50 Chemistry

8/11/2019 50 Chemistry

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The product of the uncertainty in the position (x) and the uncertainty in momentum (p)is always constant.

This is equal to or greater than h/4p, where h is planks constant.p = m

v where

m is the mass of the particle and

v shows the uncertainty in velocity.Thus, the uncertainty equation is

p. x h/4p

The mathematical expression for the Heisenberg's uncertainty principle

p. x h/4p


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By using the above equation, the calculated value of p is the minimum value of p for anyparticular value of x. Similar the calculated value of x also shows the minimum value of xfor any specific value of p.

As p = m. v,

So the equation becomes (m. v). x h/4p

Or

(v)(x) h/4pm

Principle of :

) A light phenomenon is used for measuring the position and momentum of electron.

) The microscope is used to see the reflected photon.

) The position and momentum of electron is disturbed due to hitting with photon.

) The e- has wave particle duality and it shows uncertainty position and momentum.

Significance of Heisenberg Uncertainty Principle

Heisenberg Uncertainty Principle is good for all the objects and is more significant formicroscopic particles.

For example,

i) The light on the running rat from the torch cannot change the direction and position of

rat.

Or if mass of particle is 1 mg then by using Heisenbergs uncertainty principleformula.

(v)(x) = (h/4) m

By putting the value of h = 6.626 x 10-34 kg m2s

-1,

m = 1 mg or 10-6

kg.

So (v) (x) = (6.626 x 10-34

/ 4) x 3.1416 x 10-6

,

Or (v) (x) = 10-28

m2s

-1

ii) If the mass of an electron is 10-27kg and the uncertainty in position is equal to 10-11m then

find the uncertainty in velocity.Solution:

(v) (x) = (h4) m,

Put the value of x =10-11m,h = 6.626 x 10

-34kg m

2s

-1and m =10

-27kg.

So (v) = (h4) m (x),


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Or

v = 6.626x103443.141610271011

v = 5.27 x 105

m s-1

iii) (

E S

. A . H

.

Time-dependent Schrdinger equation(general)

T T I S E

S , S E,

. T .

A .

Plug this into the Schrdinger Equation.

Put everything that depends on on the left and everything that depends on on the right.


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Since we have a function of only set equal to a function of only ,they both must equal a

constant. In the equation above, we call the constant , (with some knowledge of the

outcome). We now have an equation in set equal to a constant

which has a simple general solution,

and an equation in set equal to a constant

which depends on the problem to be solved (through ).

The equation is often called the Time Independent Schrdinger Equation.

Here, is a constant. The full time dependent solution is.


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S H ".

E -() 4 .

I .

Q

T :

D

D

E

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I . Q

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I H.

T 3 .

T : =1,2,3,4,..

A : = 0,1,2,3,1

M : =,1,12,.,1

:


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:

: .

:

I . T

.

I N .

E; A : N (=0.192) C(=0.099)

I R: N(=0.095) C(=0.181)

I .

I .

C . I 2

.

R , , .

:

H

H H .

D

S

C.


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:

I P .

I . T

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I .

S U

D 2 :

C +

.

G , .

I . B H C 2 G

M B F H.

T B H

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S

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T .

BH C . I M B F H 1919.

T BH

. I

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T .

L+() + F

-() > LF() LE = 1047J

M+() + O

2() > MO()LE = 3916J


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, (NC)

788 /

.

NC() N+() + C () LH= 788 /

N+() + C() NC() LH = 788 /

W ,

.

B H , , ,

.

:

I .

I .

C .

I .I

.

I . I

+

E: H2O .

:

L .

P


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: W 2

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:

1. D .

2. L .

3. D .

D

=

D , M , .

:

I .

I 2 .

T

.

H L V B

.

:

i) A 2 .

ii) T () . I

2 .

iii)D 2 .

iv) G .

:


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I

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I .

:

.

T .

E MO MO.

A B :

B 2

. F W.H F.L 1927

2 .

.

.

R .

C

. I 2

.

B 2 .

P F.H R.S. M 1932.

T .


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A

.

2 :

B M

A .

B .

C .

: I 2 .

o S 1

o D 2

o T 3

B B

. B .

:

I 2 .

I 2 ,

, 3 .

: 3.


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SOLUTION

1) D L S.1 .JPG

2) C 2 .T 4.

3) C .T

3.

4) D .

4/3= 1.33 1.33

:

C : I . C ,

3 .

: T . O

:

.

' :

I XR

. T S W.L. B.

T :-


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W XR

.

T XR

B L.

The path difference between the ray reflected at atom X and the ray reflected at atom Y can be

seen to be 2YX. From the Law of Sines we can express this distance YX in terms of the lattice

distance and the X-ray incident angle:

If the path difference is equal to an integer multiple of the wavelength, then X-rays A and B (and

by extension C) will arrive at atom X in the same phase. In other words, given the following

conditions:

then the scattered radiation will undergo constructive interference and thus the crystal willappear to have reflected the X-radiation. If, however, this condition is not satisfied, then

destructive interference will occur. Braggs Law

=2

W,

=

= ( )

= ( )


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=

T B B

, .

:

I .

I .

I .

I , .

T X

I . T

.

:

M . T 2 .

T C C P H P .

:

i) C

I .

ii) C . T

R .


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T CC

C+ 8 C

.

T ,

, . C

'D W A T' .

T , , :

a = 2r-

A , C+ C

, ,

:

d = r-+ 2r++ r-= 2r++ 2r-

T C+ CC

.

U P , :

d2= a

2+ a

2+ a

2= 3a

2= 3 4r-

2= 12r-

2

d = 2(3)1/2

r-

,

2r-+ 2r+= 2r(3)1/2

r-

r+/ r-= (3)1/2

1 = 0.732

A 73% , CC ,

M , . I ,


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. I ,

. A .

'

o T M .

: T

.

M M .

:

: T . I .

:

()/ () = (2 /RT) = (/)

=

() =

()=

=

=

R , T

E:

S C

1 0.12

1.1 0.0126

2 1.73


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: I

I .

: I . T

.

I 3 : GAS, LIQUID AND SOLID.

.

:I .

: I

. I .

4 :

Z

F

S

T .

: ,

: E B,

MM M M.

W G :

C V P

C P P

C T P


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F : T L . I

. I

.

:

I

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I .

I Q

.

: I

.

:

T C R C B

T

. This behavior can be explained with the Clausius-Clapeyron equation.

It is a way of characterizing a discontinuous phase transition between 2

phases of matter of a single constituent.

Debye-Huckel theory of strong electrolytes

Peter Debye and Erich Huckel was proposed the Debye-Huckel

theory.It is a linearilized Poisson Boltzman model. This model assumes

an extremely simplified model of the electrolyte solution.

This theory based on 3 assumptions of how ions act in solution:-

I. Electrolytes completely dissociate into ions in solution.

II. Solutions of Electrolytes are very dilute, on the order of 0.01 M.


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Each ion is surrounded by ions of the opposite charge, on average.

Debye and Hckel developed the following equation to calculate the mean ionic activity

coefficient :

log=1.824106(T)3/2z+zI

where

is the dielectric constant,

z+and zare the charges of the cation and anion, respectively, and Iis a quantity called the ionic strength of the solution.

The above equation is known as the Debye-Hckel Limiting Law. The ionic strength iscalculated by the following relation:

I=12imiz2i

where miand ziare the molality and the charge of the ith ion in the electrolyte. Sincemost of the electrolyte solutions we study are aqueous (=78.54)and have atemperature of 298 K, the Limiting Law reduces to

log=0.509z+zI.

Galvanic cells:

It is also known as voltaic cell.

It was named after Luigi Galvani or Alessandro Volta

respectively.

Galvanic cell is an electrochemical cell that releases

energy.

It consists of 2 half cells joined by two salt bridge.


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These are the devices in which electron transfer occurs via

an external circuit.

If a strip of Zn is placed in a solution of CuSO4, Cu is deposited on the

Zn and the Zn dissolves by forming Zn2+.

Zn is spontaneously oxidized to Zn2+ by Cu2+.

The Cu2+is spontaneously reduced to Cu0by Zn.

Galvanic cells consist of :

Anode: Zn2+(aq) + 2e2

Cathode: Cu2+(aq) + 2e-Cu(s)

Salt bridge: cations move from anode to cathode, anions move from cathodeto anode.

Below is a galvanic cell in which the reaction between A+and B is exothermic, with a G of -10

kJ/mol under standard conditions and a value of E0of 0.10 V.


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Concentration Cells:

It is an electrolyte cell.

It is comprised of two half cells with the same electrodes but differing

in concentration.

It acts to dilute the more concentrations solutions.

Uses of concentration cells

A pH meter is a specific type of concentration cell that uses the basic setup

of a concentration cell to determine the Ph or the acidity/basicity of a

specific solution.

Electrochemical series:

The electrochemical series is built up by arranging various redox

equilibria in order of their standard electrode potential.

Most negative E values are placed at the top of the electrochemical

series. Most positive at the bottom.

equilibrium E (volts)

-3.03

-2.92

-2.87

-2.71

-2.37

-1.66

-0.76

-0.44

-0.13


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0

+0.34

+0.80

+1.50

EMF: It is the maximum potential difference between 2 electrodes of a

galvanic cells.

: , ,

D : I .

Zero-Order Reaction: The rate of reaction is a constant. When the limiting reactant is

completely consumed, the reaction abrupts stops.

Differential Rate Law: r= k

The rate constant, k, has units of mole L-1

sec-1

.

First-Order Reaction: The rate of reaction is directly proportional to the concentrationof one of the reactants.

Differential Rate Law: r= k[A]

The rate constant, k, has units of sec-1

.

Second-Order Reaction: The rate of reaction is directly proportional to the square of the

concentration of one of the reactants.

Differential Rate Law: r= k[A]2

The rate constant, k, has units of L mole-1sec-1.


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P,

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F D .

P

CO2 H2O.

P

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T .

T .

L . H

.

50 Chemistry

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