A solution of urea in water has a boiling point of 100.128 *C. Calculate the freezing point of the same solution: Given Kb and K: for water are 0.512 ‘C/m and 1.86 “C/m respectively: Answer: T; =-0.465 %
The Correct Answer and Explanation is:1
To determine the freezing point of the urea solution, begin by calculating the molality using the boiling point elevation, then apply that to determine the freezing point depression.
Step 1: Use boiling point elevation to find molality
Boiling point elevation formula:ΔTb=i⋅Kb⋅m\Delta T_b = i \cdot K_b \cdot mΔTb=i⋅Kb⋅m
Where:
- ΔTb=Tboiling,solution−Tboiling,pure water=100.128∘C−100.000∘C=0.128∘C\Delta T_b = T_{boiling, solution} – T_{boiling, pure\ water} = 100.128^\circ C – 100.000^\circ C = 0.128^\circ CΔTb=Tboiling,solution−Tboiling,pure water=100.128∘C−100.000∘C=0.128∘C
- iii is the van’t Hoff factor for urea, which is 1 (non-electrolyte)
- Kb=0.512∘C/mK_b = 0.512^\circ C/mKb=0.512∘C/m
- mmm is molality
Solving for molality mmm:m=ΔTbi⋅Kb=0.1281⋅0.512=0.25 mol/kgm = \frac{\Delta T_b}{i \cdot K_b} = \frac{0.128}{1 \cdot 0.512} = 0.25\ \text{mol/kg}m=i⋅KbΔTb=1⋅0.5120.128=0.25 mol/kg
Step 2: Use freezing point depression formula
Freezing point depression formula:ΔTf=i⋅Kf⋅m\Delta T_f = i \cdot K_f \cdot mΔTf=i⋅Kf⋅m
Where:
- Kf=1.86∘C/mK_f = 1.86^\circ C/mKf=1.86∘C/m
- i=1i = 1i=1 (urea does not dissociate)
- m=0.25 mol/kgm = 0.25\ mol/kgm=0.25 mol/kg
ΔTf=1⋅1.86⋅0.25=0.465∘C\Delta T_f = 1 \cdot 1.86 \cdot 0.25 = 0.465^\circ CΔTf=1⋅1.86⋅0.25=0.465∘C
Step 3: Calculate the freezing point
The freezing point of pure water is 0.000∘C0.000^\circ C0.000∘C. Since freezing point is depressed:Tf=0.000∘C−0.465∘C=−0.465∘CT_f = 0.000^\circ C – 0.465^\circ C = -0.465^\circ CTf=0.000∘C−0.465∘C=−0.465∘C
Conclusion:
The freezing point of the urea solution is −0.465∘C-0.465^\circ C−0.465∘C.
This outcome demonstrates how a solute such as urea affects the colligative properties of a solvent like water. Despite being a non-electrolyte, urea still lowers the freezing point proportionally to its molality. The calculation involves the use of fundamental relationships between temperature changes and solution concentration, using the known constants KbK_bKb and KfK_fKf for water.To determine the freezing point of the urea solution, begin by calculating the molality using the boiling point elevation, then apply that to determine the freezing point depression.
Step 1: Use boiling point elevation to find molality
Boiling point elevation formula:ΔTb=i⋅Kb⋅m\Delta T_b = i \cdot K_b \cdot mΔTb=i⋅Kb⋅m
Where:
- ΔTb=Tboiling,solution−Tboiling,pure water=100.128∘C−100.000∘C=0.128∘C\Delta T_b = T_{boiling, solution} – T_{boiling, pure\ water} = 100.128^\circ C – 100.000^\circ C = 0.128^\circ CΔTb=Tboiling,solution−Tboiling,pure water=100.128∘C−100.000∘C=0.128∘C
- iii is the van’t Hoff factor for urea, which is 1 (non-electrolyte)
- Kb=0.512∘C/mK_b = 0.512^\circ C/mKb=0.512∘C/m
- mmm is molality
Solving for molality mmm:m=ΔTbi⋅Kb=0.1281⋅0.512=0.25 mol/kgm = \frac{\Delta T_b}{i \cdot K_b} = \frac{0.128}{1 \cdot 0.512} = 0.25\ \text{mol/kg}m=i⋅KbΔTb=1⋅0.5120.128=0.25 mol/kg
Step 2: Use freezing point depression formula
Freezing point depression formula:ΔTf=i⋅Kf⋅m\Delta T_f = i \cdot K_f \cdot mΔTf=i⋅Kf⋅m
Where:
- Kf=1.86∘C/mK_f = 1.86^\circ C/mKf=1.86∘C/m
- i=1i = 1i=1 (urea does not dissociate)
- m=0.25 mol/kgm = 0.25\ mol/kgm=0.25 mol/kg
ΔTf=1⋅1.86⋅0.25=0.465∘C\Delta T_f = 1 \cdot 1.86 \cdot 0.25 = 0.465^\circ CΔTf=1⋅1.86⋅0.25=0.465∘C
Step 3: Calculate the freezing point
The freezing point of pure water is 0.000∘C0.000^\circ C0.000∘C. Since freezing point is depressed:Tf=0.000∘C−0.465∘C=−0.465∘CT_f = 0.000^\circ C – 0.465^\circ C = -0.465^\circ CTf=0.000∘C−0.465∘C=−0.465∘C
Conclusion:
The freezing point of the urea solution is −0.465∘C-0.465^\circ C−0.465∘C.
This outcome demonstrates how a solute such as urea affects the colligative properties of a solvent like water. Despite being a non-electrolyte, urea still lowers the freezing point proportionally to its molality. The calculation involves the use of fundamental relationships between temperature changes and solution concentration, using the known constants KbK_bKb and KfK_fKf for water.
