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

このデッキのカード

1. カード 1

   質問

   Which relationship gives average velocity over a time interval?

   回答

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

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

2. カード 2

   質問

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

   回答

   $n=m/M$.

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

3. カード 3

   質問

   What is the electrostatic force between two point charges?

   回答

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

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

4. カード 4

   質問

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

   回答

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. カード 5

   質問

   How are period and frequency related?

   回答

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. カード 6

   質問

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

   回答

   $q=mc\Delta T$.

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

7. カード 7

   質問

   Which relationship defines mass density?

   回答

   $\rho=m/V$.

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

8. カード 8

   質問

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

   回答

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. カード 9

   質問

   How is photon energy related to frequency and wavelength?

   回答

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. カード 10

    質問

    How is standard cell potential calculated from reduction potentials?

    回答

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

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

11. カード 11

    質問

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

    回答

    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. カード 12

    質問

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

    回答

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

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

13. カード 13

    質問

    Which relationship gives average acceleration over a time interval?

    回答

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

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

14. カード 14

    質問

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

    回答

    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. カード 15

    質問

    What electric-field magnitude does a point charge produce?

    回答

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

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

16. カード 16

    質問

    How do moles relate to the number of microscopic particles?

    回答

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

17. カード 17

    質問

    For constant acceleration, how does velocity change with time?

    回答

    $v=v_0+at$.

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

18. カード 18

    質問

    How is pOH defined?

    回答

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

19. カード 19

    質問

    How is specific gravity defined?

    回答

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

    It is dimensionless because it is a density ratio.

20. カード 20

    質問

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

    回答

    $q=C\Delta T$.

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

21. カード 21

    質問

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

    回答

    $c=f\lambda$.

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

22. カード 22

    質問

    Which species are omitted from a heterogeneous equilibrium expression?

    回答

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

23. カード 23

    質問

    What force does an electric field exert on a charge?

    回答

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. カード 24

    質問

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

    回答

    $PV=nRT$.

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

25. カード 25

    質問

    Which equation relates wave speed, frequency, and wavelength?

    回答

    $v=f\lambda$.

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

26. カード 26

    質問

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

    回答

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

    Its value changes with temperature.

27. カード 27

    質問

    What base-unit dimensions define one newton?

    回答

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

    A force must have dimensions of mass times acceleration.

28. カード 28

    質問

    How is cell potential related to reaction free energy?

    回答

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

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

29. カード 29

    質問

    For constant acceleration, how does displacement depend on time?

    回答

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

    Choose a positive direction first, then keep signs consistent.

30. カード 30

    質問

    How is molarity defined?

    回答

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

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

31. カード 31

    質問

    What electric potential does a point charge produce?

    回答

    $V=k_e q/r$.

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

32. カード 32

    質問

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

    回答

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

33. カード 33

    質問

    Which constant-acceleration equation avoids time?

    回答

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

    It connects speed and displacement when time is absent.

34. カード 34

    質問

    What is the general experimental rate-law form?

    回答

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

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

35. カード 35

    質問

    Which relationship defines pressure from a normal force?

    回答

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. カード 36

    質問

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

    回答

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

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

37. カード 37

    質問

    How is wave intensity related to transmitted power and area?

    回答

    $I=P/A$.

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

38. カード 38

    質問

    How is molality defined?

    回答

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

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

39. カード 39

    質問

    What base-unit dimensions define one joule?

    回答

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

    Work, energy, and heat share this unit.

40. カード 40

    質問

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

    回答

    $\Delta U=q+w$.

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

41. カード 41

    質問

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

    回答

    $n=c/v$.

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

42. カード 42

    質問

    What equation links net force and acceleration?

    回答

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

    The vector sum of external forces determines the acceleration.

43. カード 43

    質問

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

    回答

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. カード 44

    質問

    How is electric potential energy related to charge and voltage?

    回答

    $\Delta U=q\Delta V$.

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

45. カード 45

    質問

    How are standard cell potential and the equilibrium constant related?

    回答

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

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

46. カード 46

    質問

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

    回答

    $W=mg$.

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

47. カード 47

    質問

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

    回答

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

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

48. カード 48

    質問

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

    回答

    $P=P_0+\rho gh$.

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

49. カード 49

    質問

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

    回答

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

50. カード 50

    質問

    Which relationship defines electric current?

    回答

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

    Conventional current points in the direction positive charge would move.

51. カード 51

    質問

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

    回答

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

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

52. カード 52

    質問

    What equation governs refraction at a boundary?

    回答

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

    Angles are measured from the normal, not the surface.

53. カード 53

    質問

    How is mole fraction defined for component $i$?

    回答

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. カード 54

    質問

    What SI units and base dimensions define pressure?

    回答

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

55. カード 55

    質問

    What pressure–volume work occurs against constant external pressure?

    回答

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

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

56. カード 56

    質問

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

    回答

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

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

57. カード 57

    質問

    How large can static friction become before slipping begins?

    回答

    $f_s\leq\mu_sN$, 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. カード 58

    質問

    Which relationship handles dilution when solute amount is conserved?

    回答

    $M_1V_1=M_2V_2$.

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

59. カード 59

    質問

    What is Ohm's law for an ohmic element?

    回答

    $V=IR$.

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

60. カード 60

    質問

    How is the reaction quotient $Q$ constructed?

    回答

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

61. カード 61

    質問

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

    回答

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. カード 62

    質問

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

    回答

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

63. カード 63

    質問

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

    回答

    $F_1/A_1=F_2/A_2$.

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

64. カード 64

    質問

    How much charge passes through a cell carrying constant current?

    回答

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. カード 65

    質問

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

    回答

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

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

66. カード 66

    質問

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

    回答

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

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

67. カード 67

    質問

    How is the coulomb expressed through SI base units?

    回答

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

    Charge equals current multiplied by time.

68. カード 68

    質問

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    回答

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

69. カード 69

    質問

    How is sound intensity level in decibels defined?

    回答

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

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

70. カード 70

    質問

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

    回答

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

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

71. カード 71

    質問

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

    回答

    $R=\rho L/A$.

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

72. カード 72

    質問

    Which equation gives the magnitude of torque from a force?

    回答

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

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

73. カード 73

    質問

    How is mass percent composition calculated?

    回答

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

74. カード 74

    質問

    What buoyant force acts on a submerged object?

    回答

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

    It equals the weight of displaced fluid.

75. カード 75

    質問

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

    回答

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

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

76. カード 76

    質問

    What two conditions define static mechanical equilibrium?

    回答

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

    Both translational and rotational equilibrium are required.

77. カード 77

    質問

    How does Hess's law combine reaction enthalpies?

    回答

    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. カード 78

    質問

    Which equivalent forms give electrical power in a resistor?

    回答

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

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

79. カード 79

    質問

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

    回答

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

80. カード 80

    質問

    What decibel change corresponds to multiplying sound intensity by 10?

    回答

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

81. カード 81

    質問

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

    回答

    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. カード 82

    質問

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

    回答

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

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

83. カード 83

    質問

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

    回答

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

84. カード 84

    質問

    How is the volt expressed through joules and coulombs?

    回答

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

    Voltage is energy transferred per unit charge.

85. カード 85

    質問

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

    回答

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

86. カード 86

    質問

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

    回答

    $W=Fd\cos\theta$.

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

87. カード 87

    質問

    How is volume percent calculated for a liquid mixture?

    回答

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

    Use it only when the problem defines composition by volume.

88. カード 88

    質問

    How do resistors combine in series?

    回答

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

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

89. カード 89

    質問

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

    回答

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

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

90. カード 90

    質問

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

    回答

    $Q=Av$.

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

    

    180枚のカード

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

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91. カード 91

    質問

    How can average bond energies estimate reaction enthalpy?

    回答

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

    Breaking bonds costs energy; forming bonds releases it.

92. カード 92

    質問

    What is the translational kinetic energy of a point mass?

    回答

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. カード 93

    質問

    What ratio defines parts per million by mass?

    回答

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

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

94. カード 94

    質問

    How do resistors combine in parallel?

    回答

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

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

95. カード 95

    質問

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

    回答

    $K_aK_b=K_w$.

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

96. カード 96

    質問

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

    回答

    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. カード 97

    質問

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

    回答

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

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

98. カード 98

    質問

    How is lateral magnification related to image and object distances?

    回答

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

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

99. カード 99

    質問

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

    回答

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. カード 100

     質問

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

     回答

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

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

101. カード 101

     質問

     How does reversing a reaction change its equilibrium constant?

     回答

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

102. カード 102

     質問

     What does the work–energy theorem say?

     回答

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

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

103. カード 103

     質問

     What entropy change accompanies reversible heat transfer at constant temperature?

     回答

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

     Temperature must be in kelvin.

104. カード 104

     質問

     What does Kirchhoff's junction rule require?

     回答

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

     It follows from conservation of charge at a node.

105. カード 105

     質問

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

     回答

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

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

106. カード 106

     質問

     What continuity relationship applies to steady incompressible flow?

     回答

     $A_1v_1=A_2v_2$.

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

107. カード 107

     質問

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

     回答

     $m=\rho V$.

     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. カード 108

     質問

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

     回答

     $U_g=mgh$.

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

109. カード 109

     質問

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

     回答

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

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

110. カード 110

     質問

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

     回答

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

     Both open ends are displacement antinodes.

111. カード 111

     質問

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

     回答

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

     Use compatible energy units and absolute temperature.

112. カード 112

     質問

     What does Kirchhoff's loop rule require?

     回答

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

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

113. カード 113

     質問

     What elastic potential energy is stored in an ideal spring?

     回答

     $U_s=\tfrac12kx^2$.

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

114. カード 114

     質問

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

     回答

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

     Dividing coefficients by $n$ takes the corresponding root.

115. カード 115

     質問

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

     回答

     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. カード 116

     質問

     How is lens power related to focal length?

     回答

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

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

117. カード 117

     質問

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

     回答

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

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

118. カード 118

     質問

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

     回答

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

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

119. カード 119

     質問

     What is the Nernst equation for a cell reaction?

     回答

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

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

120. カード 120

     質問

     What force does an ideal spring exert?

     回答

     $F_s=-kx$.

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

121. カード 121

     質問

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

     回答

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. カード 122

     質問

     Which relationship defines capacitance?

     回答

     $C=Q/V$.

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

123. カード 123

     質問

     How do elemental mass percentages lead to an empirical formula?

     回答

     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. カード 124

     質問

     When can mechanical energy be conserved?

     回答

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

125. カード 125

     質問

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

     回答

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

126. カード 126

     質問

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

     回答

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

127. カード 127

     質問

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

     回答

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

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

128. カード 128

     質問

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

     回答

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

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

129. カード 129

     質問

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

     回答

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

     It is independent of initial concentration.

130. カード 130

     質問

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

     回答

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. カード 131

     質問

     How is a molecular formula obtained from an empirical formula?

     回答

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

132. カード 132

     質問

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

     回答

     $C=\kappa\varepsilon_0A/d$.

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

133. カード 133

     質問

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

     回答

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

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

134. カード 134

     質問

     Which relationship gives laminar flow through a cylindrical tube?

     回答

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

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

135. カード 135

     質問

     How do equilibrium constants combine when reactions are added?

     回答

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

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

136. カード 136

     質問

     Which relationship defines average power?

     回答

     $P=W/\Delta t$.

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

137. カード 137

     質問

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

     回答

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

138. カード 138

     質問

     Which equivalent forms give energy stored in a capacitor?

     回答

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

     Use the form matching the known variables.

139. カード 139

     質問

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

     回答

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

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

140. カード 140

     質問

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

     回答

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

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

141. カード 141

     質問

     How is percent yield calculated?

     回答

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

142. カード 142

     質問

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

     回答

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

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

143. カード 143

     質問

     What stoichiometric condition marks acid–base equivalence?

     回答

     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. カード 144

     質問

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

     回答

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

145. カード 145

     質問

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

     回答

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

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

146. カード 146

     質問

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

     回答

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

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

147. カード 147

     質問

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     回答

     $Re=\rho vD/\eta$.

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

148. カード 148

     質問

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

     回答

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

     This predicts the favorable direction under nonstandard conditions.

149. カード 149

     質問

     What is linear momentum?

     回答

     $\vec p=m\vec v$.

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

150. カード 150

     質問

     How do you identify the limiting reactant from available moles?

     回答

     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. カード 151

     質問

     How do capacitors combine in parallel?

     回答

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

     Parallel capacitors share voltage and their stored charges add.

152. カード 152

     質問

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

     回答

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

153. カード 153

     質問

     What relationship connects impulse and momentum change?

     回答

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

154. カード 154

     質問

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

     回答

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

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

155. カード 155

     質問

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

     回答

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

     The central maximum lies between the first minima.

156. カード 156

     質問

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

     回答

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

157. カード 157

     質問

     How do capacitors combine in series?

     回答

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

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

158. カード 158

     質問

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

     回答

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

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

159. カード 159

     質問

     What beat frequency is heard from two nearby tones?

     回答

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

     Beats arise from alternating constructive and destructive interference.

160. カード 160

     質問

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

     回答

     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. カード 161

     質問

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

     回答

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

162. カード 162

     質問

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

     回答

     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. カード 163

     質問

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

     回答

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

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

164. カード 164

     質問

     When is total linear momentum conserved?

     回答

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

165. カード 165

     質問

     What relationship connects absorbance and concentration in a dilute solution?

     回答

     $A=\varepsilon bc$.

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

166. カード 166

     質問

     What magnetic force acts on a moving charge?

     回答

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

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

167. カード 167

     質問

     How does the Arrhenius equation relate rate constant and temperature?

     回答

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

168. カード 168

     質問

     What is centripetal acceleration for uniform circular motion?

     回答

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

     It points toward the center even when speed is constant.

169. カード 169

     質問

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

     回答

     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. カード 170

     質問

     What is the maximum kinetic energy in the photoelectric effect?

     回答

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

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

171. カード 171

     質問

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

     回答

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

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

172. カード 172

     質問

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

     回答

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

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

173. カード 173

     質問

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

     回答

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

     This relation changes when a common ion is already present.

174. カード 174

     質問

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

     回答

     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. カード 175

     質問

     How is percent ionization of a weak acid calculated?

     回答

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

176. カード 176

     質問

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

     回答

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

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

177. カード 177

     質問

     What energy balance applies in an insulated calorimetry problem?

     回答

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

178. カード 178

     質問

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

     回答

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

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

179. カード 179

     質問

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

     回答

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

180. カード 180

     質問

     What net inward force is required for circular motion?

     回答

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

     “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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