MCAT Physics & Chemistry Equation Flashcards: Formulas, Units & When to Use Them

这套卡组中的卡片

1. 卡片 1

   问题

   Which relationship gives average velocity over a time interval?

   答案

   $\bar v=\Delta x/\Delta t$.

   Displacement $\Delta x$ includes direction; average speed instead uses total distance.

2. 卡片 2

   问题

   How do you convert a sample's mass to moles?

   答案

   $n=m/M$.

   Divide mass $m$ by molar mass $M$ using compatible units.

3. 卡片 3

   问题

   What is the electrostatic force between two point charges?

   答案

   $F=k_e|q_1q_2|/r^2$.

   It acts along the line joining the charges; like charges repel and unlike charges attract.

4. 卡片 4

   问题

   How is pH defined from hydrogen-ion activity in the usual MCAT approximation?

   答案

   $\mathrm{pH}=-\log[H^+]$.

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. 卡片 5

   问题

   How are period and frequency related?

   答案

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. 卡片 6

   问题

   Which relationship gives sensible heat for a sample with known specific heat?

   答案

   $q=mc\Delta T$.

   Use it within one phase when the specific heat $c$ is approximately constant.

7. 卡片 7

   问题

   Which relationship defines mass density?

   答案

   $\rho=m/V$.

   Density has SI units of $\mathrm{kg/m^3}$; $1\ \mathrm{g/mL}=1000\ \mathrm{kg/m^3}$.

8. 卡片 8

   问题

   What is the concentration equilibrium constant for $aA+bB\rightleftharpoons cC+dD$?

   答案

   $K_c=[C]^c[D]^d/([A]^a[B]^b)$.

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. 卡片 9

   问题

   How is photon energy related to frequency and wavelength?

   答案

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. 卡片 10

    问题

    How is standard cell potential calculated from reduction potentials?

    答案

    $E^\circ_{\mathrm{cell}}=E^\circ_{\mathrm{cathode}}-E^\circ_{\mathrm{anode}}$.

    Use both tabulated values as reductions; do not multiply potentials by stoichiometric coefficients.

11. 卡片 11

    问题

    Which SI base units cover the quantities most often used in MCAT mechanics and circuits?

    答案

    Use meters (m) for length, kilograms (kg) for mass, seconds (s) for time, and amperes (A) for electric current. Amount of substance uses moles (mol), and thermodynamic temperature uses kelvin (K).

12. 卡片 12

    问题

    How do you convert Celsius temperature to kelvin for gas-law work?

    答案

    $T_K=T_{^\circ C}+273.15$.

    Gas-law temperatures must be absolute; a Celsius value cannot be inserted directly.

13. 卡片 13

    问题

    Which relationship gives average acceleration over a time interval?

    答案

    $\bar a=\Delta v/\Delta t$.

    Acceleration has SI units of $\mathrm{m/s^2}$.

14. 卡片 14

    问题

    How is reaction rate related to a species concentration and its stoichiometric coefficient?

    答案

    For $aA\rightarrow cC$, $\mathrm{rate}=-(1/a)d[A]/dt=(1/c)d[C]/dt$.

    The signs and coefficients make one reaction rate consistent across species.

15. 卡片 15

    问题

    What electric-field magnitude does a point charge produce?

    答案

    $E=k_e|q|/r^2$.

    The field points away from a positive source charge and toward a negative one.

16. 卡片 16

    问题

    How do moles relate to the number of microscopic particles?

    答案

    $N=nN_A$, with $N_A\approx6.022\times10^{23}\ \mathrm{mol^{-1}}$.

17. 卡片 17

    问题

    For constant acceleration, how does velocity change with time?

    答案

    $v=v_0+at$.

    Use it when acceleration is constant and the elapsed time is known.

18. 卡片 18

    问题

    How is pOH defined?

    答案

    $\mathrm{pOH}=-\log[OH^-]$.

19. 卡片 19

    问题

    How is specific gravity defined?

    答案

    $SG=\rho_{\mathrm{substance}}/\rho_{\mathrm{water}}$.

    It is dimensionless because it is a density ratio.

20. 卡片 20

    问题

    How is an object's heat capacity related to heat and temperature change?

    答案

    $q=C\Delta T$.

    Heat capacity $C$ applies to the whole object; specific heat is per unit mass.

21. 卡片 21

    问题

    How are frequency and wavelength related for electromagnetic radiation in vacuum?

    答案

    $c=f\lambda$.

    Use $c\approx3.00\times10^8\ \mathrm{m/s}$.

22. 卡片 22

    问题

    Which species are omitted from a heterogeneous equilibrium expression?

    答案

    Pure solids and pure liquids are omitted because their activities are effectively constant. Gases and dissolved species remain.

23. 卡片 23

    问题

    What force does an electric field exert on a charge?

    答案

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. 卡片 24

    问题

    Which equation relates pressure, volume, amount, and temperature for an ideal gas?

    答案

    $PV=nRT$.

    Use absolute temperature and a gas constant whose units match pressure and volume.

25. 卡片 25

    问题

    Which equation relates wave speed, frequency, and wavelength?

    答案

    $v=f\lambda$.

    The medium sets the wave speed; changing frequency then changes wavelength.

26. 卡片 26

    问题

    What is the water-ion product at $25^\circ\mathrm{C}$?

    答案

    $K_w=[H^+][OH^-]\approx1.0\times10^{-14}$.

    Its value changes with temperature.

27. 卡片 27

    问题

    What base-unit dimensions define one newton?

    答案

    $1\ \mathrm{N}=1\ \mathrm{kg\,m\,s^{-2}}$.

    A force must have dimensions of mass times acceleration.

28. 卡片 28

    问题

    How is cell potential related to reaction free energy?

    答案

    $\Delta G=-nFE_{\mathrm{cell}}$.

    A positive galvanic-cell potential gives negative $\Delta G$ for the written reaction.

29. 卡片 29

    问题

    For constant acceleration, how does displacement depend on time?

    答案

    $\Delta x=v_0t+\tfrac12at^2$.

    Choose a positive direction first, then keep signs consistent.

30. 卡片 30

    问题

    How is molarity defined?

    答案

    $M=n_{\mathrm{solute}}/V_{\mathrm{solution}}$.

    Use solution volume in liters, so molarity has units of $\mathrm{mol/L}$.

31. 卡片 31

    问题

    What electric potential does a point charge produce?

    答案

    $V=k_e q/r$.

    Potential is scalar, so contributions from multiple charges add algebraically.

32. 卡片 32

    问题

    Which relationship gives heat absorbed or released during a phase change?

    答案

    $q=n\Delta H_{\mathrm{phase}}$, or $q=mL$ when latent heat is given per unit mass. Temperature stays constant during an ideal equilibrium phase change.

33. 卡片 33

    问题

    Which constant-acceleration equation avoids time?

    答案

    $v^2=v_0^2+2a\Delta x$.

    It connects speed and displacement when time is absent.

34. 卡片 34

    问题

    What is the general experimental rate-law form?

    答案

    $\mathrm{rate}=k[A]^m[B]^n$.

    The exponents are determined experimentally and need not equal overall-reaction coefficients.

35. 卡片 35

    问题

    Which relationship defines pressure from a normal force?

    答案

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. 卡片 36

    问题

    What pH–pOH relationship applies at $25^\circ\mathrm{C}$?

    答案

    $\mathrm{pH}+\mathrm{pOH}=14.00$.

    More generally, $\mathrm{pH}+\mathrm{pOH}=\mathrm{p}K_w$.

37. 卡片 37

    问题

    How is wave intensity related to transmitted power and area?

    答案

    $I=P/A$.

    Intensity is power per area, measured in $\mathrm{W/m^2}$.

38. 卡片 38

    问题

    How is molality defined?

    答案

    $m=n_{\mathrm{solute}}/(\mathrm{kg\ of\ solvent})$.

    Molality uses solvent mass, not solution volume, and is temperature-independent.

39. 卡片 39

    问题

    What base-unit dimensions define one joule?

    答案

    $1\ \mathrm{J}=1\ \mathrm{N\,m}=1\ \mathrm{kg\,m^2\,s^{-2}}$.

    Work, energy, and heat share this unit.

40. 卡片 40

    问题

    What is the chemistry sign-convention form of the first law?

    答案

    $\Delta U=q+w$.

    $q>0$ means heat enters the system, and $w>0$ means work is done on the system.

41. 卡片 41

    问题

    How is refractive index related to light speed in a medium?

    答案

    $n=c/v$.

    A larger refractive index means a lower phase speed in the material.

42. 卡片 42

    问题

    What equation links net force and acceleration?

    答案

    $\sum \vec F=m\vec a$.

    The vector sum of external forces determines the acceleration.

43. 卡片 43

    问题

    Which relationship compares two states of a fixed amount of ideal gas?

    答案

    $P_1V_1/T_1=P_2V_2/T_2$.

    It assumes the amount of gas is unchanged. Holding one variable constant gives Boyle's, Charles's, or Gay-Lussac's law.

44. 卡片 44

    问题

    How is electric potential energy related to charge and voltage?

    答案

    $\Delta U=q\Delta V$.

    A positive charge gains potential energy when moved to higher potential; a negative charge does the opposite.

45. 卡片 45

    问题

    How are standard cell potential and the equilibrium constant related?

    答案

    $\ln K=nFE^\circ_{\mathrm{cell}}/(RT)$.

    At equilibrium, the Nernst equation gives $E_{\mathrm{cell}}=0$.

46. 卡片 46

    问题

    What is an object's weight near Earth's surface?

    答案

    $W=mg$.

    Weight is a force in newtons; mass remains in kilograms.

47. 卡片 47

    问题

    How are $K_p$ and $K_c$ related for an ideal-gas reaction?

    答案

    $K_p=K_c(RT)^{\Delta n_{\mathrm{gas}}}$.

    $\Delta n_{\mathrm{gas}}$ is gaseous product coefficients minus gaseous reactant coefficients.

48. 卡片 48

    问题

    How does pressure change with depth in a static incompressible fluid?

    答案

    $P=P_0+\rho gh$.

    $h$ is depth below the surface; the gauge pressure is $\rho gh$.

49. 卡片 49

    问题

    How do the units of a rate constant depend on overall reaction order $N$?

    答案

    $[k]=\mathrm{M^{1-N}s^{-1}}$ when rate is in $\mathrm{M/s}$. For example, first-order $k$ has units of $\mathrm{s^{-1}}$.

50. 卡片 50

    问题

    Which relationship defines electric current?

    答案

    $I=\Delta Q/\Delta t$.

    Conventional current points in the direction positive charge would move.

51. 卡片 51

    问题

    What is the acid-dissociation expression for $HA\rightleftharpoons H^++A^-$?

    答案

    $K_a=[H^+][A^-]/[HA]$.

    A larger $K_a$ means a stronger acid under comparable conditions.

52. 卡片 52

    问题

    What equation governs refraction at a boundary?

    答案

    $n_1\sin\theta_1=n_2\sin\theta_2$.

    Angles are measured from the normal, not the surface.

53. 卡片 53

    问题

    How is mole fraction defined for component $i$?

    答案

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. 卡片 54

    问题

    What SI units and base dimensions define pressure?

    答案

    Pressure is measured in pascals: $1\ \mathrm{Pa}=1\ \mathrm{N/m^2}=1\ \mathrm{kg\,m^{-1}\,s^{-2}}$.

55. 卡片 55

    问题

    What pressure–volume work occurs against constant external pressure?

    答案

    $w=-P_{\mathrm{ext}}\Delta V$.

    Expansion has $\Delta V>0$ and therefore negative work on the system.

56. 卡片 56

    问题

    How does intensity from an isotropic point source vary with distance?

    答案

    $I=P/(4\pi r^2)$.

    Doubling distance reduces intensity to one quarter if absorption is negligible.

57. 卡片 57

    问题

    How large can static friction become before slipping begins?

    答案

    $f_s\leq\mu_sN$, with $f_{s,\max}=\mu_sN$.

    Static friction matches the needed opposing force up to its maximum; it isn't always equal to $\mu_sN$.

58. 卡片 58

    问题

    Which relationship handles dilution when solute amount is conserved?

    答案

    $M_1V_1=M_2V_2$.

    It applies when solvent is added without reaction or solute loss.

59. 卡片 59

    问题

    What is Ohm's law for an ohmic element?

    答案

    $V=IR$.

    It applies when resistance is approximately constant over the operating range.

60. 卡片 60

    问题

    How is the reaction quotient $Q$ constructed?

    答案

    Use the same expression as $K$, but insert the current—not necessarily equilibrium—activities or concentrations.

61. 卡片 61

    问题

    What is the usual model for kinetic friction on a sliding surface?

    答案

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. 卡片 62

    问题

    What is the base-dissociation expression for $B+H_2O\rightleftharpoons HB^++OH^-$?

    答案

    $K_b=[HB^+][OH^-]/[B]$.

63. 卡片 63

    问题

    What equation expresses Pascal's principle in a hydraulic device?

    答案

    $F_1/A_1=F_2/A_2$.

    An applied pressure change is transmitted through a confined incompressible fluid.

64. 卡片 64

    问题

    How much charge passes through a cell carrying constant current?

    答案

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. 卡片 65

    问题

    What is the critical-angle condition for total internal reflection?

    答案

    $\sin\theta_c=n_2/n_1$ when $n_1>n_2$.

    Total internal reflection occurs only when light starts in the higher-index medium and $\theta_1>\theta_c$.

66. 卡片 66

    问题

    How is total pressure related to component pressures in an ideal gas mixture?

    答案

    $P_{\mathrm{tot}}=\sum_iP_i$.

    Dalton's law treats each gas as contributing its own partial pressure.

67. 卡片 67

    问题

    How is the coulomb expressed through SI base units?

    答案

    $1\ \mathrm{C}=1\ \mathrm{A\,s}$.

    Charge equals current multiplied by time.

68. 卡片 68

    问题

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    答案

    $\Delta H^\circ_{\mathrm{rxn}}=\sum\nu\Delta H_f^\circ(\mathrm{products})-\sum\nu\Delta H_f^\circ(\mathrm{reactants})$.

69. 卡片 69

    问题

    How is sound intensity level in decibels defined?

    答案

    $\beta=10\log_{10}(I/I_0)$.

    The reference intensity is commonly $I_0=10^{-12}\ \mathrm{W/m^2}$.

70. 卡片 70

    问题

    What is the integrated rate law for a zero-order reactant?

    答案

    $[A]_t=[A]_0-kt$.

    A plot of $[A]$ versus time is linear with slope $-k$.

71. 卡片 71

    问题

    How does a uniform wire's resistance depend on material and geometry?

    答案

    $R=\rho L/A$.

    Longer wires have more resistance; larger cross-sectional area lowers it. Here $\rho$ is resistivity.

72. 卡片 72

    问题

    Which equation gives the magnitude of torque from a force?

    答案

    $\tau=rF\sin\theta=r_\perp F$.

    Here $r_\perp$ is the perpendicular lever arm from the pivot to the force's line of action.

73. 卡片 73

    问题

    How is mass percent composition calculated?

    答案

    $\%\mathrm{\ by\ mass}=100\times m_{\mathrm{component}}/m_{\mathrm{total}}$.

74. 卡片 74

    问题

    What buoyant force acts on a submerged object?

    答案

    $F_B=\rho_{\mathrm{fluid}}V_{\mathrm{displaced}}g$.

    It equals the weight of displaced fluid.

75. 卡片 75

    问题

    How is $\mathrm{p}K_a$ related to $K_a$?

    答案

    $\mathrm{p}K_a=-\log K_a$.

    Lower $\mathrm{p}K_a$ corresponds to the stronger acid.

76. 卡片 76

    问题

    What two conditions define static mechanical equilibrium?

    答案

    $\sum \vec F=0$ and $\sum\tau=0$.

    Both translational and rotational equilibrium are required.

77. 卡片 77

    问题

    How does Hess's law combine reaction enthalpies?

    答案

    Add the manipulated step equations and add their $\Delta H$ values. Reversing a step changes the sign; multiplying a step multiplies $\Delta H$ by the same factor.

78. 卡片 78

    问题

    Which equivalent forms give electrical power in a resistor?

    答案

    $P=IV=I^2R=V^2/R$.

    Choose the form that uses the known current, voltage, and resistance.

79. 卡片 79

    问题

    How does mole fraction determine an ideal gas's partial pressure?

    答案

    $P_i=X_iP_{\mathrm{tot}}$, where $X_i=n_i/n_{\mathrm{tot}}$.

80. 卡片 80

    问题

    What decibel change corresponds to multiplying sound intensity by 10?

    答案

    A tenfold intensity increase adds $10\ \mathrm{dB}$ because $10\log_{10}(10)=10$. A hundredfold increase adds $20\ \mathrm{dB}$.

81. 卡片 81

    问题

    How does comparing $Q$ with $K$ predict reaction direction?

    答案

    If $Q<K$, the forward direction is favored. If $Q>K$, the reverse direction is favored. If $Q=K$, the system is at equilibrium.

82. 卡片 82

    问题

    Which equation relates object, image, and focal distances for a thin lens or spherical mirror?

    答案

    $1/f=1/d_o+1/d_i$.

    Use the adopted sign convention consistently; positive $d_i$ usually denotes a real image.

83. 卡片 83

    问题

    How do charge and Faraday's constant give moles of electrons?

    答案

    $n_{e^-}=Q/F$, where $F\approx9.6485\times10^4\ \mathrm{C/mol\ e^-}$.

84. 卡片 84

    问题

    How is the volt expressed through joules and coulombs?

    答案

    $1\ \mathrm{V}=1\ \mathrm{J/C}$.

    Voltage is energy transferred per unit charge.

85. 卡片 85

    问题

    How is $\mathrm{p}K_b$ related to $K_b$?

    答案

    $\mathrm{p}K_b=-\log K_b$.

86. 卡片 86

    问题

    What work is done by a constant force through a displacement?

    答案

    $W=Fd\cos\theta$.

    $\theta$ is the angle between the force and displacement; perpendicular force does zero work.

87. 卡片 87

    问题

    How is volume percent calculated for a liquid mixture?

    答案

    $\%\mathrm{\ by\ volume}=100\times V_{\mathrm{component}}/V_{\mathrm{solution}}$.

    Use it only when the problem defines composition by volume.

88. 卡片 88

    问题

    How do resistors combine in series?

    答案

    $R_{\mathrm{eq}}=\sum_iR_i$.

    Series elements carry the same current and their voltage drops add.

89. 卡片 89

    问题

    What is the half-life of a zero-order reactant?

    答案

    $t_{1/2}=[A]_0/(2k)$.

    Unlike first-order half-life, it depends on starting concentration.

90. 卡片 90

    问题

    How is volumetric flow rate related to cross-sectional area and speed?

    答案

    $Q=Av$.

    $Q$ has SI units of $\mathrm{m^3/s}$ and assumes the average speed across the section.

    

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91. 卡片 91

    问题

    How can average bond energies estimate reaction enthalpy?

    答案

    $\Delta H_{\mathrm{rxn}}\approx\sum D(\mathrm{bonds\ broken})-\sum D(\mathrm{bonds\ formed})$.

    Breaking bonds costs energy; forming bonds releases it.

92. 卡片 92

    问题

    What is the translational kinetic energy of a point mass?

    答案

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. 卡片 93

    问题

    What ratio defines parts per million by mass?

    答案

    $\mathrm{ppm}=10^6\times m_{\mathrm{solute}}/m_{\mathrm{solution}}$.

    For dilute aqueous solutions, $1\ \mathrm{ppm}$ is often approximately $1\ \mathrm{mg/L}$ when density is near $1\ \mathrm{kg/L}$.

94. 卡片 94

    问题

    How do resistors combine in parallel?

    答案

    $1/R_{\mathrm{eq}}=\sum_i1/R_i$.

    Parallel branches share the same voltage, and the equivalent resistance is below the smallest branch resistance.

95. 卡片 95

    问题

    How are the dissociation constants of a conjugate acid–base pair related?

    答案

    $K_aK_b=K_w$.

    At $25^\circ\mathrm{C}$, $\mathrm{p}K_a+\mathrm{p}K_b=14.00$.

96. 卡片 96

    问题

    How do powers of ten combine when multiplying quantities in scientific notation?

    答案

    Multiply the coefficients and add the exponents: $(a\times10^m)(b\times10^n)=ab\times10^{m+n}$. Then normalize the result so its final coefficient $c$ satisfies $1\leq|c|<10$; a coefficient of exactly 10 becomes 1 while the exponent increases by 1.

97. 卡片 97

    问题

    How many moles of a product requiring $z$ electrons per mole form during electrolysis?

    答案

    $n_{\mathrm{product}}=Q/(zF)=It/(zF)$.

    This is the ideal Faraday-law result before any stated efficiency correction.

98. 卡片 98

    问题

    How is lateral magnification related to image and object distances?

    答案

    $m=h_i/h_o=-d_i/d_o$.

    A negative magnification indicates inversion; $|m|$ gives the size ratio.

99. 卡片 99

    问题

    What is the average translational kinetic energy per mole of an ideal gas?

    答案

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. 卡片 100

     问题

     What are the allowed frequencies of a string fixed at both ends?

     答案

     $f_n=nv/(2L)$ for $n=1,2,3,\ldots$.

     Both ends are nodes, so every positive integer harmonic is allowed.

101. 卡片 101

     问题

     How does reversing a reaction change its equilibrium constant?

     答案

     $K_{\mathrm{reverse}}=1/K_{\mathrm{forward}}$.

102. 卡片 102

     问题

     What does the work–energy theorem say?

     答案

     $W_{\mathrm{net}}=\Delta K$.

     Net work changes kinetic energy, even when individual forces are nonconservative.

103. 卡片 103

     问题

     What entropy change accompanies reversible heat transfer at constant temperature?

     答案

     $\Delta S=q_{\mathrm{rev}}/T$.

     Temperature must be in kelvin.

104. 卡片 104

     问题

     What does Kirchhoff's junction rule require?

     答案

     $\sum I_{\mathrm{in}}=\sum I_{\mathrm{out}}$.

     It follows from conservation of charge at a node.

105. 卡片 105

     问题

     Which equation estimates the pH of a buffer made from a weak acid and its conjugate base?

     答案

     $\mathrm{pH}=\mathrm{p}K_a+\log([A^-]/[HA])$.

     Henderson–Hasselbalch works best when both buffer components are present in meaningful amounts.

106. 卡片 106

     问题

     What continuity relationship applies to steady incompressible flow?

     答案

     $A_1v_1=A_2v_2$.

     A narrower section has a larger average speed when the same volume passes each second.

107. 卡片 107

     问题

     A liquid has known density and volume. Which rearranged density relationship gives its mass?

     答案

     $m=\rho V$.

     Here $m$ is mass, $\rho$ is density, and $V$ is volume; use compatible units when density and volume are known. For example, $25\ \mathrm{mL}$ of a $1.20\ \mathrm{g/mL}$ solution has mass $m=(1.20)(25)=30\ \mathrm{g}$.

108. 卡片 108

     问题

     What is local gravitational potential energy near Earth's surface?

     答案

     $U_g=mgh$.

     Only changes matter: $\Delta U_g=mg\Delta h$ when $g$ is approximately constant.

109. 卡片 109

     问题

     What is the integrated rate law for a first-order reactant?

     答案

     $\ln[A]_t=\ln[A]_0-kt$.

     A plot of $\ln[A]$ versus time is linear with slope $-k$.

110. 卡片 110

     问题

     What are the allowed frequencies of a pipe open at both ends?

     答案

     $f_n=nv/(2L)$ for $n=1,2,3,\ldots$.

     Both open ends are displacement antinodes.

111. 卡片 111

     问题

     Which equation relates Gibbs free energy, enthalpy, and entropy at constant temperature?

     答案

     $\Delta G=\Delta H-T\Delta S$.

     Use compatible energy units and absolute temperature.

112. 卡片 112

     问题

     What does Kirchhoff's loop rule require?

     答案

     $\sum\Delta V=0$ around any closed loop.

     Voltage rises and drops must be assigned consistently with the chosen traversal direction.

113. 卡片 113

     问题

     What elastic potential energy is stored in an ideal spring?

     答案

     $U_s=\tfrac12kx^2$.

     $x$ is displacement from equilibrium and $k$ has units of $\mathrm{N/m}$.

114. 卡片 114

     问题

     How does multiplying every reaction coefficient by a factor $n$ change $K$?

     答案

     $K_{\mathrm{new}}=K^n$.

     Dividing coefficients by $n$ takes the corresponding root.

115. 卡片 115

     问题

     How can you estimate the order of magnitude of a quotient without a calculator?

     答案

     Divide the leading coefficients and subtract powers of ten: $(a\times10^m)/(b\times10^n)=(a/b)\times10^{m-n}$. Normalize the result so its final coefficient $c$ satisfies $1\leq|c|<10$; if the coefficient is exactly 10, write it as 1 and increase the exponent by 1.

116. 卡片 116

     问题

     How is lens power related to focal length?

     答案

     $P=1/f$ with $f$ in meters.

     Power is measured in diopters; converging lenses have positive power and diverging lenses negative power.

117. 卡片 117

     问题

     How does root-mean-square molecular speed depend on molar mass?

     答案

     $v_{\mathrm{rms}}=\sqrt{3RT/M}$.

     Use molar mass $M$ in $\mathrm{kg/mol}$; lighter gases move faster at the same temperature.

118. 卡片 118

     问题

     Which equation relates pressure, speed, and height along ideal fluid flow?

     答案

     $P+\tfrac12\rho v^2+\rho gy=\text{constant}$.

     Bernoulli's equation assumes steady, incompressible, nonviscous flow along a streamline.

119. 卡片 119

     问题

     What is the Nernst equation for a cell reaction?

     答案

     $E=E^\circ-(RT/(nF))\ln Q$.

     At $25^\circ\mathrm{C}$, $E=E^\circ-(0.0592\ \mathrm{V}/n)\log Q$.

120. 卡片 120

     问题

     What force does an ideal spring exert?

     答案

     $F_s=-kx$.

     The minus sign means the spring force points back toward equilibrium.

121. 卡片 121

     问题

     What conjugate-base-to-acid ratio gives a target buffer pH?

     答案

     $[A^-]/[HA]=10^{\mathrm{pH}-\mathrm{p}K_a}$.

     This is Henderson–Hasselbalch solved for the composition ratio.

122. 卡片 122

     问题

     Which relationship defines capacitance?

     答案

     $C=Q/V$.

     Capacitance is charge stored per potential difference and is measured in farads.

123. 卡片 123

     问题

     How do elemental mass percentages lead to an empirical formula?

     答案

     Convert each element's mass to moles, divide every mole amount by the smallest, then multiply to obtain the smallest whole-number ratio. The retrieval target is the mole ratio, not the mass ratio.

124. 卡片 124

     问题

     When can mechanical energy be conserved?

     答案

     $K_i+U_i=K_f+U_f$ when only conservative forces do work. With nonconservative work, use $W_{nc}=\Delta(K+U)$.

125. 卡片 125

     问题

     What sign of $\Delta G$ indicates a thermodynamically spontaneous forward process at constant temperature and pressure?

     答案

     $\Delta G<0$. At equilibrium $\Delta G=0$; $\Delta G>0$ favors the reverse direction. Spontaneity does not say the reaction is fast.

126. 卡片 126

     问题

     Which metric-prefix factors correspond to milli-, micro-, and nano-?

     答案

     Milli is $10^{-3}$, micro is $10^{-6}$, and nano is $10^{-9}$. Each step is a factor of $10^3$.

127. 卡片 127

     问题

     What is the pH at the half-equivalence point of a weak-acid/strong-base titration?

     答案

     $\mathrm{pH}=\mathrm{p}K_a$.

     Half of the original weak acid has become conjugate base, so $[A^-]=[HA]$.

128. 卡片 128

     问题

     What are the allowed frequencies of a pipe closed at one end?

     答案

     $f_n=nv/(4L)$ for odd $n=1,3,5,\ldots$.

     The closed end is a displacement node and the open end is an antinode.

129. 卡片 129

     问题

     What is the half-life of a first-order reaction?

     答案

     $t_{1/2}=\ln2/k$.

     It is independent of initial concentration.

130. 卡片 130

     问题

     How is the focal length of a spherical mirror related to its radius of curvature?

     答案

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. 卡片 131

     问题

     How is a molecular formula obtained from an empirical formula?

     答案

     $k=M_{\mathrm{molecular}}/M_{\mathrm{empirical}}$, then multiply every empirical subscript by the integer $k$.

132. 卡片 132

     问题

     What is the capacitance of an ideal parallel-plate capacitor?

     答案

     $C=\kappa\varepsilon_0A/d$.

     Larger plate area or dielectric constant raises capacitance; greater separation lowers it.

133. 卡片 133

     问题

     What does Graham's law predict for two gas effusion rates?

     答案

     $r_1/r_2=\sqrt{M_2/M_1}$.

     At the same temperature, effusion rate is inversely proportional to the square root of molar mass.

134. 卡片 134

     问题

     Which relationship gives laminar flow through a cylindrical tube?

     答案

     $Q=\dfrac{\pi r^4\Delta P}{8\eta L}$.

     Poiseuille flow is extremely sensitive to radius and assumes a Newtonian fluid in a long rigid tube.

135. 卡片 135

     问题

     How do equilibrium constants combine when reactions are added?

     答案

     Multiply them: $K_{\mathrm{overall}}=K_1K_2\cdots$.

     Reverse or scale each component reaction before applying the reciprocal or power rule.

136. 卡片 136

     问题

     Which relationship defines average power?

     答案

     $P=W/\Delta t$.

     Power is the rate of energy transfer and is measured in watts, where $1\ \mathrm{W}=1\ \mathrm{J/s}$.

137. 卡片 137

     问题

     What voltage does an ideal concentration cell produce at $25^\circ\mathrm{C}$?

     答案

     $E=(0.0592\ \mathrm{V}/n)\log(C_{\mathrm{high}}/C_{\mathrm{low}})$ for the simple same-ion setup. The voltage vanishes when concentrations equalize.

138. 卡片 138

     问题

     Which equivalent forms give energy stored in a capacitor?

     答案

     $U=\tfrac12CV^2=\tfrac12QV=Q^2/(2C)$.

     Use the form matching the known variables.

139. 卡片 139

     问题

     How is standard free-energy change related to the equilibrium constant?

     答案

     $\Delta G^\circ=-RT\ln K$.

     A large $K$ corresponds to negative $\Delta G^\circ$.

140. 卡片 140

     问题

     What instantaneous power is delivered by a force to a moving object?

     答案

     $P=\vec F\cdot\vec v=Fv\cos\theta$.

     Only the force component parallel to velocity transfers energy at that instant.

141. 卡片 141

     问题

     How is percent yield calculated?

     答案

     $\%\mathrm{yield}=100\times(\mathrm{actual\ yield})/(\mathrm{theoretical\ yield})$.

142. 卡片 142

     问题

     What condition gives constructive interference in a double-slit experiment?

     答案

     $d\sin\theta=m\lambda$ for integers $m$.

     For small angles on a screen, fringe position is approximately $y_m=m\lambda L/d$.

143. 卡片 143

     问题

     What stoichiometric condition marks acid–base equivalence?

     答案

     Acid equivalents equal base equivalents: $n_a|z_a|=n_b|z_b|$. For molarity and volume, $M_aV_a|z_a|=M_bV_b|z_b|$.

144. 卡片 144

     问题

     What value is useful for the speed of light in vacuum?

     答案

     Use $c\approx3.00\times10^8\ \mathrm{m/s}$. In a material, light travels at $v=c/n$.

145. 卡片 145

     问题

     Which Doppler relationship applies to collinear motion in a stationary medium?

     答案

     $f'=f\dfrac{v\pm v_o}{v\mp v_s}$.

     Choose signs that raise $f'$ when source and observer approach and lower it when they separate.

146. 卡片 146

     问题

     What is the integrated rate law for a second-order reaction in one reactant?

     答案

     $1/[A]_t=1/[A]_0+kt$.

     A plot of $1/[A]$ versus time is linear with slope $k$.

147. 卡片 147

     问题

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     答案

     $Re=\rho vD/\eta$.

     Lower Reynolds number favors laminar flow; higher values make turbulence more likely.

148. 卡片 148

     问题

     How is reaction free energy related to standard free energy and reaction quotient?

     答案

     $\Delta G=\Delta G^\circ+RT\ln Q$.

     This predicts the favorable direction under nonstandard conditions.

149. 卡片 149

     问题

     What is linear momentum?

     答案

     $\vec p=m\vec v$.

     Momentum is a vector with SI units of $\mathrm{kg\,m/s}$.

150. 卡片 150

     问题

     How do you identify the limiting reactant from available moles?

     答案

     Compare $n_i/\nu_i$ for each reactant, where $\nu_i$ is its stoichiometric coefficient. The smallest ratio runs out first and sets the reaction extent.

151. 卡片 151

     问题

     How do capacitors combine in parallel?

     答案

     $C_{\mathrm{eq}}=\sum_iC_i$.

     Parallel capacitors share voltage and their stored charges add.

152. 卡片 152

     问题

     How do you estimate the pH of a dilute strong monoprotic acid of concentration $C$?

     答案

     Assuming complete dissociation and negligible water autoionization, $[H^+]\approx C$ and $\mathrm{pH}\approx-\log C$.

153. 卡片 153

     问题

     What relationship connects impulse and momentum change?

     答案

     $\vec J=\int\vec F\,dt=\Delta\vec p$. For a constant force, $\vec J=\vec F\Delta t$.

154. 卡片 154

     问题

     What is the solubility-product expression for $M_aX_b(s)\rightleftharpoons aM+bX$?

     答案

     $K_{sp}=[M]^a[X]^b$.

     The solid is omitted; dissolved-ion concentrations carry their stoichiometric exponents.

155. 卡片 155

     问题

     What condition gives minima from a single slit of width $a$?

     答案

     $a\sin\theta=m\lambda$ for $m=1,2,3,\ldots$.

     The central maximum lies between the first minima.

156. 卡片 156

     问题

     Which way do electrons flow in both galvanic and electrolytic cells?

     答案

     Electrons flow through the external circuit from anode to cathode. Oxidation is always at the anode; reduction is always at the cathode.

157. 卡片 157

     问题

     How do capacitors combine in series?

     答案

     $1/C_{\mathrm{eq}}=\sum_i1/C_i$.

     Series capacitors carry equal charge magnitude, and the equivalent capacitance is below the smallest one.

158. 卡片 158

     问题

     Which equation adds molecular size and attraction corrections to the ideal gas law?

     答案

     $\left(P+a\dfrac{n^2}{V^2}\right)(V-nb)=nRT$.

     The $a$ term corrects attractions; $b$ corrects finite molecular volume.

159. 卡片 159

     问题

     What beat frequency is heard from two nearby tones?

     答案

     $f_{\mathrm{beat}}=|f_1-f_2|$.

     Beats arise from alternating constructive and destructive interference.

160. 卡片 160

     问题

     What near-Earth gravitational acceleration is useful for MCAT estimates?

     答案

     Use $g\approx9.8\ \mathrm{m/s^2}$, or $10\ \mathrm{m/s^2}$ for quick order-of-magnitude work when the choices allow it.

161. 卡片 161

     问题

     What weak-acid approximation estimates $[H^+]$ for initial concentration $C$?

     答案

     $[H^+]\approx\sqrt{K_aC}$ when dissociation is small compared with $C$. Check that the resulting ionization is roughly below 5%.

162. 卡片 162

     问题

     Why does a constriction in a horizontal ideal-fluid tube usually have lower static pressure?

     答案

     Continuity raises the speed in the narrow section, and Bernoulli's relationship then requires lower static pressure when height is unchanged. This is the Venturi effect.

163. 卡片 163

     问题

     How does a solid's length change for a small temperature shift?

     答案

     $\Delta L=\alpha L_0\Delta T$.

     $\alpha$ is the linear expansion coefficient; the approximation assumes it stays nearly constant.

164. 卡片 164

     问题

     When is total linear momentum conserved?

     答案

     $\sum\vec p_i=\sum\vec p_f$ when the net external impulse on the chosen system is zero. Internal forces can redistribute momentum without changing the total.

165. 卡片 165

     问题

     What relationship connects absorbance and concentration in a dilute solution?

     答案

     $A=\varepsilon bc$.

     Beer–Lambert law uses molar absorptivity $\varepsilon$, path length $b$, and concentration $c$; it is most reliable in the linear dilute range.

166. 卡片 166

     问题

     What magnetic force acts on a moving charge?

     答案

     $F=|q|vB\sin\theta$.

     The force is perpendicular to both velocity and magnetic field, so it changes direction but does no work.

167. 卡片 167

     问题

     How does the Arrhenius equation relate rate constant and temperature?

     答案

     $k=Ae^{-E_a/(RT)}$. Equivalently, $\ln k=\ln A-E_a/(RT)$. Higher temperature or lower activation energy increases $k$.

168. 卡片 168

     问题

     What is centripetal acceleration for uniform circular motion?

     答案

     $a_c=v^2/r=\omega^2r$.

     It points toward the center even when speed is constant.

169. 卡片 169

     问题

     How do ions in a salt bridge move to maintain electroneutrality in a galvanic cell?

     答案

     Anions migrate toward the anode compartment, where oxidation creates excess positive charge. Cations migrate toward the cathode compartment, where reduction creates relative excess negative charge by consuming cations or producing anions. These migrations maintain charge neutrality.

170. 卡片 170

     问题

     What is the maximum kinetic energy in the photoelectric effect?

     答案

     $K_{\max}=hf-\phi$.

     Electrons are emitted when $hf\geq\phi$. Exactly at threshold, $hf=\phi$ and $K_{\max}=0$; positive kinetic energy requires $hf>\phi$.

171. 卡片 171

     问题

     What molar volume is a useful ideal-gas reference at $0^\circ\mathrm{C}$ and $1\ \mathrm{atm}$?

     答案

     About $22.4\ \mathrm{L/mol}$.

     This shortcut is tied to those stated conditions, not every convention labeled STP.

172. 卡片 172

     问题

     What is the period of an ideal mass–spring oscillator?

     答案

     $T=2\pi\sqrt{m/k}$.

     The small-amplitude period depends on mass and spring stiffness, not amplitude.

173. 卡片 173

     问题

     For $MX_2(s)\rightleftharpoons M^{2+}+2X^-$, how is $K_{sp}$ related to molar solubility $s$ in pure water?

     答案

     $K_{sp}=s(2s)^2=4s^3$.

     This relation changes when a common ion is already present.

174. 卡片 174

     问题

     What does a dimensional-consistency check require of an equation?

     答案

     Every term that is added or equated must have the same dimensions. A mismatch, such as adding energy to force, proves the equation or unit conversion is wrong.

175. 卡片 175

     问题

     How is percent ionization of a weak acid calculated?

     答案

     $\%\mathrm{ionization}=100\times[H^+]_{\mathrm{eq}}/[HA]_0$ for a monoprotic acid. Dilution generally raises percent ionization even while lowering $[H^+]$.

176. 卡片 176

     问题

     What pressure difference does surface tension create across one spherical liquid–gas interface?

     答案

     $\Delta P=2\gamma/r$.

     For a soap bubble with two interfaces, $\Delta P=4\gamma/r$. Smaller radii require larger pressure differences.

177. 卡片 177

     问题

     What energy balance applies in an insulated calorimetry problem?

     答案

     $\sum q=0$, so heat lost by hotter parts equals heat gained by colder parts and the calorimeter. Include every component named in the setup.

178. 卡片 178

     问题

     What radius does a charged particle follow when moving perpendicular to a uniform magnetic field?

     答案

     $r=mv/(|q|B)$.

     The magnetic force supplies centripetal force; faster or heavier particles curve less.

179. 卡片 179

     问题

     How do you find concentration after mixing solutions of the same nonreacting solute?

     答案

     $M_f=(M_1V_1+M_2V_2)/(V_1+V_2)$ when volumes are additive. If the solutes react, do stoichiometry before calculating the remaining concentration.

180. 卡片 180

     问题

     What net inward force is required for circular motion?

     答案

     $F_c=mv^2/r=m\omega^2r$.

     “Centripetal force” is the inward net force supplied by real forces, not an extra force.

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MCAT Physics & Chemistry Equation Flashcards: Formulas, Units & When to Use Them

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