Question

A solution containing \[6.35g\] of nonelectrolyte dissolved in \[500g\] of water freezes at \[ - {0.465^o}C\]. Determine the molecular weight of the solute. \[[{K_f}\] for water \[{1.86^o}C/mol]\]
A.\[25.4g/mol\]
B.\[50.8g/mol\]
C.\[76.2g/mol\]
D.\[90.2g/mol\]

Answer 1

Hint: We need to know that the molecular weight is equal to the sum of atomic mass of every atom which is present in a compound or the molecule. And the molecular weight is another term of molar mass which is used for the molecular compounds, and it will not depend on the size of the sample. The molecular weight is expressed in terms of kg/mol. The nonelectrolyte compounds are not completely ionized in all the solutions. And the nonelectrolyte solutions will not conduct the electricity.

Complete answer:
As we know that the molecular weight of the solute is not equal to\[25.4g/mol\]. Hence, option (A) is incorrect.
The depression in the freezing point is equal to change in molal freezing point. That is,
\[\Delta {T_f} = \Delta {{\rm K}_f} = 0 - \left( { - 0.465} \right) = 0.465\]
And \[\Delta {T_f} = {{\rm K}_f}\]
Hence, \[0.465 = 1.86m\]and m is equal to \[0.25m\]
Let M be the molecular weight of the solute. The number of moles of the solute can be found by dividing the given weight with the molecular weight of the solute. Hence,
Number of moles of solute\[ = \dfrac{{6.35}}{M}\]
The molality of the solution is equal to the number of moles of solute present in the \[1000g\] of the water. Therefore,
Molality\[ = \dfrac{{6.35 \times 1000}}{{M \times 500}} = 0.25\]
Hence, by rearranging the equation, we will get the value of molecular weight of the solute.
Molecular weight of the solute, \[M = 50.8g/mol\]
Hence, option B is correct.
The molecular weight of the solute is not equal to \[76.2g/mol\]. Hence, option (C) is incorrect.
The molecular weight of the solute is not equal to; \[90.2g/mol\]. Hence, option (D) is incorrect.

Hence, option B is correct.

Note:
We need to know that the nonelectrolyte solutions are bonded together by using the covalent bond and not by ionic bond. And the examples of the nonelectrolyte solutions are nonpolar compounds like, hydrogen, methane, noble gases, gaseous hydrocarbons etc. Nonpolar gases and mineral solid solution like pyroxene, feldspar are also the examples of nonelectrolyte compounds.