Question

The molar mass calculated through colligative properties is sometimes different from that of experimentally determined molecular mass and is known as abnormal molecular mass. This difference is due to the solute particles that undergo association or dissociation.

Consider the two cases given below and answer the questions that follow.

1. The freezing point of a solution containing 5.85g of NaCl in 100g of water is −3.348^oC. (K_f of water = 1.86 K kg mol^-1 , molecular mass of NaCl = 58.5)
2. The freezing point of benzene solution decreases by 0.45^oC when 0.2g of acetic acid is added to 20g of benzene. (K_f of benzene = 5.12 K kg mol^-1 , molecular mass of acetic acid = 60)

Answer the following questions.

1. Calculate the abnormal molecular mass of solute in both the cases.
2. Inferring the value of van’t Hoff factor in both the cases, find out which solution undergoes association and which solution undergoes dissociation.
3. Given below is the increasing order of depression in freezing point of water observed for equimolar concentrations of the compounds,
   acetic acid < trichloro acetic acid < trifluoro acetic acid
   Provide a reason to explain if the above ordered arrangement is correct or not.

Answer 1

(i) Molecular Mass Calculation of NaCl in Water.

Given: `"M"_"solute"` = 58.5 g mol⁻¹

n = `3.348/1.86 xx 0.1` = 0.18 moles

As we know,

M = `"m"_("solute")/"n"`

= `5.85/0.18`

∴ Molecular mass [A] = 32.5 g mol^-1

Molecular Mass Calculation of Acetic Acid in Benzene.

Given: `"M"_"solute"` = 60 g mol^-1

n = `0.45/5.12 xx 0.02` = 0.00176 moles

As we know,

M = `"m"_("solute")/"n"`

= `0.2/0.00176`

∴ Molecular mass [B] = 113.79 g mol^-1

(ii) [A] undergoes Dissociation while [B] undergoes Association

(iii) The given order of depression in the freezing point is correct, as ΔT_f depends on the number of moles of solute.