100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Summary Extended Formulae sheet for Chemical Thermodynamics $10.96
Add to cart

Summary

Summary Extended Formulae sheet for Chemical Thermodynamics

 0 view  0 purchase
  • Course
  • Institution

Provide extend and more equations required for exams. Important to learn and understand. I personally got 95% for this module, so I think that this formula sheet is very effective when using it for past papers and revisions.

Preview 2 out of 6  pages

  • December 24, 2024
  • 6
  • 2023/2024
  • Summary
  • Unknown
avatar-seller
CHEN10192 – Chemical Thermodynamics
Formulae Sheet



Pressure: 1 bar = 105 Pa

Temperature: T (K) = T (°C) + 273.15

Ideal gas constant: R = 8.314 J mol–1 K–1

Thermodynamic potentials:

𝜕𝑈
𝑑𝑈 = 𝑇𝑑𝑆 − 𝑃𝑑𝑉 + ∑ ( ) 𝑑𝑛𝑖
𝜕𝑛𝑖 𝑆,𝑉,𝑛
𝑖 𝑗
𝜕𝐻
𝑑𝐻 = 𝑇𝑑𝑆 + 𝑉𝑑𝑃 + ∑ ( ) 𝑑𝑛𝑖
𝜕𝑛𝑖 𝑆,𝑃,𝑛
𝑖 𝑗
𝜕𝐴
𝑑𝐴 = −𝑆𝑑𝑇 − 𝑃𝑑𝑉 + ∑ ( ) 𝑑𝑛𝑖
𝜕𝑛𝑖 𝑇,𝑉,𝑛
𝑖 𝑗
𝜕𝐺
𝑑𝐺 = −𝑆𝑑𝑇 + 𝑉𝑑𝑃 + ∑ ( ) 𝑑𝑛𝑖
𝜕𝑛𝑖 𝑇,𝑃,𝑛
𝑖 𝑗
-
Maxwell relations: ↳ Chemical
potential (Mil
𝜕𝑇 𝜕𝑃
( ) = −( )
𝜕𝑉 𝑆,𝑛𝑖 𝜕𝑆 𝑉,𝑛𝑖
𝜕𝑇 𝜕𝑉
( ) =( )
𝜕𝑃 𝑆,𝑛𝑖 𝜕𝑆 𝑃,𝑛𝑖
𝜕𝑃 𝜕𝑆
( ) =( )
𝜕𝑇 𝑉,𝑛𝑖 𝜕𝑉 𝑇,𝑛𝑖
𝜕𝑉 𝜕𝑆
( ) = −( )
𝜕𝑇 𝑃,𝑛𝑖 𝜕𝑃 𝑇,𝑛𝑖

Ideal gas:
𝑇
ℎ𝐼𝐺 (𝑇) = ℎ𝐼𝐺 (𝑇0 ) + ∫ 𝑐𝑃𝐼𝐺 𝑑𝑇 gF0 = hE0 .
TsF =
gFP(T ,
P) +
RTInG
𝑇0
𝑇 𝐼𝐺
𝑐𝑃 𝑃 PuEr
git gFP (T
F6
P) -
RT
𝑠 𝐼𝐺 (𝑇, 𝑃) = 𝑠 𝐼𝐺 (𝑇0 , 𝑃0 ) + ∫
:
a
𝑑𝑇 − 𝑅 𝑙𝑛
.
,



𝑇 𝑃0
𝑀,𝐼𝐷
𝑇0
d
ℎ (𝑇, 𝑥⃗) = 0
= RTCE -
1)
𝑠 𝑀,𝐼𝐷 (𝑇, 𝑃, 𝑥⃗) = −𝑅 ∑ 𝑥𝑖 𝑙𝑛𝑥𝑖
𝑖
𝑀,𝐼𝐷 (𝑇,
𝑔 𝑃, 𝑥⃗) = −𝑊𝑚𝑖𝑛 = 𝑅𝑇 ∑ 𝑥𝑖 𝑙𝑛𝑥𝑖
𝑖


Compressibility Factor (2) =
behavior
↳ represents deviation of real
gas
from ideal


Ideal : 1
gas z =

, B(T)




ia = /P :
Virial EoS: -z = 1 +
Bp

𝐵𝑀𝐼𝑋 = ∑ ∑ 𝑦𝑖 𝑦𝑗 𝐵𝑖𝑗 =>
,B B
y , Ba
y 2y
+ +
,
, y ,
, z


𝑖 𝑗 -




(1 − 𝛿𝑖𝑗 ) S
𝐵𝑖𝑖 + 𝐵𝑗𝑗
𝐵𝑖𝑗 = 𝐵𝑗𝑖 =
2


pl-togeth
𝑃

- ( +a
𝜕𝑣


Residual i s
𝛥ℎ𝑅 (𝑇, 𝑃) = ∫ [𝑣 − 𝑇 ( ) ] 𝑑𝑃 + =


0 𝜕𝑇 𝑃
𝑃
𝜕𝑣 𝑅
𝛥𝑠 𝑅 (𝑇, 𝑃) = − ∫ [( ) − ] 𝑑𝑃
𝑃
0 𝜕𝑇 𝑃 𝑃 :
Fugi - 𝑙𝑛 𝜑 = ∫ (𝑅𝑇 − 𝑃) 𝑑𝑃 -
𝑣 1
0 B B Brix &
- Zy 2y Zy Baz 2y B Brix
+ -




/lim Flim
+
,
,
, 2
, -
𝑃 ,

𝑣̄ 𝑖 1
, ,




𝑙𝑛𝜑𝑖 = ∫ ( − ) 𝑑𝑃
0 𝑅𝑇 𝑃 · ziBij-Brix)
Underwa SoreRedlich-Eng (1
Peng-Ros a




=b
a(T)
z
= Cubic EoS: - P
(v + (b)(v + db)
=> ,
d = - m)
a f (Tc f(T
P,
=- Energy pramater w)
=
-
> a =
Tc Pc
𝑎𝑀𝐼𝑋 = ∑ ∑ 𝑦𝑖 𝑦𝑗 𝑎𝑖𝑗 ya
,
=>
yea 2y
, ,
+ 9 + ,

y , 2 ,


Substituting b f (Tc
&
,
,
P ) Cordur
f(Tc
=

b
-
=
𝑖 𝑗 , . >
- =
0. )
,


these into the
𝑎𝑖𝑗 = 𝑎𝑗𝑖 = √𝑎𝑖𝑖 𝑎𝑗𝑗 (1 − 𝑘𝑖𝑗 ) accentric factor
equation for
Mixing
elsa 𝑏𝑀𝐼𝑋 = ∑ 𝑦𝑖 𝑏𝑖
-



𝑖
= >
y ,
b
,
+
y ,
b
~ =

-log ,

(
𝑣
+
𝜕𝑃
𝛥ℎ𝑅 (𝑇, 𝑃) = 𝑅𝑇(𝑧 − 1) + ∫ [𝑇 ( ) − 𝑃] 𝑑𝑣 RT(z-1) =
d =
RT(t -
1) -




2
∞ 𝜕𝑇 𝑣

em()
𝑣
𝜕𝑃 𝑅
𝛥𝑠 𝑅 (𝑇, 𝑃) = 𝑅 𝑙𝑛 𝑧 + ∫ [( ) − ] 𝑑𝑣
∞ 𝜕𝑇 𝑣 𝑣
rInz -Edu ·
+ :
Rit +


𝑣
1 𝑃
𝑙𝑛 𝜑 = (𝑧 − 1) − 𝑙𝑛 𝑧 + ∫ ( − ) 𝑑𝑣
∞ 𝑣 𝑅𝑇

~

1 𝜕𝑃 1
𝑙𝑛𝜑𝑖 = − 𝑙𝑛𝑧𝑀𝐼𝑋 + ∫ [ ( ) − ] 𝑑𝑉
𝑅𝑇 𝜕𝑛𝑖 𝑉
Intrix In ) =
- +


𝑉




Partial Molar
(U) Activity coefficients:

𝑙𝑛𝛾𝑖 = (
𝜕(𝐺 𝐸 /𝑅𝑇)
)
-chri i
,
o
P (v" -

v") : a " av -




&
specific Helmholtz
V
energy

--For-a

~
-

Properties 𝜕𝑛𝑖 𝑇,𝑃,𝑛 𝑗 reference
State
Asymmetric 𝛾𝑖
Activity
> 𝛾𝑖∗ =
𝛾𝑖∞ >
-
symmetric activity crefficient at infinite dilution
Coefficient

ideal
Vapour-liquid equilibrium: vapor liquid ideal
:


At low Pressure :
↓ d
Component 𝑦𝑖 Ideal mixture :
y
P =
xi P Real mixture : P ViciP
𝐾𝑖 = y:
:

>
- :


Volatility 𝑥𝑖




i
𝑉 U
. > 1 ,
repulsive forces prevail Ceasier to bril
𝑉𝑎𝑝𝑜𝑢𝑟 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝛼 =
𝐹 Vi < 1 attractive furces prevail (harder to boil
𝑧𝑖 𝐾𝑖 ,




&
𝑦𝑖 =
1 + 𝛼(𝐾𝑖 − 1) Vi
: k
+ P


- v. s : (1 )

F =D
y x
-




, ,

= d =



(1 y )x ,
F
-




, zi ,




T 2x ,

y =

, 1 + (a 1)x ,
-




I
↳ ,:

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller Bung. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $10.96. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

52355 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$10.96
  • (0)
Add to cart
Added