Answer to Question #139662 in General Chemistry for Harvey Jed A. Iman

Question

Calculate the boiling point elevation of the given electrolytic solution:

5.7 g CaCl2 (calcium chloride) in 48.6 kg H2O (water)

Round your answer to 3 decimal places.

Answer 1

Calculate the boiling point elevation of the given electrolytic solution:

5.7 g CaCl₂ (calcium chloride) in 48.6 kg H₂O(water)

Round your answer to 3 decimal places.

Solution :

Elevation in boiling point : It is a phenomenon that occurs when the Boiling point of a liquid (solvent ) is increased on the addition of a non-volatile compound.

It is a colligative property which means it depends on the 'number of solute' particles in the solution.

The formula for Elevation in Boiling point is

ΔT_b = i * K_b * m -------------------- Equation 1

where ‘ i ’ is the van’t hoff factor of solute.

K_b = boiling point elevation constant of solvent

m = molality of the solution.

Here CaCl₂ is the solute and water is the solvent.

K_b of water = 0.512 ⁰C/m

Step 1 : To find the van’t hoff factor ‘i ‘

We are not given the van’t hoff factor in the question. So we will consider complete dissociation of CaCl₂ .

CaCl₂ ----> 1 Ca²⁺ (aq) + 2Cl^- (aq)

Each unit of CaCl₂ gives 1 ion of Ca²⁺ and 2 ions of Cl^- ,

so van’t hoff factor ‘ i ’ = 1+2 = 3

Step 2 : To find molality of the solution

mass of CaCl₂ (solute ) = 5.7g

mass of water (solvent ) = 48.6kg

molar mass of CaCl₂ = 1 * atomic mass of Ca + 2 * atomic mass of Cl

= 1 * 40.078g/mol + 2 * 35.453g/mol

= 110.984g/mol

moles of CaCl₂ = 5.7g CaCl₂ * 1 mol CaCl₂ / 110.984g CaCl₂ = 0.05136 mol CaCl₂

molality = moles of solute/ ‘kg’ of solvent = 0.05136mol CaCl₂ /48.6kg

= 0.001057mol/kg or 0.001057m

Substitute i = 3, m = 0.001057m and K_b = 0.512 ⁰C/m in the Boiling point Elevation formula (Equation 1 ), we have

ΔT_b = i * K_b * m = 3 * 0.512 ⁰C/m * 0.001057m

ΔT_b = 0.001623 ⁰ C.

In question we are told to write our answer to 3 decimal places.

So the boiling point elevation = 0.002 ⁰C

Note : In the question we were not given van't factor 'i' . So we considered the complete dissociation of CaCl₂ and consider i = 3. In case if you are given the van't hoff factor then instead of 3 you should use the given van't hoff factor.