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.

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Answer 1

Question

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

Answer to Problem 7.84E

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

$lnxsolvent=−ΔvapHR(1T−1TBP)$

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 $xsolvent=(1−xsolute)$ . Substitute the value of $xsolvent$ with $(1−xsolute)$ as shown below,

$ln(1−xsolute)=−ΔvapHR(1T−1TBP)$

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

$xsolute≈ΔvapHR(1T−1TBP)$

Rearrange the temperature terms as shown below.

$xsolute≈ΔvapHR(TBP−TT.TBP)$

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 $TBP−T$ can be rewritten as $ΔTBP$ as shown below.

$xsolute≈ΔvapHR(ΔTBPTBP2)$

The relationship between molality and mole fraction is,

$msolute=1000⋅xsolutexsolvent⋅Msolvent$

Where,

• $msolute$ is molality of solute.

• $xsolute$ and $xsolvent$ 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.

$ΔTBP≈(MsolventRTBP2ΔvapH⋅1000)msolute$

Explanation of Solution

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

$lnxsolvent=−ΔvapHR(1T−1TBP)$

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 $xsolvent=(1−xsolute)$ . Substitute the value of $xsolvent$ with $(1−xsolute)$ as shown below,

$ln(1−xsolute)=−ΔvapHR(1T−1TBP)$

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

$xsolute≈ΔvapHR(1T−1TBP)$

Rearrange the temperature terms as shown below.

$xsolute≈ΔvapHR(TBP−TT.TBP)$

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 $TBP−T$ can be rewritten as $ΔTBP$ as shown below.

$xsolute≈ΔvapHR(ΔTBPTBP2)$

The relationship between molality and mole fraction is,

$msolute=1000⋅xsolutexsolvent⋅Msolvent$

Where,

• $msolute$ is molality of solute.

• $xsolute$ and $xsolvent$ 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.

$ΔTBP≈(MsolventRTBP2ΔvapH⋅1000)msolute$

Conclusion

The derivation of equation of 7.49 has been rightfully stated.

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Answer 2

Question

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

Answer to Problem 7.84E

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

$lnxsolvent=−ΔvapHR(1T−1TBP)$

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 $xsolvent=(1−xsolute)$ . Substitute the value of $xsolvent$ with $(1−xsolute)$ as shown below,

$ln(1−xsolute)=−ΔvapHR(1T−1TBP)$

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

$xsolute≈ΔvapHR(1T−1TBP)$

Rearrange the temperature terms as shown below.

$xsolute≈ΔvapHR(TBP−TT.TBP)$

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 $TBP−T$ can be rewritten as $ΔTBP$ as shown below.

$xsolute≈ΔvapHR(ΔTBPTBP2)$

The relationship between molality and mole fraction is,

$msolute=1000⋅xsolutexsolvent⋅Msolvent$

Where,

• $msolute$ is molality of solute.

• $xsolute$ and $xsolvent$ 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.

$ΔTBP≈(MsolventRTBP2ΔvapH⋅1000)msolute$

Explanation of Solution

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

$lnxsolvent=−ΔvapHR(1T−1TBP)$

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 $xsolvent=(1−xsolute)$ . Substitute the value of $xsolvent$ with $(1−xsolute)$ as shown below,

$ln(1−xsolute)=−ΔvapHR(1T−1TBP)$

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

$xsolute≈ΔvapHR(1T−1TBP)$

Rearrange the temperature terms as shown below.

$xsolute≈ΔvapHR(TBP−TT.TBP)$

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 $TBP−T$ can be rewritten as $ΔTBP$ as shown below.

$xsolute≈ΔvapHR(ΔTBPTBP2)$

The relationship between molality and mole fraction is,

$msolute=1000⋅xsolutexsolvent⋅Msolvent$

Where,

• $msolute$ is molality of solute.

• $xsolute$ and $xsolvent$ 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.

$ΔTBP≈(MsolventRTBP2ΔvapH⋅1000)msolute$

Conclusion

The derivation of equation of 7.49 has been rightfully stated.

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Answer 3

Question

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

Answer to Problem 7.84E

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

$lnxsolvent=−ΔvapHR(1T−1TBP)$

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 $xsolvent=(1−xsolute)$ . Substitute the value of $xsolvent$ with $(1−xsolute)$ as shown below,

$ln(1−xsolute)=−ΔvapHR(1T−1TBP)$

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

$xsolute≈ΔvapHR(1T−1TBP)$

Rearrange the temperature terms as shown below.

$xsolute≈ΔvapHR(TBP−TT.TBP)$

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 $TBP−T$ can be rewritten as $ΔTBP$ as shown below.

$xsolute≈ΔvapHR(ΔTBPTBP2)$

The relationship between molality and mole fraction is,

$msolute=1000⋅xsolutexsolvent⋅Msolvent$

Where,

• $msolute$ is molality of solute.

• $xsolute$ and $xsolvent$ 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.

$ΔTBP≈(MsolventRTBP2ΔvapH⋅1000)msolute$

Explanation of Solution

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

$lnxsolvent=−ΔvapHR(1T−1TBP)$

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 $xsolvent=(1−xsolute)$ . Substitute the value of $xsolvent$ with $(1−xsolute)$ as shown below,

$ln(1−xsolute)=−ΔvapHR(1T−1TBP)$

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

$xsolute≈ΔvapHR(1T−1TBP)$

Rearrange the temperature terms as shown below.

$xsolute≈ΔvapHR(TBP−TT.TBP)$

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 $TBP−T$ can be rewritten as $ΔTBP$ as shown below.

$xsolute≈ΔvapHR(ΔTBPTBP2)$

The relationship between molality and mole fraction is,

$msolute=1000⋅xsolutexsolvent⋅Msolvent$

Where,

• $msolute$ is molality of solute.

• $xsolute$ and $xsolvent$ 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.

$ΔTBP≈(MsolventRTBP2ΔvapH⋅1000)msolute$

Conclusion

The derivation of equation of 7.49 has been rightfully stated.

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Answer 4

Question

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

Answer to Problem 7.84E

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

$lnxsolvent=−ΔvapHR(1T−1TBP)$

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 $xsolvent=(1−xsolute)$ . Substitute the value of $xsolvent$ with $(1−xsolute)$ as shown below,

$ln(1−xsolute)=−ΔvapHR(1T−1TBP)$

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

$xsolute≈ΔvapHR(1T−1TBP)$

Rearrange the temperature terms as shown below.

$xsolute≈ΔvapHR(TBP−TT.TBP)$

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 $TBP−T$ can be rewritten as $ΔTBP$ as shown below.

$xsolute≈ΔvapHR(ΔTBPTBP2)$

The relationship between molality and mole fraction is,

$msolute=1000⋅xsolutexsolvent⋅Msolvent$

Where,

• $msolute$ is molality of solute.

• $xsolute$ and $xsolvent$ 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.

$ΔTBP≈(MsolventRTBP2ΔvapH⋅1000)msolute$

Explanation of Solution

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

$lnxsolvent=−ΔvapHR(1T−1TBP)$

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 $xsolvent=(1−xsolute)$ . Substitute the value of $xsolvent$ with $(1−xsolute)$ as shown below,

$ln(1−xsolute)=−ΔvapHR(1T−1TBP)$

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

$xsolute≈ΔvapHR(1T−1TBP)$

Rearrange the temperature terms as shown below.

$xsolute≈ΔvapHR(TBP−TT.TBP)$

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 $TBP−T$ can be rewritten as $ΔTBP$ as shown below.

$xsolute≈ΔvapHR(ΔTBPTBP2)$

The relationship between molality and mole fraction is,

$msolute=1000⋅xsolutexsolvent⋅Msolvent$

Where,

• $msolute$ is molality of solute.

• $xsolute$ and $xsolvent$ 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.

$ΔTBP≈(MsolventRTBP2ΔvapH⋅1000)msolute$

Conclusion

The derivation of equation of 7.49 has been rightfully stated.

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Answer 5

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

Answer to Problem 7.84E

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

$lnxsolvent=−ΔvapHR(1T−1TBP)$

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 $xsolvent=(1−xsolute)$ . Substitute the value of $xsolvent$ with $(1−xsolute)$ as shown below,

$ln(1−xsolute)=−ΔvapHR(1T−1TBP)$

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

$xsolute≈ΔvapHR(1T−1TBP)$

Rearrange the temperature terms as shown below.

$xsolute≈ΔvapHR(TBP−TT.TBP)$

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 $TBP−T$ can be rewritten as $ΔTBP$ as shown below.

$xsolute≈ΔvapHR(ΔTBPTBP2)$

The relationship between molality and mole fraction is,

$msolute=1000⋅xsolutexsolvent⋅Msolvent$

Where,

• $msolute$ is molality of solute.

• $xsolute$ and $xsolvent$ 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.

$ΔTBP≈(MsolventRTBP2ΔvapH⋅1000)msolute$

Explanation of Solution

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

$lnxsolvent=−ΔvapHR(1T−1TBP)$

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 $xsolvent=(1−xsolute)$ . Substitute the value of $xsolvent$ with $(1−xsolute)$ as shown below,

$ln(1−xsolute)=−ΔvapHR(1T−1TBP)$

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

$xsolute≈ΔvapHR(1T−1TBP)$

Rearrange the temperature terms as shown below.

$xsolute≈ΔvapHR(TBP−TT.TBP)$

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 $TBP−T$ can be rewritten as $ΔTBP$ as shown below.

$xsolute≈ΔvapHR(ΔTBPTBP2)$

The relationship between molality and mole fraction is,

$msolute=1000⋅xsolutexsolvent⋅Msolvent$

Where,

• $msolute$ is molality of solute.

• $xsolute$ and $xsolvent$ 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.

$ΔTBP≈(MsolventRTBP2ΔvapH⋅1000)msolute$

Conclusion

The derivation of equation of 7.49 has been rightfully stated.

Answer 6

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

Answer to Problem 7.84E

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

$lnxsolvent=−ΔvapHR(1T−1TBP)$

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 $xsolvent=(1−xsolute)$ . Substitute the value of $xsolvent$ with $(1−xsolute)$ as shown below,

$ln(1−xsolute)=−ΔvapHR(1T−1TBP)$

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

$xsolute≈ΔvapHR(1T−1TBP)$

Rearrange the temperature terms as shown below.

$xsolute≈ΔvapHR(TBP−TT.TBP)$

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 $TBP−T$ can be rewritten as $ΔTBP$ as shown below.

$xsolute≈ΔvapHR(ΔTBPTBP2)$

The relationship between molality and mole fraction is,

$msolute=1000⋅xsolutexsolvent⋅Msolvent$

Where,

• $msolute$ is molality of solute.

• $xsolute$ and $xsolvent$ 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.

$ΔTBP≈(MsolventRTBP2ΔvapH⋅1000)msolute$

Explanation of Solution

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

$lnxsolvent=−ΔvapHR(1T−1TBP)$

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 $xsolvent=(1−xsolute)$ . Substitute the value of $xsolvent$ with $(1−xsolute)$ as shown below,

$ln(1−xsolute)=−ΔvapHR(1T−1TBP)$

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

$xsolute≈ΔvapHR(1T−1TBP)$

Rearrange the temperature terms as shown below.

$xsolute≈ΔvapHR(TBP−TT.TBP)$

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 $TBP−T$ can be rewritten as $ΔTBP$ as shown below.

$xsolute≈ΔvapHR(ΔTBPTBP2)$

The relationship between molality and mole fraction is,

$msolute=1000⋅xsolutexsolvent⋅Msolvent$

Where,

• $msolute$ is molality of solute.

• $xsolute$ and $xsolvent$ 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.

$ΔTBP≈(MsolventRTBP2ΔvapH⋅1000)msolute$

Conclusion

The derivation of equation of 7.49 has been rightfully stated.

Answer 7

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.

Answer 8

Expert Solution & Answer

Answer to Problem 7.84E

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

$lnxsolvent=−ΔvapHR(1T−1TBP)$

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 $xsolvent=(1−xsolute)$ . Substitute the value of $xsolvent$ with $(1−xsolute)$ as shown below,

$ln(1−xsolute)=−ΔvapHR(1T−1TBP)$

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

$xsolute≈ΔvapHR(1T−1TBP)$

Rearrange the temperature terms as shown below.

$xsolute≈ΔvapHR(TBP−TT.TBP)$

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 $TBP−T$ can be rewritten as $ΔTBP$ as shown below.

$xsolute≈ΔvapHR(ΔTBPTBP2)$

The relationship between molality and mole fraction is,

$msolute=1000⋅xsolutexsolvent⋅Msolvent$

Where,

• $msolute$ is molality of solute.

• $xsolute$ and $xsolvent$ 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.

$ΔTBP≈(MsolventRTBP2ΔvapH⋅1000)msolute$

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

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

$lnxsolvent=−ΔvapHR(1T−1TBP)$

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 $xsolvent=(1−xsolute)$ . Substitute the value of $xsolvent$ with $(1−xsolute)$ as shown below,

$ln(1−xsolute)=−ΔvapHR(1T−1TBP)$

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

$xsolute≈ΔvapHR(1T−1TBP)$

Rearrange the temperature terms as shown below.

$xsolute≈ΔvapHR(TBP−TT.TBP)$

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 $TBP−T$ can be rewritten as $ΔTBP$ as shown below.