The freezing point of an aqueous solution that contains a nonelectrolyte is #-4.0^@"C"#. What is the molal concentration of the solution? #Kf = 1.86^@"C/m"#
1 Answer
Explanation:
The first thing to do here is use the freezing point of the solution to calculate the freezing-point depression,
As you know, the freezing-point depression is a measure of how low the freezing point of a solution is compared with the freezing point of the pure solvent.
You're dealing with an aqueous solution, so right from the start you know that the solvent is water. Pure water freezes at
Your solution freezes at
#color(purple)(|bar(ul(color(white)(a/a)color(black)(T_"f sol" = T_"f pure solvent" - DeltaT_f)color(white)(a/a)|)))#
#-4.0^@"C" = - DeltaT_f implies DeltaT_f = 4.0^@"C"#
Now, the freezing-point depression is calculated sing the equation
#color(blue)(|bar(ul(color(white)(a/a)DeltaT_f = i * K_f * bcolor(white)(a/a)|)))#
Here
Your solute is a non-electrolyte, which means that its molecules do not dissociate in aqueous solution. This implies that the van't Hoff factor will be equal to
Rearrange the above equation to solve for
#DeltaT_f = i * K_f * b implies b = (DeltaT_f)/(i * K_f)#
Plug in your values to find
#b = (4.0 color(red)(cancel(color(black)(""^@"C"))))/(1 * 1.86 color(red)(cancel(color(black)(""^@"C"))) "kg mol"^(-1)) = color(green)(|bar(ul(color(white)(a/a)color(black)("2.2 mol kg"^(-1))color(white)(a/a)|)))#
The answer is rounded to two sig figs, the number of sig figs you have for the freezing point of the solution.