Answer to Question #139767 in General Chemistry for Crescent Licci

Question

What is the boiling point and freezing point of a 0.773 M solution of magnesium chloride , MgCl 2 , an electrolyte ?

Answer 1

Given,

Molar concentration of MgCl2, C = 0.773 M

taking the solution as a dilute one,

We can say the molal concentration of this MgCl2 solution, m = 0.773 m

Boiling point:

Normal boiling point of water,

T = (100+273) K

= 373 K

Let, boiling point of the solution = T'

We know,

∆T = i×k_b×m

Where, ∆T = T'–T

i = vant Hoff factory for electrolyte for MgCl2, i = 3 as it produced 3 iones

m = molal concentration of MgCl2

K_b = molar boiling point elevation constant of water

So, (T'–T) = i × k_b × m

Putting , k_b = 0.512 K kg/mol (from the standard value table) and other values

T'–373 = 3 × 0.512 × 0.773

Or, T' = 374.187 K

Boiling point in celcius =(374.187 – 273) °C

= 101.187°C

Hence boiling point of the MgCl2 solution = 101.187 °C

Freezing point:

Normal freezing point of water,

T = (0+273)K

= 273 K

Let, freezing point of the solution = T"

We know,

∆T = i×k_f×m

Where, ∆T = T–T"

i = vant Hoff factory for electrolyte for MgCl2, i = 3, as it produced 3 iones

m = molal concentration of MgCl2

K_f = molar freezing point depression constant of water

So, (T–T") = i × k_f × m

Putting , k_f = 1.86 K kg/mol (from the standard value table) and other values

273–T" = 3 × 1.86 × 0.773

Or, T'' = 268.686 K

Freezing point in celcius = (268.686– 273) °C

= –4.313 °C

Hence freezing point of the MgCl2 solution = –4.313°C