PHYSICAL CHEMISTRY-STUDENT SOLN.MAN.
PHYSICAL CHEMISTRY-STUDENT SOLN.MAN.
2nd Edition
ISBN: 9781285074788
Author: Ball
Publisher: CENGAGE L
Question
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Chapter 7, Problem 7.84E
Interpretation Introduction

Interpretation:

The equation 7.49 is to be derived.

Concept introduction:

When a non-volatile solute is added to a solvent, the boiling point of the solution gets raised in comparison to the pure solvent. This phenomenon is known as elevation in boiling point. Elevation in boiling point is a colligative property.

Expert Solution & Answer
Check Mark

Answer to Problem 7.84E

The equation 7.41 can be represented for the vaporization process as shown below.

lnxsolvent=ΔvapHR(1T1TBP)

Where,

 xsolvent is the mole fraction of the solvent in the solution.

 ΔvapH is the enthalpy change for vaporization process.

 TBP is the boiling point of solvent.

The xsolvent can be written in the form of solute as xsolvent=(1xsolute). Substitute the value of xsolvent with (1xsolute) as shown below,

ln(1xsolute)=ΔvapHR(1T1TBP)

Applying the Taylor-series expansion on ln(1x)x and substitute the ln(1xsolute) with xsolute as shown below.

xsoluteΔvapHR(1T1TBP)

Rearrange the temperature terms as shown below.

xsoluteΔvapHR(TBPTT.TBP)

The term T.TBP can be approximated to TBP2 as dilute solution are considered in this case and the temperature at equilibrium is not much different from boiling point. Also TBPT can be rewritten as ΔTBP as shown below.

xsoluteΔvapHR(ΔTBPTBP2)

The relationship between molality and mole fraction is,

msolute=1000xsolutexsolventMsolvent

Where,

 msolute is molality of solute.

 xsoluteand xsolvent is mole fraction of solute and solvent.

 Msolvent is the molecular weight of solvent.

Substitute the value of xsolute in the given equation and rearrange for the value of ΔTBP as shown below.

ΔTBP(MsolventRTBP2ΔvapH1000)msolute

Explanation of Solution

The equation 7.41 can be represented for the vaporization process as shown below.

lnxsolvent=ΔvapHR(1T1TBP)

Where,

 xsolvent is the mole fraction of the solvent in the solution.

 ΔvapH is the enthalpy change for vaporization process.

 TBP is the boiling point of solvent.

The xsolvent can be written in the form of solute as xsolvent=(1xsolute). Substitute the value of xsolvent with (1xsolute) as shown below,

ln(1xsolute)=ΔvapHR(1T1TBP)

Applying the Taylor-series expansion on ln(1x)x and substitute the ln(1xsolute) with xsolute as shown below.

xsoluteΔvapHR(1T1TBP)

Rearrange the temperature terms as shown below.

xsoluteΔvapHR(TBPTT.TBP)

The term T.TBP can be approximated to TBP2 as dilute solution are considered in this case and the temperature at equilibrium is not much different from boiling point. Also TBPT can be rewritten as ΔTBP as shown below.

xsoluteΔvapHR(ΔTBPTBP2)

The relationship between molality and mole fraction is,

msolute=1000xsolutexsolventMsolvent

Where,

 msolute is molality of solute.

 xsoluteand xsolvent is mole fraction of solute and solvent.

 Msolvent is the molecular weight of solvent.

Substitute the value of xsolute in the given equation and rearrange for the value of ΔTBP as shown below.

ΔTBP(MsolventRTBP2ΔvapH1000)msolute

Conclusion

The derivation of equation of 7.49 has been rightfully stated.

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Chapter 7 Solutions

PHYSICAL CHEMISTRY-STUDENT SOLN.MAN.

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