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

Карточки в этой колоде

1. Карточка 1

   Вопрос

   Which relationship gives average velocity over a time interval?

   Ответ

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

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

2. Карточка 2

   Вопрос

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

   Ответ

   $n=m/M$.

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

3. Карточка 3

   Вопрос

   What is the electrostatic force between two point charges?

   Ответ

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

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

4. Карточка 4

   Вопрос

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

   Ответ

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. Карточка 5

   Вопрос

   How are period and frequency related?

   Ответ

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. Карточка 6

   Вопрос

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

   Ответ

   $q=mc\Delta T$.

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

7. Карточка 7

   Вопрос

   Which relationship defines mass density?

   Ответ

   $\rho=m/V$.

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

8. Карточка 8

   Вопрос

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

   Ответ

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. Карточка 9

   Вопрос

   How is photon energy related to frequency and wavelength?

   Ответ

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. Карточка 10

    Вопрос

    How is standard cell potential calculated from reduction potentials?

    Ответ

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

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

11. Карточка 11

    Вопрос

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

    Ответ

    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. Карточка 12

    Вопрос

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

    Ответ

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

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

13. Карточка 13

    Вопрос

    Which relationship gives average acceleration over a time interval?

    Ответ

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

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

14. Карточка 14

    Вопрос

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

    Ответ

    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. Карточка 15

    Вопрос

    What electric-field magnitude does a point charge produce?

    Ответ

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

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

16. Карточка 16

    Вопрос

    How do moles relate to the number of microscopic particles?

    Ответ

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

17. Карточка 17

    Вопрос

    For constant acceleration, how does velocity change with time?

    Ответ

    $v=v_0+at$.

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

18. Карточка 18

    Вопрос

    How is pOH defined?

    Ответ

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

19. Карточка 19

    Вопрос

    How is specific gravity defined?

    Ответ

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

    It is dimensionless because it is a density ratio.

20. Карточка 20

    Вопрос

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

    Ответ

    $q=C\Delta T$.

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

21. Карточка 21

    Вопрос

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

    Ответ

    $c=f\lambda$.

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

22. Карточка 22

    Вопрос

    Which species are omitted from a heterogeneous equilibrium expression?

    Ответ

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

23. Карточка 23

    Вопрос

    What force does an electric field exert on a charge?

    Ответ

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. Карточка 24

    Вопрос

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

    Ответ

    $PV=nRT$.

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

25. Карточка 25

    Вопрос

    Which equation relates wave speed, frequency, and wavelength?

    Ответ

    $v=f\lambda$.

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

26. Карточка 26

    Вопрос

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

    Ответ

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

    Its value changes with temperature.

27. Карточка 27

    Вопрос

    What base-unit dimensions define one newton?

    Ответ

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

    A force must have dimensions of mass times acceleration.

28. Карточка 28

    Вопрос

    How is cell potential related to reaction free energy?

    Ответ

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

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

29. Карточка 29

    Вопрос

    For constant acceleration, how does displacement depend on time?

    Ответ

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

    Choose a positive direction first, then keep signs consistent.

30. Карточка 30

    Вопрос

    How is molarity defined?

    Ответ

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

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

31. Карточка 31

    Вопрос

    What electric potential does a point charge produce?

    Ответ

    $V=k_e q/r$.

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

32. Карточка 32

    Вопрос

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

    Ответ

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

33. Карточка 33

    Вопрос

    Which constant-acceleration equation avoids time?

    Ответ

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

    It connects speed and displacement when time is absent.

34. Карточка 34

    Вопрос

    What is the general experimental rate-law form?

    Ответ

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

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

35. Карточка 35

    Вопрос

    Which relationship defines pressure from a normal force?

    Ответ

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. Карточка 36

    Вопрос

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

    Ответ

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

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

37. Карточка 37

    Вопрос

    How is wave intensity related to transmitted power and area?

    Ответ

    $I=P/A$.

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

38. Карточка 38

    Вопрос

    How is molality defined?

    Ответ

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

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

39. Карточка 39

    Вопрос

    What base-unit dimensions define one joule?

    Ответ

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

    Work, energy, and heat share this unit.

40. Карточка 40

    Вопрос

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

    Ответ

    $\Delta U=q+w$.

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

41. Карточка 41

    Вопрос

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

    Ответ

    $n=c/v$.

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

42. Карточка 42

    Вопрос

    What equation links net force and acceleration?

    Ответ

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

    The vector sum of external forces determines the acceleration.

43. Карточка 43

    Вопрос

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

    Ответ

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. Карточка 44

    Вопрос

    How is electric potential energy related to charge and voltage?

    Ответ

    $\Delta U=q\Delta V$.

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

45. Карточка 45

    Вопрос

    How are standard cell potential and the equilibrium constant related?

    Ответ

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

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

46. Карточка 46

    Вопрос

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

    Ответ

    $W=mg$.

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

47. Карточка 47

    Вопрос

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

    Ответ

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

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

48. Карточка 48

    Вопрос

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

    Ответ

    $P=P_0+\rho gh$.

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

49. Карточка 49

    Вопрос

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

    Ответ

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

50. Карточка 50

    Вопрос

    Which relationship defines electric current?

    Ответ

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

    Conventional current points in the direction positive charge would move.

51. Карточка 51

    Вопрос

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

    Ответ

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

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

52. Карточка 52

    Вопрос

    What equation governs refraction at a boundary?

    Ответ

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

    Angles are measured from the normal, not the surface.

53. Карточка 53

    Вопрос

    How is mole fraction defined for component $i$?

    Ответ

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. Карточка 54

    Вопрос

    What SI units and base dimensions define pressure?

    Ответ

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

55. Карточка 55

    Вопрос

    What pressure–volume work occurs against constant external pressure?

    Ответ

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

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

56. Карточка 56

    Вопрос

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

    Ответ

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

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

57. Карточка 57

    Вопрос

    How large can static friction become before slipping begins?

    Ответ

    $f_s\leq\mu_sN$, 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. Карточка 58

    Вопрос

    Which relationship handles dilution when solute amount is conserved?

    Ответ

    $M_1V_1=M_2V_2$.

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

59. Карточка 59

    Вопрос

    What is Ohm's law for an ohmic element?

    Ответ

    $V=IR$.

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

60. Карточка 60

    Вопрос

    How is the reaction quotient $Q$ constructed?

    Ответ

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

61. Карточка 61

    Вопрос

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

    Ответ

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. Карточка 62

    Вопрос

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

    Ответ

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

63. Карточка 63

    Вопрос

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

    Ответ

    $F_1/A_1=F_2/A_2$.

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

64. Карточка 64

    Вопрос

    How much charge passes through a cell carrying constant current?

    Ответ

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. Карточка 65

    Вопрос

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

    Ответ

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

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

66. Карточка 66

    Вопрос

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

    Ответ

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

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

67. Карточка 67

    Вопрос

    How is the coulomb expressed through SI base units?

    Ответ

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

    Charge equals current multiplied by time.

68. Карточка 68

    Вопрос

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    Ответ

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

69. Карточка 69

    Вопрос

    How is sound intensity level in decibels defined?

    Ответ

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

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

70. Карточка 70

    Вопрос

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

    Ответ

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

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

71. Карточка 71

    Вопрос

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

    Ответ

    $R=\rho L/A$.

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

72. Карточка 72

    Вопрос

    Which equation gives the magnitude of torque from a force?

    Ответ

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

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

73. Карточка 73

    Вопрос

    How is mass percent composition calculated?

    Ответ

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

74. Карточка 74

    Вопрос

    What buoyant force acts on a submerged object?

    Ответ

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

    It equals the weight of displaced fluid.

75. Карточка 75

    Вопрос

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

    Ответ

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

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

76. Карточка 76

    Вопрос

    What two conditions define static mechanical equilibrium?

    Ответ

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

    Both translational and rotational equilibrium are required.

77. Карточка 77

    Вопрос

    How does Hess's law combine reaction enthalpies?

    Ответ

    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. Карточка 78

    Вопрос

    Which equivalent forms give electrical power in a resistor?

    Ответ

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

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

79. Карточка 79

    Вопрос

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

    Ответ

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

80. Карточка 80

    Вопрос

    What decibel change corresponds to multiplying sound intensity by 10?

    Ответ

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

81. Карточка 81

    Вопрос

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

    Ответ

    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. Карточка 82

    Вопрос

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

    Ответ

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

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

83. Карточка 83

    Вопрос

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

    Ответ

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

84. Карточка 84

    Вопрос

    How is the volt expressed through joules and coulombs?

    Ответ

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

    Voltage is energy transferred per unit charge.

85. Карточка 85

    Вопрос

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

    Ответ

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

86. Карточка 86

    Вопрос

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

    Ответ

    $W=Fd\cos\theta$.

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

87. Карточка 87

    Вопрос

    How is volume percent calculated for a liquid mixture?

    Ответ

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

    Use it only when the problem defines composition by volume.

88. Карточка 88

    Вопрос

    How do resistors combine in series?

    Ответ

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

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

89. Карточка 89

    Вопрос

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

    Ответ

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

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

90. Карточка 90

    Вопрос

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

    Ответ

    $Q=Av$.

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

    

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91. Карточка 91

    Вопрос

    How can average bond energies estimate reaction enthalpy?

    Ответ

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

    Breaking bonds costs energy; forming bonds releases it.

92. Карточка 92

    Вопрос

    What is the translational kinetic energy of a point mass?

    Ответ

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. Карточка 93

    Вопрос

    What ratio defines parts per million by mass?

    Ответ

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

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

94. Карточка 94

    Вопрос

    How do resistors combine in parallel?

    Ответ

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

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

95. Карточка 95

    Вопрос

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

    Ответ

    $K_aK_b=K_w$.

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

96. Карточка 96

    Вопрос

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

    Ответ

    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. Карточка 97

    Вопрос

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

    Ответ

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

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

98. Карточка 98

    Вопрос

    How is lateral magnification related to image and object distances?

    Ответ

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

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

99. Карточка 99

    Вопрос

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

    Ответ

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. Карточка 100

     Вопрос

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

     Ответ

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

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

101. Карточка 101

     Вопрос

     How does reversing a reaction change its equilibrium constant?

     Ответ

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

102. Карточка 102

     Вопрос

     What does the work–energy theorem say?

     Ответ

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

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

103. Карточка 103

     Вопрос

     What entropy change accompanies reversible heat transfer at constant temperature?

     Ответ

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

     Temperature must be in kelvin.

104. Карточка 104

     Вопрос

     What does Kirchhoff's junction rule require?

     Ответ

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

     It follows from conservation of charge at a node.

105. Карточка 105

     Вопрос

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

     Ответ

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

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

106. Карточка 106

     Вопрос

     What continuity relationship applies to steady incompressible flow?

     Ответ

     $A_1v_1=A_2v_2$.

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

107. Карточка 107

     Вопрос

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

     Ответ

     $m=\rho V$.

     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. Карточка 108

     Вопрос

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

     Ответ

     $U_g=mgh$.

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

109. Карточка 109

     Вопрос

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

     Ответ

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

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

110. Карточка 110

     Вопрос

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

     Ответ

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

     Both open ends are displacement antinodes.

111. Карточка 111

     Вопрос

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

     Ответ

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

     Use compatible energy units and absolute temperature.

112. Карточка 112

     Вопрос

     What does Kirchhoff's loop rule require?

     Ответ

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

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

113. Карточка 113

     Вопрос

     What elastic potential energy is stored in an ideal spring?

     Ответ

     $U_s=\tfrac12kx^2$.

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

114. Карточка 114

     Вопрос

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

     Ответ

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

     Dividing coefficients by $n$ takes the corresponding root.

115. Карточка 115

     Вопрос

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

     Ответ

     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. Карточка 116

     Вопрос

     How is lens power related to focal length?

     Ответ

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

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

117. Карточка 117

     Вопрос

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

     Ответ

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

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

118. Карточка 118

     Вопрос

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

     Ответ

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

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

119. Карточка 119

     Вопрос

     What is the Nernst equation for a cell reaction?

     Ответ

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

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

120. Карточка 120

     Вопрос

     What force does an ideal spring exert?

     Ответ

     $F_s=-kx$.

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

121. Карточка 121

     Вопрос

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

     Ответ

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. Карточка 122

     Вопрос

     Which relationship defines capacitance?

     Ответ

     $C=Q/V$.

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

123. Карточка 123

     Вопрос

     How do elemental mass percentages lead to an empirical formula?

     Ответ

     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. Карточка 124

     Вопрос

     When can mechanical energy be conserved?

     Ответ

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

125. Карточка 125

     Вопрос

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

     Ответ

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

126. Карточка 126

     Вопрос

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

     Ответ

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

127. Карточка 127

     Вопрос

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

     Ответ

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

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

128. Карточка 128

     Вопрос

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

     Ответ

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

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

129. Карточка 129

     Вопрос

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

     Ответ

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

     It is independent of initial concentration.

130. Карточка 130

     Вопрос

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

     Ответ

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. Карточка 131

     Вопрос

     How is a molecular formula obtained from an empirical formula?

     Ответ

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

132. Карточка 132

     Вопрос

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

     Ответ

     $C=\kappa\varepsilon_0A/d$.

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

133. Карточка 133

     Вопрос

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

     Ответ

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

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

134. Карточка 134

     Вопрос

     Which relationship gives laminar flow through a cylindrical tube?

     Ответ

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

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

135. Карточка 135

     Вопрос

     How do equilibrium constants combine when reactions are added?

     Ответ

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

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

136. Карточка 136

     Вопрос

     Which relationship defines average power?

     Ответ

     $P=W/\Delta t$.

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

137. Карточка 137

     Вопрос

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

     Ответ

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

138. Карточка 138

     Вопрос

     Which equivalent forms give energy stored in a capacitor?

     Ответ

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

     Use the form matching the known variables.

139. Карточка 139

     Вопрос

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

     Ответ

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

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

140. Карточка 140

     Вопрос

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

     Ответ

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

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

141. Карточка 141

     Вопрос

     How is percent yield calculated?

     Ответ

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

142. Карточка 142

     Вопрос

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

     Ответ

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

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

143. Карточка 143

     Вопрос

     What stoichiometric condition marks acid–base equivalence?

     Ответ

     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. Карточка 144

     Вопрос

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

     Ответ

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

145. Карточка 145

     Вопрос

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

     Ответ

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

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

146. Карточка 146

     Вопрос

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

     Ответ

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

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

147. Карточка 147

     Вопрос

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     Ответ

     $Re=\rho vD/\eta$.

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

148. Карточка 148

     Вопрос

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

     Ответ

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

     This predicts the favorable direction under nonstandard conditions.

149. Карточка 149

     Вопрос

     What is linear momentum?

     Ответ

     $\vec p=m\vec v$.

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

150. Карточка 150

     Вопрос

     How do you identify the limiting reactant from available moles?

     Ответ

     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. Карточка 151

     Вопрос

     How do capacitors combine in parallel?

     Ответ

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

     Parallel capacitors share voltage and their stored charges add.

152. Карточка 152

     Вопрос

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

     Ответ

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

153. Карточка 153

     Вопрос

     What relationship connects impulse and momentum change?

     Ответ

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

154. Карточка 154

     Вопрос

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

     Ответ

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

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

155. Карточка 155

     Вопрос

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

     Ответ

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

     The central maximum lies between the first minima.

156. Карточка 156

     Вопрос

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

     Ответ

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

157. Карточка 157

     Вопрос

     How do capacitors combine in series?

     Ответ

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

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

158. Карточка 158

     Вопрос

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

     Ответ

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

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

159. Карточка 159

     Вопрос

     What beat frequency is heard from two nearby tones?

     Ответ

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

     Beats arise from alternating constructive and destructive interference.

160. Карточка 160

     Вопрос

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

     Ответ

     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. Карточка 161

     Вопрос

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

     Ответ

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

162. Карточка 162

     Вопрос

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

     Ответ

     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. Карточка 163

     Вопрос

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

     Ответ

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

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

164. Карточка 164

     Вопрос

     When is total linear momentum conserved?

     Ответ

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

165. Карточка 165

     Вопрос

     What relationship connects absorbance and concentration in a dilute solution?

     Ответ

     $A=\varepsilon bc$.

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

166. Карточка 166

     Вопрос

     What magnetic force acts on a moving charge?

     Ответ

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

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

167. Карточка 167

     Вопрос

     How does the Arrhenius equation relate rate constant and temperature?

     Ответ

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

168. Карточка 168

     Вопрос

     What is centripetal acceleration for uniform circular motion?

     Ответ

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

     It points toward the center even when speed is constant.

169. Карточка 169

     Вопрос

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

     Ответ

     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. Карточка 170

     Вопрос

     What is the maximum kinetic energy in the photoelectric effect?

     Ответ

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

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

171. Карточка 171

     Вопрос

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

     Ответ

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

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

172. Карточка 172

     Вопрос

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

     Ответ

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

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

173. Карточка 173

     Вопрос

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

     Ответ

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

     This relation changes when a common ion is already present.

174. Карточка 174

     Вопрос

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

     Ответ

     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. Карточка 175

     Вопрос

     How is percent ionization of a weak acid calculated?

     Ответ

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

176. Карточка 176

     Вопрос

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

     Ответ

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

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

177. Карточка 177

     Вопрос

     What energy balance applies in an insulated calorimetry problem?

     Ответ

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

178. Карточка 178

     Вопрос

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

     Ответ

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

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

179. Карточка 179

     Вопрос

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

     Ответ

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

180. Карточка 180

     Вопрос

     What net inward force is required for circular motion?

     Ответ

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

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

180 карточек

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

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