Chemistry & Chemical Reactivity
Chemistry & Chemical Reactivity
10th Edition
ISBN: 9781337399074
Author: John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher: Cengage Learning
Question
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Chapter 13, Problem 105SCQ
Interpretation Introduction

Interpretation: van’t Hoff factor for NaCl and Na2SO4 have to be determined. Whether the values are following the expectations based on trend in the table 13.4 has to be identified.

Concept introduction:

Colligative properties: Properties of solutions which having influence on the concentration of the solute in it. Colligative properties are,

  • Decrease in the vapor pressure
  • Increase in the boiling point
  • Decline in the freezing point
  • Osmotic pressure

Freezing point depression: The freezing point of the solution varies with the solute concentration.

  ΔTfp=Kfpmsolute

  where,

  Kfp is the molal freezing point depression constant.

van’t Hoff factor, i: it is the ration between change in in freezing point measured and change in in freezing point calculated. It indicates the total number of ions that are produced.

  van'tHofffactor,i=measuredΔTfpCalculatedΔTfp

Molality (m): Molality is the number of moles of solute present in one kilogram of solvent.

  Molality (m) =Numberofmolesofsolute1kgofsolvent

The number of moles of any substance can be determined using the equation

  Numberofmole=GivenmassofthesubstanceMolarmass

Expert Solution & Answer
Check Mark

Answer to Problem 105SCQ

  • van’t Hoff factor for NaCl is 1.82
  • van’t Hoff factor for Na2SO4 is 1.98
  • The continuity of trend for the value of van’t Hoff factor for Na2SO4 is decreased significantly and it is near to the value of van’t Hoff factor for NaCl. The value of van’t Hoff factor for NaCl is similar to the other values.

Explanation of Solution

Given,

  measuredΔTfpforNaCl=3.050CmeasuredΔTfpforNa2SO4=1.360CKfp=1.860C/m

  Mass of NaCl is 5100×100g=5g

  Molar mass of NaCl is 58.44g/mol

  Mass of Na2SO4 is 5100×100g=5g

  Molar mass of Na2SO4 is 142.04g/mol

  Mass of water is 100g5g=95g

The number of moles of any substance can be determined using the equation

  Numberofmole=GivenmassofthesubstanceMolarmass=5g58.44g/mol=0.086mol

Molarity of the NaCl solution is,

  Molality (m) =NumberofmolesofsoluteSolventinkg=0.086mol0.095kg=0.90m

Molarity of the NaCl solution is 0.90m

It is assumed that dissociation does not take place.

Depression in freezing point is calculated by using the equation

  ΔTfp= Kfp. msolute=(1.860C/m)(0.90m)=1.670C

Depression in freezing point when there is no dissociation is 1.670C

van'tHofffactor,i=measuredΔTfpCalculatedΔTfp

  i=3.050C1.670C=1.82

van’t Hoff factor for NaCl is 1.82

The number of moles of any substance can be determined using the equation

  Numberofmole=GivenmassofthesubstanceMolarmass=5g142.04g/mol=0.035mol

Molality of the Na2SO4 solution is,

  Molality (m) =NumberofmolesofsoluteSolventinkg=0.035mol0.095kg=0.368m

Molality of the Na2SO4 solution is 0.368m

It is assumed that dissociation does not take place.

Depression in freezing point is calculated by using the equation

  ΔTfp= Kfp. msolute=(1.860C/m)(0.368m)=0.68450C

van'tHofffactor,i=measuredΔTfpCalculatedΔTfp

  i=1.360C0.68450C=1.98

van’t Hoff factor for Na2SO4 is 1.98

van’t Hoff factor for NaCl is 1.82 whereas for Na2SO4, it is 1.98. The value of van’t Hoff factor decreases with the increase in concentration of solute. The values are steady with the trend that seen in the given data table. Since the rate is decreasing in both cases. The continuity of trend for the value of van’t Hoff factor for Na2SO4 is decreased significantly and it is near to the value of van’t Hoff factor for NaCl. The value of van’t Hoff factor for NaCl is similar to the other values.

Conclusion

van’t Hoff factor for NaCl and Na2SO4 were determined.

  • van’t Hoff factor for NaCl is 1.82
  • van’t Hoff factor for Na2SO4 is 1.98
  • The continuity of trend for the value of van’t Hoff factor for Na2SO4 is decreased significantly and it is near to the value of van’t Hoff factor for NaCl. The value of van’t Hoff factor for NaCl is similar to the other values.

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Chapter 13 Solutions

Chemistry & Chemical Reactivity

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