mass of pure water $=18.0153\text{ }g/mol$
Number of moles $=55.348$
Weight of the solvent $=0.99707\text{ }kg$
Molality $=\dfrac{55.348}{0.99707}=55.510\text{ }m$
Therefore, the molality of pure water at $273$ K is $55.510m.$

Note :
Remember that the molality of the solution is one of the major factors in calculating the concentration of the solution. There are two factors that are used for the calculation of the molality of the solution, i.e., the number of moles of the solute and the mass of the solvent in kg. When we divide the number of moles of the solute by the mass of the solvent in kg, we get the molality of the solution.