Question

The molecular weight of glucose is $ 180 $ . A solution of glucose which contains $ 18 $ grams per litre is
A. $ 2 $ molal
B. $ 1 $ molal
C. $ 0.1 $ molal
D. $ 18 $ molal

Answer 1

Hint :A measure of solute concentration in a solution which is equal to the number of moles of solute in per kg solvent is known as molality. It is also termed as molal concentration. The SI unit of molality is $ mol\,k{g^{ - 1}} $ but the concentration is often expressed as molal or with the symbol ‘m’.

Complete Step By Step Answer:
According to the question, the given data is as follows:
Molecular mass of glucose $ = 180\;gmo{l^{ - 1}} $
Mass of glucose in the solution $ = 18\;g $
As we know the number of moles of a molecule is the ratio of its mass considered and its molecular mass. Therefore, number of moles of glucose present in the solution is as follows:
 $ n = \dfrac{{{\text{mass of glucose in solution}}}}{{{\text{molecular mass of glucose}}}} $
Substituting values:
 $ n = \dfrac{{18}}{{180}} $
 $ n = 0.1 $
As the given volume of solvent i.e., water $ = 1\;L $
Density of solvent $ = 1\;kg{L^{ - 1}} $
Hence, the mass of solvent will be as follows:
Mass $ = $ density $ \times $ volume
 $ \Rightarrow $ mass $ = 1\;kg{L^{ - 1}} \times 1\;L $
 $ \Rightarrow $ mass $ = 1\;kg $
Therefore, mass of solvent $ = 1\;kg $
Now, the molality of the solution is equal to the ratio of the number of moles of solute and mass of solvent in kg. Hence, the molality of the given solution will be as follows:
 $ m = \dfrac{{{\text{number of moles of glucose}}}}{{{\text{mass of solvent}}}} $
Substituting values:
 $ m = \dfrac{{{\text{0}}{\text{.1}}}}{1} $
 $ \Rightarrow m = 0.1\;{\text{molal}} $
Thus, a solution of glucose which contains $ 18 $ grams per litre is $ 0.1 $ molal. So, the correct answer is option (C).

Note :
Make sure to not get confused with the terms molality and molarity as both the terms represent the concentration of solute in solution in different ways. Molality is the number of moles of solute in per kg solvent whereas the molarity is defined as the number of moles of solute in per litre solution.