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Flashcards in EQUATIONS Deck (91):
1

RESISTANCE

(of a material used as a resistor in a circuit)

UNITS=?

 

R=ρL/A

UNITS: Ω (Ohms)

  • ρ=resistivity of the material 
  • L=length of material 
  • A=cross-sectional area 

 

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2

INTENSITY of a wave

=waves/m2

3

VELOCITY of a wave

V=λf

4

VOLTAGE in a circuit (3) 

V=PE/q

V=Ed

V=Kq/r

5

KINETIC ENERGY

KE=½mv2

6

HARMONICS

FOR:

  1. String or pipe with MATCHING ends--
    • both nodes or antinodes
  2. String or pipe open at ONE end --
    • with one node and one antinode

λ=?

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 λ = 2L/n

 λ = 4L/n

7

Snell's Law

n1sinθ1 = n2sinθ2

8

Young's Double Slit Experiment

 

x = λL/d

  • x is the distance between fringes
  • λ is the wavelength of light used
  • d is the distance between the two slits
  • L is the distance between the “double slit” and the final screen

9

TORQUE (3)

T=Fl

T=mgl

T=Frsinθ

10

GRAVITATIONAL PE

IN SPACE

PEgrav= - Gmm/r

11

PEELASTIC

PEelastic=½kx2

12

PEELECTRICAL (3)

PEelec=Kqq/r

PEelec=qEd

PEelec=qV

 

13

POTENTIAL ENERGY STORED IN A CAPACITOR (3)

PEcapacitor=½QV

PEcapacitor=½CV2

PEcapacitor=½Q2/C

14

MECHANICAL ENERGY (ME)

ME=KE+PE

15

WORK (2)

W=Δ ENERGY

W=Fdcosθ

16

RAMPS

Fm=mg (h/d)

  • h is the height of the ramp
  • d is the distance along its hypotenuse

17

LEVERS

Fm=mg( L/ L)

  •  L1 is the lever arm for the mass
  • L2 is the lever arm for the applied force

18

PULLEYS

Fm= mg / ( # of vertical ropes directly lifting the mass)

19

POWER (4)

P=ΔE/t

P=W/t

P=Fdcosθ

P=Fvcosθ

20

HYDRAULIC LIFTS (2) 

Fm=mg (h1/h2)

Fm=mg (A1/A2)

h1=distance traveled by the large plunger

h2=distance traveled by the small plunger

A1 =cross-sectional area of the small plunger

A2 cross-sectional area of the large plunger

21

FORCE FOR A CONSTANT ELEC. FIELD

F=qE

22

FORCE FOR A POINT CHARGE ELEC. FIELD

F=Kqq/r2

(Coulomb's Law)

23

STRENGTH OF FIELD ("E") FOR A CONSTANT ELEC. FIELD (2)

E=F/q

E=V/d

 

24

STRENGTH OF FIELD ("E") FOR A POINT CHARGE ELEC. FIELD 

E=Kq/r2

25

ELEC. POTENTIAL ENERGY FOR A CONSTANT ELEC. FIELD

PEelec=qEd 

26

ELEC. POTENTIAL ENERGY FOR A POINT CHARGE ELEC. FIELD

PEelec= (+/-) Kqq/r

 

27

VOLTAGE FOR A CONSTANT ELEC. FIELD

V=Ed

28

VOLTAGE FOR A POINT CHARGE ELEC. FIELD

V=Kq/r

29

Fmagnetic EXERTED ON A CHARGED PARTICLE,q, MOVING IN A MAGNETIC FIELD,B

F=qvBsinθ

30

CURRENT

I=Δq/Δt

31

OHM'S LAW

V=IR

32

ELECTRICAL POWER (3) 

P=IV

P=I2R

P=V2/R

33

VELOCITY OF A WAVE

V=λf

34

THE BEAT FREQUENCY

fbeat= |f- f2|

35

THE DOPPLER EFFECT (2)

Δf/fsource= v/c

Δλ/λsource= v/c

36

HARMONICS FOR A STRING OR PIPE WITH MATCHING ENDS--BOTH NODES OR BOTH ANTINODES

L= nλ/2

or λ=2L/n

37

HARMONICS FOR A PIPE OPEN AT ONE END ONLY--ONE NODE AND ONE ANTINODE

L=nλ/4

OR λ=4L/n

38

ENERGY OF A PHOTON

E=hf

39

INDEX OF REFRACTION, "n"

n=c/v

40

FOCAL POINT

FOR MIRRORS ONLY

f=½r

41

THIN LENS EQUATION

1/p + 1/q = 1/f

42

MAGNIFICATION

M= -q/p

43

OPTICAL POWER

P= 1/f

44

TWO LENS SYSTEMS:

MAGNIFICATION

M=m1m2

45

TWO LENS SYSTEMS:

POWER

P=p1+p2

46

FRICTION (2) 

Fkkmgcosθ

Fssmgcosθ

 

47

THE CHARGE OF AN ELECTRON=

(in Coulombs)

-1.6 x 10-19C

48

THE IDEAL GAS LAW

PV=nRT

49

THE FUNDAMENTAL THERMODYNAMIC RELATION

ΔG=ΔH-TΔS

50

EQUATION RELATING KEQ TO GIBBS FREE ENERGY (2 VARIATIONS)

 

SPONTANEOUS IF ΔG IS (+/-)?

ΔG= -RTlnKeq

OR

Keq=e-ΔG/RT

SPONTANEOUS IF ΔG IS NEGATIVE

("EXERGONIC")

 

51

HEAT CAPACITY

c =ΔQ/ΔT

52

SPECIFIC HEAT

q=McΔT

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53

FREEZING POINT DEPRESSION

The freezing point of a liquid is depressed when a non-volatile solute is added according to:

∆T = kfmi 

kis a constant

54

RAOULT'S LAW

Vapor Pressure w/ a Non-Volatile Solute =

Vapor Pressure w/ a Non-Volatile Solute = (mole fraction of the pure solvent, X)*(Vp of the pure solvent, Vp°)
Vp = XVp°  

x=mole fraction of pure solvent

Vp=Vapor pressure of pure solvent
 

55

RAOULT'S LAW

TOTAL Vapor Pressure w/ a Volatile Solute = 

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Vptotal 

= Vpsolvent + Vpsolute 

( Xsolvent Vp°solvent) + (Xsolute Vp°solute)

 (mole fraction, X, of solvent* Vp° of the solvent) + (mole fraction of the solute* Vp° of the solute)

56

OSMOTIC PRESSURE, Π

Π= iMRT

i = # of ions formed in solution
M is the solute molarity
R is the gas constant
T is the absolute temperature

57

BOILING POINT ELEVATION

∆T = kbmi

 

  • where kb is a constant,
  • m is MOLALITY (NOT molarity) 
  • i is the number of ions formed per molecule

 

58

NERNST EQUATION

Ecell =  E° - (.06/n) * log ([lower]/[higher])

 

n=# moles of electrons transferred

 Fe3+(aq)→Fe(s)

=3 e's transferred

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59

GIBBS FREE ENERGY

ΔG=ΔH-TΔS

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60

GIBBS FREE ENERGY #3

 in association with:

Free energy and Cell potentials

(+/-) ∆G =  SPONTANEOUS/ FAVORABLE?

 ∆G = -nFE

n is the number of moles of electrons transferred

F is Faraday’s constant

E is the emf of the cell

NEGATIVE ∆G =  SPONTANEOUS/ FAVORABLE?

^^OR A POSITIVE ^^

61

GIBBS FREE ENERGY #2

 in association with:

Free energy and Equilibrium Constants

(+/-) ∆G =  SPONTANEOUS/ FAVORABLE?

 ∆G = - RTlnKeq

 ∆G = free energy at any moment
 ∆G°  = standard-state free energy
R = ideal gas constant = 8.314 J/mol-K
T = temperature (Kelvin)
lnQ = natural log of the reaction quotient

(+/-) ∆G =  SPONTANEOUS/ FAVORABLE?

DEPENDS ON VALUE OF Keq

SPONTANEOUS:

∆G  < 0
K > 1

NON-SPONTANEOUS:

∆G  > 0
K < 1

62

GIBBS FREE ENERGY #1

 in association with:

TEMPERATURE and Free Energy

(+/-) ∆G =  SPONTANEOUS/ FAVORABLE?

 ∆G =∆H -T∆S

NEGATIVE ∆G= SPONTANEOUS / FAVORABLE

63

DALTON'S LAW OF PARTIAL PRESSURES 

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Ptotal=P1+P2+P3...

64

GRAHAM'S LAW

(EFFUSION & DIFFUSION)

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E1/E2=√MW2/√MW1

65

DENSITY, ρ

ρ=m/v

66

DENSITY OF WATER=?

(2) 

1000 kg/m3 OR 1.0 g/cm3

REMEMBER:

1 cm3 = 1mL

1 L H2O=1 kg

1 mL H2O=1 g

67

SPECIFIC GRAVITY

 FOR OBJECTS FLOATING IN LIQUIDS:

WHAT IS SIGNIFICANCE OF  THE FRACTION OF THE OBJECT THAT IS SUBMERGED IN WATER?

 

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SG= ρsubstancewater

ρ=density, m/v

ρwater=1 g cm3 or 1000 kg/m3 

FOR OBJECTS FLOATING IN WATER:

FRACTION OF OBJECT SUBMERGED IS EQUAL TO THE SPECIFIC GRAVITY!

68

BUOYANT FORCE, Fbuoyant

 Fbuoyant=ρvg

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69

GENERAL PRESSURE FORMULA 

P=F/A

70

FLUID PRESSURE 

P=ρgh

71

FLOW RATE

Q=AV

A=total cross-sectional area

72

BERNOULLI'S EQUATION

K=P+ρgh+½ρv2

  • P=random vibrational energy of the fluid molecules
  • ρgh= PEgravitational per volume of the fluid
  • h=height (NOT depth)
  • ½ρv2 = KE per volume of moving fluid molecules

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73

WORK FUNCTION, φ

KE=E-φ

74

ENERGY OF A PHOTON, "E"

E=hf

75

PERCENT % MASS

% MASS=

Mass of ONE element/TOTAL mass of cpd

x 100%

76

LAW OF MASS ACTION 

Keq=?

Keq=

[products]X / [reactants]Y

77

Qeq 

MORE___ THAN ___

RXN PROCEEDS TO THE ___

MORE REACTANT THAN PRODUCT

RXN PROCEEDS TO THE RIGHT

78

Q>Keq 

MORE___ THAN ___

RXN PROCEEDS TO THE ___

MORE PRODUCT THAN REACTANT

RXN PROCEEDS TO THE LEFT

79

HARDY-WEINBERG EQUILIBRIUM (2)

p2+2pq+q2=1

p+q=1

p is the frequency of the "A" allele in the population

q is the frequency of the "a" allele in the population

p2 represents the frequency of the homozygous genotype AA

q2 represents the frequency of the homozygous genotype aa

2pq represents the frequency of the heterozygous genotype Aa

 

 

80

"FORMAL CHARGE"

FORMAL CHARGE=

VALENCE - ASSIGNED

81

HÜCKEL'S RULE

4n + 2π

To exhibit aromaticity, a ring system must have exactly 4n + 2π electrons

82

CAPACITANCE

C= Q/V

83

INTENSITY IN dB

 =10*log (I/Io)

 

I=intensity of wave (in W/m2)

Io=threshold of human hearing (given)

84

PAPER OR THIN LAYER CHROMATOGRAPHY (TLC)

Rf=?

Rf= DIST. TRAVELED BY COMPONENT /DIST. TRAVELED BY SOLVENT

85

MICHAELIS-MENTEN EQUATION 

Vo= Vmax [S] / Km+[S]

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86

MICHAELIS CONSTANT, Km 

 

Km IS A MEASURE OF...?

Km=[S] at ½Vmax

KmMEASURE OF AN ENZYME'S AFFINITY FOR ITS SUBSTRATE

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87

LINEWEAVER-BURKE PLOTS

Y-INTERCEPT=?

1/Vmax

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88

LINEWEAVER-BURKE PLOTS

X-INTERCEPT=?

-1/Km

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89

LINEWEAVER-BURKE PLOTS

SLOPE=?

Km/Vmax

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90

CAPACITANCE

(NOT PEcapacitor !) 

How do Capacitance and PEcapacitor relate?

C=Q/V

 

Once solving for C, plug that into one of the 3 PEcapacitor formulas:

=½QV

CV2   OR

=½Q2/C

 

91

CAPACITANCE

wrt AREA OF OVERLAP, A b/t plates

and DISTANCE, D  b/t plates

C=εA/d

 

  • C is the capacitance (Farads)
  • A is the area of overlap of the two plates (m2)
  • ε is the dialectric constant of the material between the plates
    • for a vacuum, εr = 1
  • d is the separation between the plates (m)

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