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

Tarjetas de este mazo

1. Tarjeta 1

   Pregunta

   Which relationship gives average velocity over a time interval?

   Respuesta

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

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

2. Tarjeta 2

   Pregunta

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

   Respuesta

   $n=m/M$.

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

3. Tarjeta 3

   Pregunta

   What is the electrostatic force between two point charges?

   Respuesta

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

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

4. Tarjeta 4

   Pregunta

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

   Respuesta

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. Tarjeta 5

   Pregunta

   How are period and frequency related?

   Respuesta

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. Tarjeta 6

   Pregunta

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

   Respuesta

   $q=mc\Delta T$.

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

7. Tarjeta 7

   Pregunta

   Which relationship defines mass density?

   Respuesta

   $\rho=m/V$.

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

8. Tarjeta 8

   Pregunta

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

   Respuesta

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. Tarjeta 9

   Pregunta

   How is photon energy related to frequency and wavelength?

   Respuesta

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. Tarjeta 10

    Pregunta

    How is standard cell potential calculated from reduction potentials?

    Respuesta

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

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

11. Tarjeta 11

    Pregunta

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

    Respuesta

    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. Tarjeta 12

    Pregunta

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

    Respuesta

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

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

13. Tarjeta 13

    Pregunta

    Which relationship gives average acceleration over a time interval?

    Respuesta

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

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

14. Tarjeta 14

    Pregunta

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

    Respuesta

    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. Tarjeta 15

    Pregunta

    What electric-field magnitude does a point charge produce?

    Respuesta

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

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

16. Tarjeta 16

    Pregunta

    How do moles relate to the number of microscopic particles?

    Respuesta

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

17. Tarjeta 17

    Pregunta

    For constant acceleration, how does velocity change with time?

    Respuesta

    $v=v_0+at$.

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

18. Tarjeta 18

    Pregunta

    How is pOH defined?

    Respuesta

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

19. Tarjeta 19

    Pregunta

    How is specific gravity defined?

    Respuesta

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

    It is dimensionless because it is a density ratio.

20. Tarjeta 20

    Pregunta

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

    Respuesta

    $q=C\Delta T$.

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

21. Tarjeta 21

    Pregunta

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

    Respuesta

    $c=f\lambda$.

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

22. Tarjeta 22

    Pregunta

    Which species are omitted from a heterogeneous equilibrium expression?

    Respuesta

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

23. Tarjeta 23

    Pregunta

    What force does an electric field exert on a charge?

    Respuesta

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. Tarjeta 24

    Pregunta

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

    Respuesta

    $PV=nRT$.

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

25. Tarjeta 25

    Pregunta

    Which equation relates wave speed, frequency, and wavelength?

    Respuesta

    $v=f\lambda$.

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

26. Tarjeta 26

    Pregunta

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

    Respuesta

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

    Its value changes with temperature.

27. Tarjeta 27

    Pregunta

    What base-unit dimensions define one newton?

    Respuesta

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

    A force must have dimensions of mass times acceleration.

28. Tarjeta 28

    Pregunta

    How is cell potential related to reaction free energy?

    Respuesta

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

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

29. Tarjeta 29

    Pregunta

    For constant acceleration, how does displacement depend on time?

    Respuesta

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

    Choose a positive direction first, then keep signs consistent.

30. Tarjeta 30

    Pregunta

    How is molarity defined?

    Respuesta

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

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

31. Tarjeta 31

    Pregunta

    What electric potential does a point charge produce?

    Respuesta

    $V=k_e q/r$.

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

32. Tarjeta 32

    Pregunta

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

    Respuesta

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

33. Tarjeta 33

    Pregunta

    Which constant-acceleration equation avoids time?

    Respuesta

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

    It connects speed and displacement when time is absent.

34. Tarjeta 34

    Pregunta

    What is the general experimental rate-law form?

    Respuesta

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

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

35. Tarjeta 35

    Pregunta

    Which relationship defines pressure from a normal force?

    Respuesta

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. Tarjeta 36

    Pregunta

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

    Respuesta

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

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

37. Tarjeta 37

    Pregunta

    How is wave intensity related to transmitted power and area?

    Respuesta

    $I=P/A$.

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

38. Tarjeta 38

    Pregunta

    How is molality defined?

    Respuesta

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

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

39. Tarjeta 39

    Pregunta

    What base-unit dimensions define one joule?

    Respuesta

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

    Work, energy, and heat share this unit.

40. Tarjeta 40

    Pregunta

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

    Respuesta

    $\Delta U=q+w$.

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

41. Tarjeta 41

    Pregunta

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

    Respuesta

    $n=c/v$.

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

42. Tarjeta 42

    Pregunta

    What equation links net force and acceleration?

    Respuesta

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

    The vector sum of external forces determines the acceleration.

43. Tarjeta 43

    Pregunta

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

    Respuesta

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. Tarjeta 44

    Pregunta

    How is electric potential energy related to charge and voltage?

    Respuesta

    $\Delta U=q\Delta V$.

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

45. Tarjeta 45

    Pregunta

    How are standard cell potential and the equilibrium constant related?

    Respuesta

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

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

46. Tarjeta 46

    Pregunta

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

    Respuesta

    $W=mg$.

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

47. Tarjeta 47

    Pregunta

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

    Respuesta

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

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

48. Tarjeta 48

    Pregunta

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

    Respuesta

    $P=P_0+\rho gh$.

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

49. Tarjeta 49

    Pregunta

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

    Respuesta

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

50. Tarjeta 50

    Pregunta

    Which relationship defines electric current?

    Respuesta

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

    Conventional current points in the direction positive charge would move.

51. Tarjeta 51

    Pregunta

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

    Respuesta

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

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

52. Tarjeta 52

    Pregunta

    What equation governs refraction at a boundary?

    Respuesta

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

    Angles are measured from the normal, not the surface.

53. Tarjeta 53

    Pregunta

    How is mole fraction defined for component $i$?

    Respuesta

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. Tarjeta 54

    Pregunta

    What SI units and base dimensions define pressure?

    Respuesta

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

55. Tarjeta 55

    Pregunta

    What pressure–volume work occurs against constant external pressure?

    Respuesta

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

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

56. Tarjeta 56

    Pregunta

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

    Respuesta

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

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

57. Tarjeta 57

    Pregunta

    How large can static friction become before slipping begins?

    Respuesta

    $f_s\leq\mu_sN$, 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. Tarjeta 58

    Pregunta

    Which relationship handles dilution when solute amount is conserved?

    Respuesta

    $M_1V_1=M_2V_2$.

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

59. Tarjeta 59

    Pregunta

    What is Ohm's law for an ohmic element?

    Respuesta

    $V=IR$.

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

60. Tarjeta 60

    Pregunta

    How is the reaction quotient $Q$ constructed?

    Respuesta

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

61. Tarjeta 61

    Pregunta

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

    Respuesta

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. Tarjeta 62

    Pregunta

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

    Respuesta

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

63. Tarjeta 63

    Pregunta

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

    Respuesta

    $F_1/A_1=F_2/A_2$.

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

64. Tarjeta 64

    Pregunta

    How much charge passes through a cell carrying constant current?

    Respuesta

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. Tarjeta 65

    Pregunta

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

    Respuesta

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

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

66. Tarjeta 66

    Pregunta

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

    Respuesta

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

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

67. Tarjeta 67

    Pregunta

    How is the coulomb expressed through SI base units?

    Respuesta

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

    Charge equals current multiplied by time.

68. Tarjeta 68

    Pregunta

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    Respuesta

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

69. Tarjeta 69

    Pregunta

    How is sound intensity level in decibels defined?

    Respuesta

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

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

70. Tarjeta 70

    Pregunta

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

    Respuesta

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

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

71. Tarjeta 71

    Pregunta

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

    Respuesta

    $R=\rho L/A$.

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

72. Tarjeta 72

    Pregunta

    Which equation gives the magnitude of torque from a force?

    Respuesta

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

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

73. Tarjeta 73

    Pregunta

    How is mass percent composition calculated?

    Respuesta

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

74. Tarjeta 74

    Pregunta

    What buoyant force acts on a submerged object?

    Respuesta

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

    It equals the weight of displaced fluid.

75. Tarjeta 75

    Pregunta

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

    Respuesta

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

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

76. Tarjeta 76

    Pregunta

    What two conditions define static mechanical equilibrium?

    Respuesta

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

    Both translational and rotational equilibrium are required.

77. Tarjeta 77

    Pregunta

    How does Hess's law combine reaction enthalpies?

    Respuesta

    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. Tarjeta 78

    Pregunta

    Which equivalent forms give electrical power in a resistor?

    Respuesta

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

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

79. Tarjeta 79

    Pregunta

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

    Respuesta

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

80. Tarjeta 80

    Pregunta

    What decibel change corresponds to multiplying sound intensity by 10?

    Respuesta

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

81. Tarjeta 81

    Pregunta

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

    Respuesta

    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. Tarjeta 82

    Pregunta

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

    Respuesta

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

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

83. Tarjeta 83

    Pregunta

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

    Respuesta

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

84. Tarjeta 84

    Pregunta

    How is the volt expressed through joules and coulombs?

    Respuesta

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

    Voltage is energy transferred per unit charge.

85. Tarjeta 85

    Pregunta

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

    Respuesta

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

86. Tarjeta 86

    Pregunta

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

    Respuesta

    $W=Fd\cos\theta$.

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

87. Tarjeta 87

    Pregunta

    How is volume percent calculated for a liquid mixture?

    Respuesta

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

    Use it only when the problem defines composition by volume.

88. Tarjeta 88

    Pregunta

    How do resistors combine in series?

    Respuesta

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

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

89. Tarjeta 89

    Pregunta

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

    Respuesta

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

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

90. Tarjeta 90

    Pregunta

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

    Respuesta

    $Q=Av$.

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

    

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91. Tarjeta 91

    Pregunta

    How can average bond energies estimate reaction enthalpy?

    Respuesta

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

    Breaking bonds costs energy; forming bonds releases it.

92. Tarjeta 92

    Pregunta

    What is the translational kinetic energy of a point mass?

    Respuesta

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. Tarjeta 93

    Pregunta

    What ratio defines parts per million by mass?

    Respuesta

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

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

94. Tarjeta 94

    Pregunta

    How do resistors combine in parallel?

    Respuesta

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

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

95. Tarjeta 95

    Pregunta

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

    Respuesta

    $K_aK_b=K_w$.

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

96. Tarjeta 96

    Pregunta

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

    Respuesta

    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. Tarjeta 97

    Pregunta

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

    Respuesta

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

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

98. Tarjeta 98

    Pregunta

    How is lateral magnification related to image and object distances?

    Respuesta

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

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

99. Tarjeta 99

    Pregunta

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

    Respuesta

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. Tarjeta 100

     Pregunta

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

     Respuesta

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

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

101. Tarjeta 101

     Pregunta

     How does reversing a reaction change its equilibrium constant?

     Respuesta

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

102. Tarjeta 102

     Pregunta

     What does the work–energy theorem say?

     Respuesta

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

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

103. Tarjeta 103

     Pregunta

     What entropy change accompanies reversible heat transfer at constant temperature?

     Respuesta

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

     Temperature must be in kelvin.

104. Tarjeta 104

     Pregunta

     What does Kirchhoff's junction rule require?

     Respuesta

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

     It follows from conservation of charge at a node.

105. Tarjeta 105

     Pregunta

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

     Respuesta

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

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

106. Tarjeta 106

     Pregunta

     What continuity relationship applies to steady incompressible flow?

     Respuesta

     $A_1v_1=A_2v_2$.

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

107. Tarjeta 107

     Pregunta

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

     Respuesta

     $m=\rho V$.

     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. Tarjeta 108

     Pregunta

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

     Respuesta

     $U_g=mgh$.

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

109. Tarjeta 109

     Pregunta

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

     Respuesta

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

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

110. Tarjeta 110

     Pregunta

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

     Respuesta

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

     Both open ends are displacement antinodes.

111. Tarjeta 111

     Pregunta

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

     Respuesta

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

     Use compatible energy units and absolute temperature.

112. Tarjeta 112

     Pregunta

     What does Kirchhoff's loop rule require?

     Respuesta

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

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

113. Tarjeta 113

     Pregunta

     What elastic potential energy is stored in an ideal spring?

     Respuesta

     $U_s=\tfrac12kx^2$.

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

114. Tarjeta 114

     Pregunta

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

     Respuesta

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

     Dividing coefficients by $n$ takes the corresponding root.

115. Tarjeta 115

     Pregunta

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

     Respuesta

     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. Tarjeta 116

     Pregunta

     How is lens power related to focal length?

     Respuesta

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

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

117. Tarjeta 117

     Pregunta

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

     Respuesta

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

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

118. Tarjeta 118

     Pregunta

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

     Respuesta

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

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

119. Tarjeta 119

     Pregunta

     What is the Nernst equation for a cell reaction?

     Respuesta

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

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

120. Tarjeta 120

     Pregunta

     What force does an ideal spring exert?

     Respuesta

     $F_s=-kx$.

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

121. Tarjeta 121

     Pregunta

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

     Respuesta

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. Tarjeta 122

     Pregunta

     Which relationship defines capacitance?

     Respuesta

     $C=Q/V$.

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

123. Tarjeta 123

     Pregunta

     How do elemental mass percentages lead to an empirical formula?

     Respuesta

     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. Tarjeta 124

     Pregunta

     When can mechanical energy be conserved?

     Respuesta

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

125. Tarjeta 125

     Pregunta

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

     Respuesta

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

126. Tarjeta 126

     Pregunta

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

     Respuesta

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

127. Tarjeta 127

     Pregunta

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

     Respuesta

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

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

128. Tarjeta 128

     Pregunta

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

     Respuesta

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

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

129. Tarjeta 129

     Pregunta

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

     Respuesta

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

     It is independent of initial concentration.

130. Tarjeta 130

     Pregunta

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

     Respuesta

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. Tarjeta 131

     Pregunta

     How is a molecular formula obtained from an empirical formula?

     Respuesta

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

132. Tarjeta 132

     Pregunta

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

     Respuesta

     $C=\kappa\varepsilon_0A/d$.

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

133. Tarjeta 133

     Pregunta

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

     Respuesta

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

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

134. Tarjeta 134

     Pregunta

     Which relationship gives laminar flow through a cylindrical tube?

     Respuesta

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

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

135. Tarjeta 135

     Pregunta

     How do equilibrium constants combine when reactions are added?

     Respuesta

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

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

136. Tarjeta 136

     Pregunta

     Which relationship defines average power?

     Respuesta

     $P=W/\Delta t$.

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

137. Tarjeta 137

     Pregunta

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

     Respuesta

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

138. Tarjeta 138

     Pregunta

     Which equivalent forms give energy stored in a capacitor?

     Respuesta

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

     Use the form matching the known variables.

139. Tarjeta 139

     Pregunta

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

     Respuesta

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

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

140. Tarjeta 140

     Pregunta

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

     Respuesta

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

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

141. Tarjeta 141

     Pregunta

     How is percent yield calculated?

     Respuesta

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

142. Tarjeta 142

     Pregunta

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

     Respuesta

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

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

143. Tarjeta 143

     Pregunta

     What stoichiometric condition marks acid–base equivalence?

     Respuesta

     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. Tarjeta 144

     Pregunta

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

     Respuesta

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

145. Tarjeta 145

     Pregunta

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

     Respuesta

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

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

146. Tarjeta 146

     Pregunta

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

     Respuesta

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

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

147. Tarjeta 147

     Pregunta

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     Respuesta

     $Re=\rho vD/\eta$.

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

148. Tarjeta 148

     Pregunta

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

     Respuesta

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

     This predicts the favorable direction under nonstandard conditions.

149. Tarjeta 149

     Pregunta

     What is linear momentum?

     Respuesta

     $\vec p=m\vec v$.

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

150. Tarjeta 150

     Pregunta

     How do you identify the limiting reactant from available moles?

     Respuesta

     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. Tarjeta 151

     Pregunta

     How do capacitors combine in parallel?

     Respuesta

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

     Parallel capacitors share voltage and their stored charges add.

152. Tarjeta 152

     Pregunta

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

     Respuesta

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

153. Tarjeta 153

     Pregunta

     What relationship connects impulse and momentum change?

     Respuesta

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

154. Tarjeta 154

     Pregunta

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

     Respuesta

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

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

155. Tarjeta 155

     Pregunta

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

     Respuesta

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

     The central maximum lies between the first minima.

156. Tarjeta 156

     Pregunta

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

     Respuesta

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

157. Tarjeta 157

     Pregunta

     How do capacitors combine in series?

     Respuesta

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

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

158. Tarjeta 158

     Pregunta

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

     Respuesta

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

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

159. Tarjeta 159

     Pregunta

     What beat frequency is heard from two nearby tones?

     Respuesta

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

     Beats arise from alternating constructive and destructive interference.

160. Tarjeta 160

     Pregunta

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

     Respuesta

     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. Tarjeta 161

     Pregunta

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

     Respuesta

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

162. Tarjeta 162

     Pregunta

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

     Respuesta

     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. Tarjeta 163

     Pregunta

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

     Respuesta

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

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

164. Tarjeta 164

     Pregunta

     When is total linear momentum conserved?

     Respuesta

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

165. Tarjeta 165

     Pregunta

     What relationship connects absorbance and concentration in a dilute solution?

     Respuesta

     $A=\varepsilon bc$.

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

166. Tarjeta 166

     Pregunta

     What magnetic force acts on a moving charge?

     Respuesta

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

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

167. Tarjeta 167

     Pregunta

     How does the Arrhenius equation relate rate constant and temperature?

     Respuesta

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

168. Tarjeta 168

     Pregunta

     What is centripetal acceleration for uniform circular motion?

     Respuesta

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

     It points toward the center even when speed is constant.

169. Tarjeta 169

     Pregunta

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

     Respuesta

     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. Tarjeta 170

     Pregunta

     What is the maximum kinetic energy in the photoelectric effect?

     Respuesta

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

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

171. Tarjeta 171

     Pregunta

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

     Respuesta

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

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

172. Tarjeta 172

     Pregunta

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

     Respuesta

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

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

173. Tarjeta 173

     Pregunta

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

     Respuesta

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

     This relation changes when a common ion is already present.

174. Tarjeta 174

     Pregunta

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

     Respuesta

     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. Tarjeta 175

     Pregunta

     How is percent ionization of a weak acid calculated?

     Respuesta

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

176. Tarjeta 176

     Pregunta

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

     Respuesta

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

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

177. Tarjeta 177

     Pregunta

     What energy balance applies in an insulated calorimetry problem?

     Respuesta

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

178. Tarjeta 178

     Pregunta

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

     Respuesta

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

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

179. Tarjeta 179

     Pregunta

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

     Respuesta

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

180. Tarjeta 180

     Pregunta

     What net inward force is required for circular motion?

     Respuesta

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

     “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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