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

Carte in questo mazzo

1. Carta 1

   Domanda

   Which relationship gives average velocity over a time interval?

   Risposta

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

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

2. Carta 2

   Domanda

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

   Risposta

   $n=m/M$.

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

3. Carta 3

   Domanda

   What is the electrostatic force between two point charges?

   Risposta

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

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

4. Carta 4

   Domanda

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

   Risposta

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. Carta 5

   Domanda

   How are period and frequency related?

   Risposta

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. Carta 6

   Domanda

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

   Risposta

   $q=mc\Delta T$.

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

7. Carta 7

   Domanda

   Which relationship defines mass density?

   Risposta

   $\rho=m/V$.

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

8. Carta 8

   Domanda

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

   Risposta

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. Carta 9

   Domanda

   How is photon energy related to frequency and wavelength?

   Risposta

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. Carta 10

    Domanda

    How is standard cell potential calculated from reduction potentials?

    Risposta

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

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

11. Carta 11

    Domanda

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

    Risposta

    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. Carta 12

    Domanda

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

    Risposta

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

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

13. Carta 13

    Domanda

    Which relationship gives average acceleration over a time interval?

    Risposta

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

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

14. Carta 14

    Domanda

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

    Risposta

    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. Carta 15

    Domanda

    What electric-field magnitude does a point charge produce?

    Risposta

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

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

16. Carta 16

    Domanda

    How do moles relate to the number of microscopic particles?

    Risposta

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

17. Carta 17

    Domanda

    For constant acceleration, how does velocity change with time?

    Risposta

    $v=v_0+at$.

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

18. Carta 18

    Domanda

    How is pOH defined?

    Risposta

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

19. Carta 19

    Domanda

    How is specific gravity defined?

    Risposta

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

    It is dimensionless because it is a density ratio.

20. Carta 20

    Domanda

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

    Risposta

    $q=C\Delta T$.

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

21. Carta 21

    Domanda

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

    Risposta

    $c=f\lambda$.

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

22. Carta 22

    Domanda

    Which species are omitted from a heterogeneous equilibrium expression?

    Risposta

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

23. Carta 23

    Domanda

    What force does an electric field exert on a charge?

    Risposta

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. Carta 24

    Domanda

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

    Risposta

    $PV=nRT$.

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

25. Carta 25

    Domanda

    Which equation relates wave speed, frequency, and wavelength?

    Risposta

    $v=f\lambda$.

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

26. Carta 26

    Domanda

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

    Risposta

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

    Its value changes with temperature.

27. Carta 27

    Domanda

    What base-unit dimensions define one newton?

    Risposta

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

    A force must have dimensions of mass times acceleration.

28. Carta 28

    Domanda

    How is cell potential related to reaction free energy?

    Risposta

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

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

29. Carta 29

    Domanda

    For constant acceleration, how does displacement depend on time?

    Risposta

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

    Choose a positive direction first, then keep signs consistent.

30. Carta 30

    Domanda

    How is molarity defined?

    Risposta

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

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

31. Carta 31

    Domanda

    What electric potential does a point charge produce?

    Risposta

    $V=k_e q/r$.

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

32. Carta 32

    Domanda

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

    Risposta

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

33. Carta 33

    Domanda

    Which constant-acceleration equation avoids time?

    Risposta

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

    It connects speed and displacement when time is absent.

34. Carta 34

    Domanda

    What is the general experimental rate-law form?

    Risposta

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

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

35. Carta 35

    Domanda

    Which relationship defines pressure from a normal force?

    Risposta

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. Carta 36

    Domanda

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

    Risposta

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

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

37. Carta 37

    Domanda

    How is wave intensity related to transmitted power and area?

    Risposta

    $I=P/A$.

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

38. Carta 38

    Domanda

    How is molality defined?

    Risposta

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

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

39. Carta 39

    Domanda

    What base-unit dimensions define one joule?

    Risposta

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

    Work, energy, and heat share this unit.

40. Carta 40

    Domanda

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

    Risposta

    $\Delta U=q+w$.

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

41. Carta 41

    Domanda

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

    Risposta

    $n=c/v$.

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

42. Carta 42

    Domanda

    What equation links net force and acceleration?

    Risposta

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

    The vector sum of external forces determines the acceleration.

43. Carta 43

    Domanda

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

    Risposta

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. Carta 44

    Domanda

    How is electric potential energy related to charge and voltage?

    Risposta

    $\Delta U=q\Delta V$.

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

45. Carta 45

    Domanda

    How are standard cell potential and the equilibrium constant related?

    Risposta

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

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

46. Carta 46

    Domanda

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

    Risposta

    $W=mg$.

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

47. Carta 47

    Domanda

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

    Risposta

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

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

48. Carta 48

    Domanda

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

    Risposta

    $P=P_0+\rho gh$.

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

49. Carta 49

    Domanda

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

    Risposta

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

50. Carta 50

    Domanda

    Which relationship defines electric current?

    Risposta

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

    Conventional current points in the direction positive charge would move.

51. Carta 51

    Domanda

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

    Risposta

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

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

52. Carta 52

    Domanda

    What equation governs refraction at a boundary?

    Risposta

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

    Angles are measured from the normal, not the surface.

53. Carta 53

    Domanda

    How is mole fraction defined for component $i$?

    Risposta

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. Carta 54

    Domanda

    What SI units and base dimensions define pressure?

    Risposta

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

55. Carta 55

    Domanda

    What pressure–volume work occurs against constant external pressure?

    Risposta

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

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

56. Carta 56

    Domanda

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

    Risposta

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

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

57. Carta 57

    Domanda

    How large can static friction become before slipping begins?

    Risposta

    $f_s\leq\mu_sN$, 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. Carta 58

    Domanda

    Which relationship handles dilution when solute amount is conserved?

    Risposta

    $M_1V_1=M_2V_2$.

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

59. Carta 59

    Domanda

    What is Ohm's law for an ohmic element?

    Risposta

    $V=IR$.

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

60. Carta 60

    Domanda

    How is the reaction quotient $Q$ constructed?

    Risposta

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

61. Carta 61

    Domanda

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

    Risposta

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. Carta 62

    Domanda

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

    Risposta

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

63. Carta 63

    Domanda

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

    Risposta

    $F_1/A_1=F_2/A_2$.

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

64. Carta 64

    Domanda

    How much charge passes through a cell carrying constant current?

    Risposta

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. Carta 65

    Domanda

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

    Risposta

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

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

66. Carta 66

    Domanda

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

    Risposta

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

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

67. Carta 67

    Domanda

    How is the coulomb expressed through SI base units?

    Risposta

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

    Charge equals current multiplied by time.

68. Carta 68

    Domanda

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    Risposta

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

69. Carta 69

    Domanda

    How is sound intensity level in decibels defined?

    Risposta

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

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

70. Carta 70

    Domanda

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

    Risposta

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

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

71. Carta 71

    Domanda

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

    Risposta

    $R=\rho L/A$.

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

72. Carta 72

    Domanda

    Which equation gives the magnitude of torque from a force?

    Risposta

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

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

73. Carta 73

    Domanda

    How is mass percent composition calculated?

    Risposta

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

74. Carta 74

    Domanda

    What buoyant force acts on a submerged object?

    Risposta

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

    It equals the weight of displaced fluid.

75. Carta 75

    Domanda

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

    Risposta

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

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

76. Carta 76

    Domanda

    What two conditions define static mechanical equilibrium?

    Risposta

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

    Both translational and rotational equilibrium are required.

77. Carta 77

    Domanda

    How does Hess's law combine reaction enthalpies?

    Risposta

    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. Carta 78

    Domanda

    Which equivalent forms give electrical power in a resistor?

    Risposta

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

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

79. Carta 79

    Domanda

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

    Risposta

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

80. Carta 80

    Domanda

    What decibel change corresponds to multiplying sound intensity by 10?

    Risposta

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

81. Carta 81

    Domanda

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

    Risposta

    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. Carta 82

    Domanda

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

    Risposta

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

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

83. Carta 83

    Domanda

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

    Risposta

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

84. Carta 84

    Domanda

    How is the volt expressed through joules and coulombs?

    Risposta

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

    Voltage is energy transferred per unit charge.

85. Carta 85

    Domanda

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

    Risposta

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

86. Carta 86

    Domanda

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

    Risposta

    $W=Fd\cos\theta$.

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

87. Carta 87

    Domanda

    How is volume percent calculated for a liquid mixture?

    Risposta

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

    Use it only when the problem defines composition by volume.

88. Carta 88

    Domanda

    How do resistors combine in series?

    Risposta

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

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

89. Carta 89

    Domanda

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

    Risposta

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

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

90. Carta 90

    Domanda

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

    Risposta

    $Q=Av$.

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

    

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91. Carta 91

    Domanda

    How can average bond energies estimate reaction enthalpy?

    Risposta

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

    Breaking bonds costs energy; forming bonds releases it.

92. Carta 92

    Domanda

    What is the translational kinetic energy of a point mass?

    Risposta

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. Carta 93

    Domanda

    What ratio defines parts per million by mass?

    Risposta

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

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

94. Carta 94

    Domanda

    How do resistors combine in parallel?

    Risposta

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

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

95. Carta 95

    Domanda

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

    Risposta

    $K_aK_b=K_w$.

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

96. Carta 96

    Domanda

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

    Risposta

    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. Carta 97

    Domanda

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

    Risposta

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

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

98. Carta 98

    Domanda

    How is lateral magnification related to image and object distances?

    Risposta

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

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

99. Carta 99

    Domanda

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

    Risposta

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. Carta 100

     Domanda

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

     Risposta

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

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

101. Carta 101

     Domanda

     How does reversing a reaction change its equilibrium constant?

     Risposta

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

102. Carta 102

     Domanda

     What does the work–energy theorem say?

     Risposta

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

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

103. Carta 103

     Domanda

     What entropy change accompanies reversible heat transfer at constant temperature?

     Risposta

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

     Temperature must be in kelvin.

104. Carta 104

     Domanda

     What does Kirchhoff's junction rule require?

     Risposta

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

     It follows from conservation of charge at a node.

105. Carta 105

     Domanda

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

     Risposta

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

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

106. Carta 106

     Domanda

     What continuity relationship applies to steady incompressible flow?

     Risposta

     $A_1v_1=A_2v_2$.

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

107. Carta 107

     Domanda

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

     Risposta

     $m=\rho V$.

     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. Carta 108

     Domanda

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

     Risposta

     $U_g=mgh$.

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

109. Carta 109

     Domanda

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

     Risposta

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

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

110. Carta 110

     Domanda

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

     Risposta

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

     Both open ends are displacement antinodes.

111. Carta 111

     Domanda

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

     Risposta

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

     Use compatible energy units and absolute temperature.

112. Carta 112

     Domanda

     What does Kirchhoff's loop rule require?

     Risposta

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

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

113. Carta 113

     Domanda

     What elastic potential energy is stored in an ideal spring?

     Risposta

     $U_s=\tfrac12kx^2$.

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

114. Carta 114

     Domanda

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

     Risposta

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

     Dividing coefficients by $n$ takes the corresponding root.

115. Carta 115

     Domanda

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

     Risposta

     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. Carta 116

     Domanda

     How is lens power related to focal length?

     Risposta

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

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

117. Carta 117

     Domanda

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

     Risposta

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

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

118. Carta 118

     Domanda

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

     Risposta

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

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

119. Carta 119

     Domanda

     What is the Nernst equation for a cell reaction?

     Risposta

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

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

120. Carta 120

     Domanda

     What force does an ideal spring exert?

     Risposta

     $F_s=-kx$.

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

121. Carta 121

     Domanda

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

     Risposta

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. Carta 122

     Domanda

     Which relationship defines capacitance?

     Risposta

     $C=Q/V$.

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

123. Carta 123

     Domanda

     How do elemental mass percentages lead to an empirical formula?

     Risposta

     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. Carta 124

     Domanda

     When can mechanical energy be conserved?

     Risposta

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

125. Carta 125

     Domanda

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

     Risposta

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

126. Carta 126

     Domanda

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

     Risposta

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

127. Carta 127

     Domanda

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

     Risposta

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

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

128. Carta 128

     Domanda

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

     Risposta

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

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

129. Carta 129

     Domanda

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

     Risposta

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

     It is independent of initial concentration.

130. Carta 130

     Domanda

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

     Risposta

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. Carta 131

     Domanda

     How is a molecular formula obtained from an empirical formula?

     Risposta

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

132. Carta 132

     Domanda

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

     Risposta

     $C=\kappa\varepsilon_0A/d$.

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

133. Carta 133

     Domanda

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

     Risposta

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

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

134. Carta 134

     Domanda

     Which relationship gives laminar flow through a cylindrical tube?

     Risposta

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

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

135. Carta 135

     Domanda

     How do equilibrium constants combine when reactions are added?

     Risposta

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

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

136. Carta 136

     Domanda

     Which relationship defines average power?

     Risposta

     $P=W/\Delta t$.

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

137. Carta 137

     Domanda

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

     Risposta

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

138. Carta 138

     Domanda

     Which equivalent forms give energy stored in a capacitor?

     Risposta

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

     Use the form matching the known variables.

139. Carta 139

     Domanda

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

     Risposta

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

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

140. Carta 140

     Domanda

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

     Risposta

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

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

141. Carta 141

     Domanda

     How is percent yield calculated?

     Risposta

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

142. Carta 142

     Domanda

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

     Risposta

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

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

143. Carta 143

     Domanda

     What stoichiometric condition marks acid–base equivalence?

     Risposta

     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. Carta 144

     Domanda

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

     Risposta

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

145. Carta 145

     Domanda

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

     Risposta

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

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

146. Carta 146

     Domanda

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

     Risposta

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

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

147. Carta 147

     Domanda

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     Risposta

     $Re=\rho vD/\eta$.

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

148. Carta 148

     Domanda

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

     Risposta

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

     This predicts the favorable direction under nonstandard conditions.

149. Carta 149

     Domanda

     What is linear momentum?

     Risposta

     $\vec p=m\vec v$.

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

150. Carta 150

     Domanda

     How do you identify the limiting reactant from available moles?

     Risposta

     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. Carta 151

     Domanda

     How do capacitors combine in parallel?

     Risposta

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

     Parallel capacitors share voltage and their stored charges add.

152. Carta 152

     Domanda

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

     Risposta

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

153. Carta 153

     Domanda

     What relationship connects impulse and momentum change?

     Risposta

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

154. Carta 154

     Domanda

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

     Risposta

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

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

155. Carta 155

     Domanda

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

     Risposta

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

     The central maximum lies between the first minima.

156. Carta 156

     Domanda

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

     Risposta

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

157. Carta 157

     Domanda

     How do capacitors combine in series?

     Risposta

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

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

158. Carta 158

     Domanda

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

     Risposta

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

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

159. Carta 159

     Domanda

     What beat frequency is heard from two nearby tones?

     Risposta

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

     Beats arise from alternating constructive and destructive interference.

160. Carta 160

     Domanda

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

     Risposta

     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. Carta 161

     Domanda

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

     Risposta

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

162. Carta 162

     Domanda

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

     Risposta

     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. Carta 163

     Domanda

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

     Risposta

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

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

164. Carta 164

     Domanda

     When is total linear momentum conserved?

     Risposta

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

165. Carta 165

     Domanda

     What relationship connects absorbance and concentration in a dilute solution?

     Risposta

     $A=\varepsilon bc$.

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

166. Carta 166

     Domanda

     What magnetic force acts on a moving charge?

     Risposta

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

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

167. Carta 167

     Domanda

     How does the Arrhenius equation relate rate constant and temperature?

     Risposta

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

168. Carta 168

     Domanda

     What is centripetal acceleration for uniform circular motion?

     Risposta

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

     It points toward the center even when speed is constant.

169. Carta 169

     Domanda

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

     Risposta

     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. Carta 170

     Domanda

     What is the maximum kinetic energy in the photoelectric effect?

     Risposta

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

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

171. Carta 171

     Domanda

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

     Risposta

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

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

172. Carta 172

     Domanda

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

     Risposta

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

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

173. Carta 173

     Domanda

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

     Risposta

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

     This relation changes when a common ion is already present.

174. Carta 174

     Domanda

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

     Risposta

     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. Carta 175

     Domanda

     How is percent ionization of a weak acid calculated?

     Risposta

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

176. Carta 176

     Domanda

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

     Risposta

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

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

177. Carta 177

     Domanda

     What energy balance applies in an insulated calorimetry problem?

     Risposta

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

178. Carta 178

     Domanda

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

     Risposta

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

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

179. Carta 179

     Domanda

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

     Risposta

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

180. Carta 180

     Domanda

     What net inward force is required for circular motion?

     Risposta

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

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

180 carte

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

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