How much Magnesium chloride would you need to put in 555 g of water to raise the boiling point by 11 o C

Answer 1

ΔT = imK

ΔT = change in temp = 11 degrees

i = van’t Hoff factor = 3 for MgCl₂

m = molality = moles solute/kg solvent = ?

K = boiling pt constant = 0.512

solving for m,

m = 11/(3)(.512) = 7.26 moles/kg

7.26 mol/kg x 0.555 kg = 3.97 moles needed

3.97 moles x 95.2 g/mole = 378 g MgCl₂ needed

Answer 2

colligative properties! Boiling point elevation by adding a solute (MgCl₂) to a solvent (water).

The formula for boiling point elevation is:

boiling point of the solution = boiling point of the pure solvent + K_b*m_c

where K_b = boiling point elevation constant

and

m_c = colligative molality

So let's go through the formula

Boiling point of solution = 111 C

Boiling point of pure solvent = 100 C

K_b = 0.513 K/mc

m_c = we have to calculate that

111 = 100 + (0.513)*mc

11 = 0.513*mc

21.4 = m_c

21.4 is the concentration in terms of COLLIGATIVE molality of the solution with a boiling point that is 11 C higher than it's pure boiling point.

Now remember what COLLIGATIVE molality is:

colligative molality = molality * van't Hoff factor

or

m_c = m*i

and the Van't Hoff factor (i) is essentially the NUMBER OF IONS that a species makes when it dissolves.

SO,

in the case of Magnesium Chloride, MgCl₂, it dissociates into THREE species, so van't hoff is 3:

MgCl₂ (s) -> Mg²⁺ (aq) + 2Cl^- (aq)

So

m_c = m*i

21.4 = m*3

7.15 = m

7.15 is the concentration in terms of molality of the solution that has a boiling point that is 11 C higher than it's pure solvent boiling point.

Now remember the formula for molality?

molality = moles of SOLUTE / kg of solvent

molality = 7.15

moles of solute = we don't know that, and we have to figure that out. we only know that the solute is MgCl₂

kg of solvent = 555 g water / 1000 g/kg = 0.555 kg water (this is a given in the problem.)

so

7.15 m = moles of solute / 0.555 kg

3.97 = moles of solute MgCl₂

We need the Formula weight for MgCl₂ to convert those moles into grams:

Mg + (2*Cl) = 24.305 + (2 * 35.45) = 95.2 g/mol

3.97 moles MgCl₂ * 95.2 g/mol = 378 grams of MgCl₂ are needed to raise the boiling point of 555 g water by 11 degrees Celsius!

*** Just a note about Kelvin/ Celsius. When you're talking about a temperature CHANGE there is no need to change the temperature into Kelvin, because Kelvin and Celsius degrees have the same size. So a 11 degree increase in Celsius degrees is also an 11 degree increase in Kelvin.