What is Physical Chemistry? Mathematically predictive theories - - PDF document

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Chemistry 313

• Dr. Caleb Arrington

10:30 am - 11:20 am M,W,&F

Office RMSC 306-A

Lab: Wednesday 2:00 - 5:00

What do we do the first day of every class? syllabus

What is Physical Chemistry?

Mathematically predictive theories applied to problems in chemistry.

Using mathematics to solve questions in chemistry. More similar to physics than organic synthesis.

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The problems answered by p-chem

Because we are expecting mathematics to solve our chemistry question we will be asking rather simple questions.

What is the pressure of 1 mol CO2 at 295 K in a 5 L vessel?

The first half of the course is largely about gases because they are easiest to model. Currently mathematics is not wonderful at answering important questions like:

ClH2C C H C H CH2Cl KOH

?

But it is getting better at this. C C C CH H H H

Mathematics is not useful for solving every problem in chemistry

In fact, it may not be useful for solving many problems in chemistry.

Empirically determined: solubility rules, reaction mechanisms, E2 vs. SN1., active site of an enzyme. Theoretically calculated: pH of a buffer solution, reaction rate, x-ray structure of a protein.

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How is P-Chem Structured?

There are three main subdivisions:

Thermodynamics Ch. 1 - 11

The macroscopic study of systems in equilibrium

Kinetics Ch. 18-19 (in lab)

The macroscopic study of systems approaching equilibrium

Quantum mechanics Chem 314

Microscopic study of atoms and molecules

Mathematics is critical to P-Chem

What mathematics am I going to need to be able to use?

Prerequisites for Chem. 313: Calculus I & II

Differentiation: Integration:

dV ) d(aV2

dx e d

2

• ax

Be able to use an integral

• table. There is a good one on
• ur web page.

dV V 1 dp p a

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Rules for exponents:

Textbook Appendix B. pg. 547 ChemActivity M1 pg. 329

lnV 1 lnV 0 =

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Look at math review in Appendix B. (B.2, B.4, B.6) Read sections 1.1 - 1.4. Traditional textbook: It is very thorough and requires slow reading. Terrific figures and problems. Inquiry based workbook covering the topics of kinetics and thermodynamics. Look over activities G1 - G1B before lab.

Texts for the Course:

Work through ChemActivity M1 (pg 329 - 334)

Things you already know (Highlights for starting thermodynamics) Intensive property: vs. Extensive property:

Does not depend on the amount

• f material.

Depends on the amount of material. The division of two extensive properties yields an intensive property. mass vol

= density

km s speed

Tables only list intensive properties.

vol mole Vm

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Energy

What is energy?

This is difficult to answer. Units:

kg m2 s2

= 1 joule 1 heart beat Forms of energy:

Kinetic; T = 1/2 mv2 Potential; V = mgh

V q 1 q 2 r

gravitational columbic

Also: electrical, mechanical, electromagnetic Thermal energy;

U = 3/2 RT (for a monatomic ideal gas) A property of the universe that is conserved.

Chapter 1 - Gases

A system we can describe mathematically What properties must we measure to quantify a gas?

Pressure, temperature, volume and # of moles

Use molar volume, Vm p(Vm,T) = Pressure is a function of molar volume and temperature. If volume and temperature are specified pressure is immediately known. ?

R T Vm b a T Vm Vm b

This is an equation of state.

6 kg m s2 m2

Units for gases

Pressure

p force area =

= kg m2

s2 m3

energy volume = pressure pressure volume = energy F A p = m g A = m = vol. density

How we measure pressure

A·h · A · g p = ·g · h

We measure the height a liquid is raised by a pressure.

p = 645 mm Hg 750 mm Hg = pascal

1 bar 1 105 Pa

• Pg. 6

=

Units for gases

Volume: Temperature:

The size of the container. What is temperature anyway? An indication of the direction in which heat will flow.

More rigorous definitions to come.

Unit: Kelvin (K)

T K ( ) C ( ) 273.15

° Zeroth law of thermodynamics: Heat flows from a high temperature body to a low temperature body. 1 liter (L) = 1 dm3 = 1x10-3 m3

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Vm 0.08314 L bar K mol 500 K 100 bar

How the variables (p,Vm, & T) effect each other

First observed by Robert Boyle (1662)

p V

Const Temp. p Vm 300 K constant V

p Vm T R T Vm

Isotherm

Ideal gas constant R = What is the volume of CO2 treated as and ideal gas at 500 K and 100 atm? Vm p T ( ) R T p = 0.41 L/mol Actual molar volume of CO2 is 0.37 L/mol

Good to 1 significant figure. mol K bar L 08314 0.

If the ideal gas law is a state equation then how is volume effected by temperature?

p Vm T R T Vm

T Vm y = x m·

Isobar: constant p =

Vm p T ( ) This intersection is at

• 273.15 °C or 0 K

+ b

Slope = ?

Is the pressure greater

• r smaller for this state?

Interesting intersection at Vm = 0

R p T

R/p

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Units for the gas constant R p Vm T

p Vm 1/T SI units

kg m s2 m3 mol

1 K R

8.314 kg m2 s2 K mol

=

J K mol

common atm L 1 K

0.0821 L atm K mol

Useful conversion:

R R 8.314 J K mole 0.0821 L atm K mole

= 101.3 J/ L atm

practical bar L 1 K

mol K bar L 08314 0.

p Vm

• Const. Temp.

Fixed volume

How change is expressed?

A differential is used to express change.

dP dV m Constant T

p Vm

T

Partial differential

T

p Vm =

p Vm

T

Slope is always negative. Pressure always decreases as volume increases.

p R T Vm

Differentiate the ideal gas equation

dp = R T Vm

2

dV m

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The derivative leads us back to calculus

H(T) T

T H

T

lim

How would you write the derivative shown by the green tangent line?

1.

Where is the derivative largest?

2.

What is the derivative here? What is the derivative here?

=

T H T ( ) d d

Where is the derivative negative? The derivative reports the change in a function What does an integral of a function report? The area encompassed by that function. (The area under the curve.) P(V) V

V1 V2

What are the units of the shaded area?

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