Question #e695c
1 Answer
Explanation:
I'm not entirely sure why the problem provides the density of the water, since that is not needed to find the boiling point and the freezing point of the solution.
I can only assume that your solution contains
So, the first thing would be to determine the mass of water
#465color(red)(cancel(color(black)("mL"))) * "1.00 g"/(1color(red)(cancel(color(black)("mL")))) = "465 g"#
The equation for freezing-point depression looks like this
#DeltaT_f = i * K_f * b" "# , where
In your case, glucose is a non-electrolyte, which means that it does not dissociate to form ions in solution. As a result, you have
In order to calculate the molality of the solution, you need to know two things
Use glucose's molar mass to determine how many moles you have in that sample
#57.8color(red)(cancel(color(black)("g"))) * " 1 mole glucose"/(180.156color(red)(cancel(color(black)("mL")))) = "0.3208 moles glucose"#
The molality of the solution will thus be - do not forget to convert the mass of the water from grams to kilograms
#color(blue)(b = n_"solute"/m_"solvent")#
#b = "0.3028 moles"/(465 * 10^(-3)"kg") = "0.6899 moles/kg" = "0.6899 molal"#
You can find the values of water's cryoscopic and ebullioscopic constants here
http://www.vaxasoftware.com/doc_eduen/qui/tcriosebu.pdf
So, plug in your values and determine the freezing-point depression
#DeltaT_"f" = 1 * 1.86^@"C" color(red)(cancel(color(black)("kg")))/color(red)(cancel(color(black)("mol"))) * 0.6899color(red)(cancel(color(black)("moles")))/color(red)(cancel(color(black)("kg"))) = 1.283^@"C"#
The freezing-point depression is defined as
#DeltaT_"f" = T_"f"^@ - T_"f"" "# , where
This means that the freezing point of the solution will be
#T_"f" = T_"f"^@ - DeltaT_"f"#
#T_"f" = 0^@"C" - 1.283^@"C" = color(green)(-1.28^@"C")#
I'll leave the calculation of the solution's boiling point to you as practice. The equation for boiling-point elevation is
#DeltaT_b = i * K_b * b" "# , where
Plug in your values and solve for
#DeltaT_"b" = T_"b" - T_"b"^@#