# Calculating sublimation temperature

## Homework Statement

The standard enthalpy of sublimation of dry ice (solid carbon dioxide) is 6.03 kJ/mol.
The triple point of CO2 is at 5.1 atm, -59.7 °C.

Calculate the normal sublimation temperature of CO2 at 1.00 atm pressure.

## Homework Equations

Delta G= Delta H-T(delta S)

## The Attempt at a Solution

I know delta G will be zero and and that delta H will be the same as the standard Enthalpy. I imagime I need to calculate delta entropy for sublimation at 1 atm but I have no idea how.

Chestermiller
Mentor

## Homework Statement

The standard enthalpy of sublimation of dry ice (solid carbon dioxide) is 6.03 kJ/mol.
The triple point of CO2 is at 5.1 atm, -59.7 °C.

Calculate the normal sublimation temperature of CO2 at 1.00 atm pressure.

## Homework Equations

Delta G= Delta H-T(delta S)

## The Attempt at a Solution

I know delta G will be zero and and that delta H will be the same as the standard Enthalpy. I imagime I need to calculate delta entropy for sublimation at 1 atm but I have no idea how.
This looks like a Clausius-Clapeyron problem.

Chet

I know dP/dT= delta S/ delta V. Do I find delta V using delta H= p times delta v where p is pressure specifically 5.1 atm?

Chestermiller
Mentor
I know dP/dT= delta S/ delta V. Do I find delta V using delta H= p times delta v where p is pressure specifically 5.1 atm?
No. You need to look up the derivation of the Clausius-Clapeyron equation. This will tell you how to get from your first equation to an equation you can actually use to solve this problem.

Think about this: The ΔS and the ΔV in your first equation refer to the changes in entropy and volume between two equilibrium states. What are those two equilibrium states? Is the volume in one of the equilibrium states much less than the volume in the other equilibrium state? How is the change in entropy between the two equilibrium states related to the change in enthalpy?

Chet

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Enthalpy Over Temperature Gives Entropy. Can I Treat The Vapors As An Ideal Has And Use The Idea Gas Law To Find Volume Of The Gas?

Chestermiller
Mentor
Enthalpy Over Temperature Gives Entropy. Can I Treat The Vapors As An Ideal Has And Use The Idea Gas Law To Find Volume Of The Gas?
If you mean enthalpy change over temperature gives entropy change, then yes. Regarding the ideal gas law, yes. You also neglect the specific volume of the liquid. These are the assumptions Clapeyron used.

Chet

Do I Need To Solve The ClaudiusRelation To Get P=Ce^-(L/RT)

Chestermiller
Mentor
Do I Need To Solve The ClaudiusRelation To Get P=Ce^-(L/RT)

No. This is the essentially equivalent to the Clausius Clapeyron equation. All you need to do first is use your input data to get the value of the constant of integration C for your problem.

Chet

You Mean Yes For Solving The DE I Then Use The Initial Conditions At P= 5.1 Atm To Find C Once I Have C I Can Plug In 1 ATM For The Pressure And Solve For T Right?

Chestermiller
Mentor
You Mean Yes For Solving The DE I Then Use The Initial Conditions At P= 5.1 Atm To Find C Once I Have C I Can Plug In 1 ATM For The Pressure And Solve For T Right?
Excellent. Great job.

Chet

I Got The Right Answer Of 145 K Thanks So Much.