Question #6b36c
1 Answer
The molar mass of the solute will come out to be smaller than it actually is.
Explanation:
So, you need to determine what impact the erroneous measurement of the freezing point of the pure cyclohexane will have on the molar mass of the solute.
The equation for freezing-point depression looks like this
#DeltaT_f = i * K_f * b " "# , where
Now, the freezing point depression is defined as
#DeltaT_f = T_"f"^0 - T_"f sol"#
Let's assume that you use the correct freezing point of the pure cyclohexane and calculate the molality of the solution to be
#b = (T_"f"^0 - T_"f sol")/(i * K_f)#
The molality of the solution is defined as the moles of solute divided by the mass of the solvent - expressed in kilograms. This means that you have
#n_"solute"/m_"cyclohexane" = (T_"f"^0 - T_"f sol")/(i * K_f)#
#n_"solute 1" = (T_"f"^0 - T_"f sol")/(i * K_f) * m_"cyclohexane"#
Now look what happens when you measure the freezing point of the pure cyclohexane to be
#T_"f meas"^0 = T_f^0 + 2^@"C"#
The number of moles of solute will now be
#n_"solute 2" = (T_"f"^0 + 2 - T_"f sol")/(i * K_f) * m_"cyclohexane"#
Since the nominator of the fraction is now bigger than it was when you calculated using the correct value of
#(T_"f"^0 + 2 - T_"f sol")/(i * K_f) > (T_"f"^0 - T_"f sol")/(i * K_f)#
#n_"solute 2" > n_"solute 1"#
It now appears that you have more moles of solute in the solution. Since molar mass is defined as mass per moles, you will get
#M_(M 1) = m_"solute"/n_"solute 1" " "# and#" "M_(M 2) = m_"solute"/n_"solute 2"#
Since >
#M_(M 2) < M_(M 1)#
The solute will come out as having a smaller molar mass.