Question

Question #6a5d5

Answer 1

The raising of the boiling point is one of the colligative properties of solutions.

Being a colligative property, the effect is independent of the identity of the solute, but only the amount of solute in solution.

The equation for boiling point elevation is

`DeltaT_b = imK_b`

where

• `DeltaT_b` is the change in boiling point (a positive quantity) of the solution

• `i` is the van't Hoff factor, which is essentially the number of dissolved ions per unit of solvent (assuming `"HCl"` is the solute, this value is `2`, because there is `1` `"H"^+` ion and `1` `"Cl"^-` ion per unit of `"HCl"`)

• `m` is the molality of the solution;

`"molality" = "mol solute"/"kg solvent"`

If we can figure out these two quantities, we can figure out the solution's molality.

• `K_b` is the molal boiling point elevation constant for the solvent (assumed to be benzene). We can find this value from a list online:

From this, we can see that `K_b` for benzene is `color(red)(2.53` `color(red)(""^"o""C/"m`.

Plugging in the known values for the situation, we have

`DeltaT_b = (2)m(color(red)(2.53)color(white)(l)color(red)(""^"o""C/"m))`

`DeltaT_b = (5.06color(white)(l)^"o""C/"m)*m`

As long as we know the molal concentration `m`, we can find the increase in boiling point of this solution.

Let's say there is `1.00` `"mol HCl"` dissolved in `2.00` `"kg benzene"`.

The molality would be

`"molality" = (1.00color(white)(l)"mol HCl")/(2.00color(white)(l)"kg benzene") = color(green)(0.500m`

Plugging this into the equation, we can find the boiling point elevation:

`DeltaT_b = (5.06color(white)(l)^"o""C/"cancel(m))(color(green)(0.500)cancel(color(green)(m))) = 2.53` `""^"o""C"`

This quantity represents by how much the boiling point of the solvent (benzene) increases; to find the new boiling point of this solution, we simply add this to the normal boiling point of benzene (according to the above figure, it is `80.1` `""^"o""C"`):

`"new b.p." = 80.1^"o""C" + 2.53^"o""C" = color(blue)(82.6` `color(blue)(""^"o""C"`

rounded to one decimal place.