EQUATIONS

Question 1

Circuits

RESISTANCE

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

UNITS=?

Answer 1

R=ρL/A

UNITS: Ω (Ohms)

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

Question 2

INTENSITY of a wave

Answer 2

=waves/m²

Question 3

VELOCITY of a wave

Answer 3

V=λf

Question 4

VOLTAGE in a circuit (3)

Answer 4

V=PE/q

V=Ed

V=Kq/r

Question 5

KINETIC ENERGY

Answer 5

KE=½mv²

Question 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=?

Answer 6

λ = 2L/n

λ = 4L/n

Question 7

Snell’s Law

Answer 7

n₁sinθ₁ = n₂sinθ₂

Question 8

Young’s Double Slit Experiment

Answer 8

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

Question 9

TORQUE (3)

Answer 9

T=Fl

T=mgl

T=Frsinθ

Question 10

GRAVITATIONAL PE

IN SPACE

Answer 10

PE_grav= - Gmm/r

Question 11

PE_ELASTIC

Answer 11

PE_elastic=½kx²

Question 12

PE_ELECTRICAL (3)

Answer 12

PE_elec=Kqq/r

PE_elec=qEd

PE_elec=qV

Question 13

POTENTIAL ENERGY STORED IN A CAPACITOR (3)

Answer 13

PE_capacitor=½QV

PE_capacitor=½CV²

PE_capacitor=½Q²/C

Question 14

MECHANICAL ENERGY (ME)

Answer 14

ME=KE+PE

Question 15

WORK (2)

Answer 15

W=Δ ENERGY

W=Fdcosθ

Question 16

RAMPS

Answer 16

F_m=mg (h/d)

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

Question 17

LEVERS

Answer 17

F_m=mg( L₁ / L₂ )

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

Question 18

PULLEYS

Answer 18

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

Question 19

POWER (4)

Answer 19

P=ΔE/t

P=W/t

P=Fdcosθ

P=Fvcosθ

Question 20

HYDRAULIC LIFTS (2)

Answer 20

F_m=mg (h₁/h₂)

F_m=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

Question 21

FORCE FOR A CONSTANT ELEC. FIELD

Answer 21

F=qE

Question 22

FORCE FOR A POINT CHARGE ELEC. FIELD

Answer 22

F=Kqq/r²

^{<span>(Coulomb’s Law)</span>}

Question 23

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

Answer 23

E=F/q

E=V/d

Question 24

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

Answer 24

E=Kq/r²

Question 25

**ELEC. POTENTIAL ENERGY FOR A CONSTANT ELEC. FIELD**

Answer 25

**PE_elec=qEd**

Question 26

**ELEC. POTENTIAL ENERGY FOR A POINT CHARGE ELEC. FIELD**

Answer 26

**PE_elec= (+/-) Kqq/r**

Question 27

**VOLTAGE FOR A CONSTANT ELEC. FIELD**

Answer 27

**V=Ed**

Question 28

**VOLTAGE FOR A POINT CHARGE ELEC. FIELD**

Answer 28

**V=Kq/r**

Question 29

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

Answer 29

**F=qvBsinθ**

Question 30

**CURRENT**

Answer 30

**I=Δq/Δt**

Question 31

**OHM'S LAW**

Answer 31

**V=IR**

Question 32

**ELECTRICAL POWER (3)**

Answer 32

**P=IV** **P=I²R** **P=V²/R**

Question 33

**VELOCITY OF A WAVE**

Answer 33

**V=λf**

Question 34

**THE BEAT FREQUENCY**

Answer 34

**f_beat= |f₁ - f₂|**

Question 35

**THE DOPPLER EFFECT (2)**

Answer 35

**Δf/f_source= v/c** **Δλ/λ_source= v/c**

Question 36

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

Answer 36

**L= nλ/2** ## Footnote **or λ=2L/n**

Question 37

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

Answer 37

**L=nλ/4** ## Footnote **OR λ=4L/n**

Question 38

**ENERGY OF A PHOTON**

Answer 38

**E=hf**

Question 39

**INDEX OF REFRACTION, "n"**

Answer 39

**n=c/v**

Question 40

**FOCAL POINT** **FOR MIRRORS ONLY**

Answer 40

**f=½r**

Question 41

**THIN LENS EQUATION**

Answer 41

**1/p + 1/q = 1/f**

Question 42

**MAGNIFICATION**

Answer 42

**M= -q/p**

Question 43

**OPTICAL POWER**

Answer 43

**P= 1/f**

Question 44

**TWO LENS SYSTEMS:** **MAGNIFICATION**

Answer 44

**M=m₁m₂**

Question 45

**TWO LENS SYSTEMS:** **POWER**

Answer 45

**P=p₁+p₂**

Question 46

**FRICTION (2)**

Answer 46

**F_k=μ_kmgcosθ** **F_s=μ_smgcosθ**

Question 47

**THE CHARGE OF AN ELECTRON=** **(in Coulombs)**

Answer 47

**-1.6 x 10^-19C**

Question 48

**THE IDEAL GAS LAW**

Answer 48

**PV=nRT**

Question 49

**THE FUNDAMENTAL THERMODYNAMIC RELATION**

Answer 49

**ΔG=ΔH-TΔS**

Question 50

**EQUATION RELATING K_EQ TO GIBBS FREE ENERGY (2 VARIATIONS)** **SPONTANEOUS IF ΔG IS (+/-)?**

Answer 50

**ΔG= -RTlnK_eq** **_OR** **K_eq=e^-ΔG/RT** **_SPONTANEOUS IF ΔG IS NEGATIVE_** **("EXERGONIC")**

Question 51

**HEAT CAPACITY**

Answer 51

**c =ΔQ/ΔT**

Question 52

**SPECIFIC HEAT**

Answer 52

**q=McΔT**

Question 53

**FREEZING POINT DEPRESSION**

Answer 53

The freezing point of a liquid is depressed when a non-volatile solute is added according to: **∆T = k_fmi** k_f is a constant

Question 54

**RAOULT'S LAW** **Vapor Pressure w/ a Non-Volatile Solute =**

Answer 54

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**

Question 55

**RAOULT'S LAW** **TOTAL Vapor Pressure w/ a Volatile Solute =**

Answer 55

**Vp_total** **= Vp_solvent + Vp_solute** **( X_solvent Vp°_solvent) + (X_solute Vp°_solute)** (**mole fraction, X,** of sol**_vent_**\* **Vp°** of the sol**_vent_**) + (**mole fractio**n of the sol**_ute_**\* **Vp**° of the sol**_ute_**)

Question 56

**OSMOTIC PRESSURE, Π**

Answer 56

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

Question 57

**BOILING POINT ELEVATION**

Answer 57

**∆T = k_bmi** ## Footnote * where k_b is a constant, * m is **MOLALITY** (**NOT** molarity) * i is the number of ions formed per molecule

Question 58

**NERNST EQUATION**

Answer 58

**E_cell = E° - (.06/n) \* log ([lower]/[higher])** n=# moles of electrons transferred **Fe³⁺(aq)→Fe(s)** **=3 e's transferred**

Question 59

**GIBBS FREE ENERGY**

Answer 59

**ΔG=ΔH-TΔS**

Question 60

**GIBBS FREE ENERGY #3** _in association with:_ **Free energy and Cell potentials** (+/-) ∆G = SPONTANEOUS/ FAVORABLE?

Answer 60

**∆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** E°**^^**

Question 61

**GIBBS FREE ENERGY #2** _in association with:_ **Free energy and Equilibrium Constants** (+/-) ∆G = SPONTANEOUS/ FAVORABLE?

Answer 61

**∆G = - RTlnK_eq** ## Footnote ∆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 K_eq** _SPONTANEOUS_: ∆G \< 0 K \> 1 _NON-SPONTANEOUS:_ ∆G \> 0 K \< 1

Question 62

**GIBBS FREE ENERGY #1** _in association with:_ **TEMPERATURE and Free Energy** (+/-) ∆G = SPONTANEOUS/ FAVORABLE?

Answer 62

**∆G =∆H -T∆S** **NEGATIVE** ∆G= SPONTANEOUS / FAVORABLE

Question 63

# Gases **DALTON'S LAW OF PARTIAL PRESSURES**

Answer 63

**P_total=P₁+P₂+P₃...**

Question 64

# Gases **GRAHAM'S LAW** **(EFFUSION & DIFFUSION)**

Answer 64

**E₁/E₂=√MW₂/√MW₁**

Question 65

# Density & Specific Gravity **DENSITY, ρ**

Answer 65

**ρ=m/v**

Question 66

# Give Units--No equation here **DENSITY OF WATER=?** **(2)**

Answer 66

**1000 kg/m³ OR 1.0 g/cm³** _REMEMBER_: **1 cm³ = 1mL** **1 L H₂O=1 kg** **1 mL H₂O=1 g**

Question 67

**SPECIFIC GRAVITY** _FOR OBJECTS FLOATING IN LIQUIDS:_ *WHAT IS SIGNIFICANCE OF THE **FRACTION** OF THE OBJECT THAT **IS** SUBMERGED IN WATER?*

Answer 67

**SG= ρ_substance/ρ_water** ## Footnote ρ=density, m/v ρ_water=1 g cm³ or 1000 kg/m³ *FOR OBJECTS FLOATING IN WATER:* ***FRACTION OF OBJECT SUBMERGED IS EQUAL TO THE SPECIFIC GRAVITY!***

Question 68

**BUOYANT FORCE, F_buoyant**

Answer 68

**F_buoyant=ρvg**

Question 69

# Fluid Pressure **_GENERAL_ PRESSURE FORMULA**

Answer 69

**P=F/A**

Question 70

# Fluid Pressure **FLUID PRESSURE**

Answer 70

**P=ρgh**

Question 71

# Fluid Flow **FLOW RATE**

Answer 71

**Q=AV** ## Footnote A=total cross-sectional area

Question 72

# Fluid in motion **BERNOULLI'S EQUATION**

Answer 72

**K=P+ρgh+½ρv²** ## Footnote * **P**=random vibrational energy of the fluid molecules * **ρgh**= PE_{gravitational} per volume of the fluid * **h**=height (**NOT** depth) * **½ρv²** = KE per volume of moving fluid molecules

Question 73

# Energy Levels **WORK FUNCTION, φ**

Answer 73

**KE=E-φ**

Question 74

# Energy Levels **ENERGY OF A PHOTON, "E"**

Answer 74

**E=hf**

Question 75

# Chemistry **PERCENT % MASS**

Answer 75

**% MASS=** **Mass of ONE element/TOTAL mass of cpd** **x 100%**

Question 76

# Equilibrium **LAW OF MASS ACTION** **K_eq=?**

Answer 76

**K_eq=** **[products]^X / [reactants]^Y**

Question 77

# Le Chatelier's Principle **Qeq** ## Footnote **MORE\_\_\_ THAN \_\_\_** **RXN PROCEEDS TO THE \_\_\_**

Answer 77

**MORE REACTANT THAN PRODUCT** **RXN PROCEEDS TO THE RIGHT**

Question 78

# Le Chatelier's Principle **Q\>K_eq** ## Footnote **MORE\_\_\_ THAN \_\_\_** **RXN PROCEEDS TO THE \_\_\_**

Answer 78

**MORE PRODUCT THAN REACTANT** **RXN PROCEEDS TO THE LEFT**

Question 79

# Evolution & Populations **HARDY-WEINBERG EQUILIBRIUM (2)**

Answer 79

**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 **homo**zygous genotype **AA*** ***q²** represents the frequency of the **homo**zygous genotype **aa*** ***2pq** represents the frequency of the **hetero**zygous genotype **Aa***

Question 80

# Ochem **"FORMAL CHARGE"**

Answer 80

**FORMAL CHARGE=** **VALENCE - ASSIGNED**

Question 81

**HÜCKEL'S RULE**

Answer 81

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

Question 82

# Circuits **CAPACITANCE**

Answer 82

**C= Q/V**

Question 83

# Waves-The dB System **INTENSITY IN dB**

Answer 83

**=10\*log (I/I_o)** ## Footnote **I***=intensity of wave (in W/m²)* **I_o***=threshold of human hearing (given)*

Question 84

# Chromatography **PAPER OR THIN LAYER CHROMATOGRAPHY (TLC)** **R_f=?**

Answer 84

**R_f=** DIST. TRAVELED BY **COMPONENT /**DIST. TRAVELED BY **SOLVENT**

Question 85

**MICHAELIS-MENTEN EQUATION**

Answer 85

**V_o= V_max [S] / K_m+[S]**

Question 86

**MICHAELIS CONSTANT, K_m** **K_m IS A MEASURE OF...?**

Answer 86

**K_m=[S] at ½V_max** ## Footnote **K_m**= *MEASURE OF AN **ENZYME'S** AFFINITY FOR ITS **SUBSTRATE***

Question 87

# Types of Enzyme Inhibition **LINEWEAVER-BURKE PLOTS** **Y-INTERCEPT=?**

Answer 87

**1/V_max**

Question 88

# Types of Enzyme Inhibition **LINEWEAVER-BURKE PLOTS** **X-INTERCEPT=?**

Answer 88

**-1/K_m**

Question 89

# Types of Enzyme Inhibition **LINEWEAVER-BURKE PLOTS** **SLOPE=?**

Answer 89

**K_m/V_max**

Question 90

# Circuits **CAPACIT**_ANCE_**** ## Footnote *(_NOT_ PE_capacitor !)* How do Capacit**_ance_** and PE_capacitor relate?

Answer 90

**C=Q/V** ## Footnote Once solving for C, plug ***that*** into one of the 3 PE_capacitor formulas: **=½QV** **=½CV²** OR **=½Q²/C**

Question 91

# Circuits **CAPACITANCE** ## Footnote wrt **AREA OF OVERLAP, A** b/t plates and **DISTANCE, D** b/t plates

Answer 91

**C=εA/d** ## Footnote * 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)