• Support PF! Buy your school textbooks, materials and every day products via PF Here!

How to calculate the transition temperature in this problem?

Thread moved from the technical forums, so no Template is shown
Summary: The transition Sn(s, gray) ⇌ Sn(s, white) is in equilibrium at 18°C and 1 atm pressure. If ΔS = 8.811K mol for the transition at 18°C and if the densities are 5.75 g/cm3 for gray tin and 7.28 g/cm3 for white tin, calculate the transition temperature under 100 atm pressure

20190806_170226.jpg
The transition Sn(s, gray) ⇌ Sn(s, white) is in equilibrium at 18°C and 1 atm pressure. If ΔS = 8.811K mol for the transition at 18°C and if the densities are 5.75 g/cm3 for gray tin and 7.28 g/cm3 for white tin, calculate the transition temperature under 100 atm pressure
 

mjc123

Science Advisor
777
347
You need to show an attempt of your own before receiving help, this is a forum rule.

There's no point repeating the same paragraph 3 times. And if you're going to, copy it right. ΔS = 8.8 J/K mol, not 8.811K mol.

What quantities determine the transition temperature? How might they vary with pressure?
 
dp/dT = ΔS /ΔV
dp/dT = ΔS /ΔV

(P2-P1)/(T2-T1) = ΔS/(M/d1-M/d2); where d1 and d2 are densities of gray tin and white tin, M is equal to molecular weight of tin.
P2 = 100 atm ; P1= 1atm T2=? T1= 273+ 18 =291K ;
(100-1)/(T2-291) = 8.811/ (118.71/5.75 - 118.71/ 7.28)
 

mjc123

Science Advisor
777
347
That looks OK in principle; I did it a bit differently, but it should come to the same answer. Just a few points you should be careful about:
- ΔS = 8.8, not 8.811, as I've already said.
- ΔV is Vwhite - Vgrey, make sure you get the sign right.
- Careful with units; what are the units of P? ΔV? ΔS? Be consistent.
 
Can you please tell me your way of solving?
 

mjc123

Science Advisor
777
347
I said ΔH = TΔS at equilibrium, so calculated ΔH at 291K and 1 atm.
ΔH = ΔU + PΔV
Assuming ΔU and ΔV don't change with pressure, d(ΔH)/dP = ΔV
So I calculated ΔH at 100 atm, and then T from T = ΔH/ΔS.
(I could not remember a dP/dT formula off the top of my head.)
 
19,178
3,787
Since they start out at equilibrium, the Gibbs free energy of the grey start out equal the Gibbs free energy of the white. For small changes in pressure and temperature, we have $$dG=-SdT+VdP$$. So, for the changes in pressure and temperature here, we have for the grey $$dG_g=-S_gdT+V_gdP$$and, for the white,$$dG_w=-S_wdT+V_wdP$$But to maintain equilibrium, these changes must be equal. Therefore, $$\frac{dT}{dP}=\frac{V_w-V_g}{S_w-S_g}=\frac{\Delta V}{\Delta S}$$Of course, specific volume is the reciprocal of density. And, of course, this calculation must be done using consistent units.
 

Want to reply to this thread?

"How to calculate the transition temperature in this problem?" You must log in or register to reply here.

Related Threads for: How to calculate the transition temperature in this problem?

  • Posted
Replies
7
Views
2K
  • Posted
Replies
4
Views
2K
  • Posted
Replies
3
Views
22K
  • Posted
Replies
7
Views
67K
  • Posted
Replies
1
Views
4K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top