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

Картки в цій колоді

1. Картка 1

   Питання

   Which relationship gives average velocity over a time interval?

   Відповідь

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

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

2. Картка 2

   Питання

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

   Відповідь

   $n=m/M$.

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

3. Картка 3

   Питання

   What is the electrostatic force between two point charges?

   Відповідь

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

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

4. Картка 4

   Питання

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

   Відповідь

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. Картка 5

   Питання

   How are period and frequency related?

   Відповідь

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. Картка 6

   Питання

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

   Відповідь

   $q=mc\Delta T$.

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

7. Картка 7

   Питання

   Which relationship defines mass density?

   Відповідь

   $\rho=m/V$.

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

8. Картка 8

   Питання

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

   Відповідь

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. Картка 9

   Питання

   How is photon energy related to frequency and wavelength?

   Відповідь

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. Картка 10

    Питання

    How is standard cell potential calculated from reduction potentials?

    Відповідь

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

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

11. Картка 11

    Питання

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

    Відповідь

    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. Картка 12

    Питання

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

    Відповідь

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

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

13. Картка 13

    Питання

    Which relationship gives average acceleration over a time interval?

    Відповідь

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

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

14. Картка 14

    Питання

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

    Відповідь

    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. Картка 15

    Питання

    What electric-field magnitude does a point charge produce?

    Відповідь

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

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

16. Картка 16

    Питання

    How do moles relate to the number of microscopic particles?

    Відповідь

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

17. Картка 17

    Питання

    For constant acceleration, how does velocity change with time?

    Відповідь

    $v=v_0+at$.

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

18. Картка 18

    Питання

    How is pOH defined?

    Відповідь

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

19. Картка 19

    Питання

    How is specific gravity defined?

    Відповідь

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

    It is dimensionless because it is a density ratio.

20. Картка 20

    Питання

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

    Відповідь

    $q=C\Delta T$.

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

21. Картка 21

    Питання

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

    Відповідь

    $c=f\lambda$.

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

22. Картка 22

    Питання

    Which species are omitted from a heterogeneous equilibrium expression?

    Відповідь

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

23. Картка 23

    Питання

    What force does an electric field exert on a charge?

    Відповідь

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. Картка 24

    Питання

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

    Відповідь

    $PV=nRT$.

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

25. Картка 25

    Питання

    Which equation relates wave speed, frequency, and wavelength?

    Відповідь

    $v=f\lambda$.

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

26. Картка 26

    Питання

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

    Відповідь

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

    Its value changes with temperature.

27. Картка 27

    Питання

    What base-unit dimensions define one newton?

    Відповідь

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

    A force must have dimensions of mass times acceleration.

28. Картка 28

    Питання

    How is cell potential related to reaction free energy?

    Відповідь

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

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

29. Картка 29

    Питання

    For constant acceleration, how does displacement depend on time?

    Відповідь

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

    Choose a positive direction first, then keep signs consistent.

30. Картка 30

    Питання

    How is molarity defined?

    Відповідь

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

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

31. Картка 31

    Питання

    What electric potential does a point charge produce?

    Відповідь

    $V=k_e q/r$.

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

32. Картка 32

    Питання

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

    Відповідь

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

33. Картка 33

    Питання

    Which constant-acceleration equation avoids time?

    Відповідь

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

    It connects speed and displacement when time is absent.

34. Картка 34

    Питання

    What is the general experimental rate-law form?

    Відповідь

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

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

35. Картка 35

    Питання

    Which relationship defines pressure from a normal force?

    Відповідь

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. Картка 36

    Питання

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

    Відповідь

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

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

37. Картка 37

    Питання

    How is wave intensity related to transmitted power and area?

    Відповідь

    $I=P/A$.

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

38. Картка 38

    Питання

    How is molality defined?

    Відповідь

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

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

39. Картка 39

    Питання

    What base-unit dimensions define one joule?

    Відповідь

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

    Work, energy, and heat share this unit.

40. Картка 40

    Питання

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

    Відповідь

    $\Delta U=q+w$.

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

41. Картка 41

    Питання

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

    Відповідь

    $n=c/v$.

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

42. Картка 42

    Питання

    What equation links net force and acceleration?

    Відповідь

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

    The vector sum of external forces determines the acceleration.

43. Картка 43

    Питання

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

    Відповідь

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. Картка 44

    Питання

    How is electric potential energy related to charge and voltage?

    Відповідь

    $\Delta U=q\Delta V$.

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

45. Картка 45

    Питання

    How are standard cell potential and the equilibrium constant related?

    Відповідь

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

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

46. Картка 46

    Питання

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

    Відповідь

    $W=mg$.

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

47. Картка 47

    Питання

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

    Відповідь

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

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

48. Картка 48

    Питання

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

    Відповідь

    $P=P_0+\rho gh$.

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

49. Картка 49

    Питання

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

    Відповідь

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

50. Картка 50

    Питання

    Which relationship defines electric current?

    Відповідь

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

    Conventional current points in the direction positive charge would move.

51. Картка 51

    Питання

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

    Відповідь

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

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

52. Картка 52

    Питання

    What equation governs refraction at a boundary?

    Відповідь

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

    Angles are measured from the normal, not the surface.

53. Картка 53

    Питання

    How is mole fraction defined for component $i$?

    Відповідь

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. Картка 54

    Питання

    What SI units and base dimensions define pressure?

    Відповідь

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

55. Картка 55

    Питання

    What pressure–volume work occurs against constant external pressure?

    Відповідь

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

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

56. Картка 56

    Питання

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

    Відповідь

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

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

57. Картка 57

    Питання

    How large can static friction become before slipping begins?

    Відповідь

    $f_s\leq\mu_sN$, 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. Картка 58

    Питання

    Which relationship handles dilution when solute amount is conserved?

    Відповідь

    $M_1V_1=M_2V_2$.

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

59. Картка 59

    Питання

    What is Ohm's law for an ohmic element?

    Відповідь

    $V=IR$.

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

60. Картка 60

    Питання

    How is the reaction quotient $Q$ constructed?

    Відповідь

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

61. Картка 61

    Питання

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

    Відповідь

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. Картка 62

    Питання

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

    Відповідь

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

63. Картка 63

    Питання

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

    Відповідь

    $F_1/A_1=F_2/A_2$.

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

64. Картка 64

    Питання

    How much charge passes through a cell carrying constant current?

    Відповідь

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. Картка 65

    Питання

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

    Відповідь

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

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

66. Картка 66

    Питання

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

    Відповідь

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

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

67. Картка 67

    Питання

    How is the coulomb expressed through SI base units?

    Відповідь

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

    Charge equals current multiplied by time.

68. Картка 68

    Питання

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    Відповідь

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

69. Картка 69

    Питання

    How is sound intensity level in decibels defined?

    Відповідь

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

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

70. Картка 70

    Питання

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

    Відповідь

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

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

71. Картка 71

    Питання

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

    Відповідь

    $R=\rho L/A$.

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

72. Картка 72

    Питання

    Which equation gives the magnitude of torque from a force?

    Відповідь

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

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

73. Картка 73

    Питання

    How is mass percent composition calculated?

    Відповідь

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

74. Картка 74

    Питання

    What buoyant force acts on a submerged object?

    Відповідь

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

    It equals the weight of displaced fluid.

75. Картка 75

    Питання

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

    Відповідь

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

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

76. Картка 76

    Питання

    What two conditions define static mechanical equilibrium?

    Відповідь

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

    Both translational and rotational equilibrium are required.

77. Картка 77

    Питання

    How does Hess's law combine reaction enthalpies?

    Відповідь

    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. Картка 78

    Питання

    Which equivalent forms give electrical power in a resistor?

    Відповідь

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

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

79. Картка 79

    Питання

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

    Відповідь

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

80. Картка 80

    Питання

    What decibel change corresponds to multiplying sound intensity by 10?

    Відповідь

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

81. Картка 81

    Питання

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

    Відповідь

    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. Картка 82

    Питання

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

    Відповідь

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

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

83. Картка 83

    Питання

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

    Відповідь

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

84. Картка 84

    Питання

    How is the volt expressed through joules and coulombs?

    Відповідь

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

    Voltage is energy transferred per unit charge.

85. Картка 85

    Питання

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

    Відповідь

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

86. Картка 86

    Питання

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

    Відповідь

    $W=Fd\cos\theta$.

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

87. Картка 87

    Питання

    How is volume percent calculated for a liquid mixture?

    Відповідь

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

    Use it only when the problem defines composition by volume.

88. Картка 88

    Питання

    How do resistors combine in series?

    Відповідь

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

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

89. Картка 89

    Питання

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

    Відповідь

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

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

90. Картка 90

    Питання

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

    Відповідь

    $Q=Av$.

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

    

    180 карток

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

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91. Картка 91

    Питання

    How can average bond energies estimate reaction enthalpy?

    Відповідь

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

    Breaking bonds costs energy; forming bonds releases it.

92. Картка 92

    Питання

    What is the translational kinetic energy of a point mass?

    Відповідь

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. Картка 93

    Питання

    What ratio defines parts per million by mass?

    Відповідь

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

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

94. Картка 94

    Питання

    How do resistors combine in parallel?

    Відповідь

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

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

95. Картка 95

    Питання

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

    Відповідь

    $K_aK_b=K_w$.

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

96. Картка 96

    Питання

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

    Відповідь

    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. Картка 97

    Питання

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

    Відповідь

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

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

98. Картка 98

    Питання

    How is lateral magnification related to image and object distances?

    Відповідь

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

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

99. Картка 99

    Питання

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

    Відповідь

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. Картка 100

     Питання

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

     Відповідь

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

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

101. Картка 101

     Питання

     How does reversing a reaction change its equilibrium constant?

     Відповідь

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

102. Картка 102

     Питання

     What does the work–energy theorem say?

     Відповідь

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

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

103. Картка 103

     Питання

     What entropy change accompanies reversible heat transfer at constant temperature?

     Відповідь

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

     Temperature must be in kelvin.

104. Картка 104

     Питання

     What does Kirchhoff's junction rule require?

     Відповідь

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

     It follows from conservation of charge at a node.

105. Картка 105

     Питання

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

     Відповідь

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

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

106. Картка 106

     Питання

     What continuity relationship applies to steady incompressible flow?

     Відповідь

     $A_1v_1=A_2v_2$.

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

107. Картка 107

     Питання

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

     Відповідь

     $m=\rho V$.

     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. Картка 108

     Питання

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

     Відповідь

     $U_g=mgh$.

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

109. Картка 109

     Питання

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

     Відповідь

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

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

110. Картка 110

     Питання

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

     Відповідь

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

     Both open ends are displacement antinodes.

111. Картка 111

     Питання

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

     Відповідь

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

     Use compatible energy units and absolute temperature.

112. Картка 112

     Питання

     What does Kirchhoff's loop rule require?

     Відповідь

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

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

113. Картка 113

     Питання

     What elastic potential energy is stored in an ideal spring?

     Відповідь

     $U_s=\tfrac12kx^2$.

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

114. Картка 114

     Питання

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

     Відповідь

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

     Dividing coefficients by $n$ takes the corresponding root.

115. Картка 115

     Питання

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

     Відповідь

     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. Картка 116

     Питання

     How is lens power related to focal length?

     Відповідь

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

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

117. Картка 117

     Питання

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

     Відповідь

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

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

118. Картка 118

     Питання

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

     Відповідь

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

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

119. Картка 119

     Питання

     What is the Nernst equation for a cell reaction?

     Відповідь

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

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

120. Картка 120

     Питання

     What force does an ideal spring exert?

     Відповідь

     $F_s=-kx$.

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

121. Картка 121

     Питання

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

     Відповідь

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. Картка 122

     Питання

     Which relationship defines capacitance?

     Відповідь

     $C=Q/V$.

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

123. Картка 123

     Питання

     How do elemental mass percentages lead to an empirical formula?

     Відповідь

     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. Картка 124

     Питання

     When can mechanical energy be conserved?

     Відповідь

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

125. Картка 125

     Питання

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

     Відповідь

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

126. Картка 126

     Питання

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

     Відповідь

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

127. Картка 127

     Питання

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

     Відповідь

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

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

128. Картка 128

     Питання

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

     Відповідь

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

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

129. Картка 129

     Питання

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

     Відповідь

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

     It is independent of initial concentration.

130. Картка 130

     Питання

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

     Відповідь

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. Картка 131

     Питання

     How is a molecular formula obtained from an empirical formula?

     Відповідь

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

132. Картка 132

     Питання

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

     Відповідь

     $C=\kappa\varepsilon_0A/d$.

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

133. Картка 133

     Питання

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

     Відповідь

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

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

134. Картка 134

     Питання

     Which relationship gives laminar flow through a cylindrical tube?

     Відповідь

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

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

135. Картка 135

     Питання

     How do equilibrium constants combine when reactions are added?

     Відповідь

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

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

136. Картка 136

     Питання

     Which relationship defines average power?

     Відповідь

     $P=W/\Delta t$.

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

137. Картка 137

     Питання

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

     Відповідь

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

138. Картка 138

     Питання

     Which equivalent forms give energy stored in a capacitor?

     Відповідь

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

     Use the form matching the known variables.

139. Картка 139

     Питання

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

     Відповідь

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

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

140. Картка 140

     Питання

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

     Відповідь

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

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

141. Картка 141

     Питання

     How is percent yield calculated?

     Відповідь

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

142. Картка 142

     Питання

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

     Відповідь

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

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

143. Картка 143

     Питання

     What stoichiometric condition marks acid–base equivalence?

     Відповідь

     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. Картка 144

     Питання

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

     Відповідь

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

145. Картка 145

     Питання

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

     Відповідь

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

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

146. Картка 146

     Питання

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

     Відповідь

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

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

147. Картка 147

     Питання

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     Відповідь

     $Re=\rho vD/\eta$.

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

148. Картка 148

     Питання

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

     Відповідь

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

     This predicts the favorable direction under nonstandard conditions.

149. Картка 149

     Питання

     What is linear momentum?

     Відповідь

     $\vec p=m\vec v$.

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

150. Картка 150

     Питання

     How do you identify the limiting reactant from available moles?

     Відповідь

     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. Картка 151

     Питання

     How do capacitors combine in parallel?

     Відповідь

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

     Parallel capacitors share voltage and their stored charges add.

152. Картка 152

     Питання

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

     Відповідь

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

153. Картка 153

     Питання

     What relationship connects impulse and momentum change?

     Відповідь

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

154. Картка 154

     Питання

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

     Відповідь

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

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

155. Картка 155

     Питання

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

     Відповідь

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

     The central maximum lies between the first minima.

156. Картка 156

     Питання

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

     Відповідь

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

157. Картка 157

     Питання

     How do capacitors combine in series?

     Відповідь

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

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

158. Картка 158

     Питання

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

     Відповідь

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

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

159. Картка 159

     Питання

     What beat frequency is heard from two nearby tones?

     Відповідь

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

     Beats arise from alternating constructive and destructive interference.

160. Картка 160

     Питання

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

     Відповідь

     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. Картка 161

     Питання

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

     Відповідь

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

162. Картка 162

     Питання

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

     Відповідь

     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. Картка 163

     Питання

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

     Відповідь

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

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

164. Картка 164

     Питання

     When is total linear momentum conserved?

     Відповідь

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

165. Картка 165

     Питання

     What relationship connects absorbance and concentration in a dilute solution?

     Відповідь

     $A=\varepsilon bc$.

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

166. Картка 166

     Питання

     What magnetic force acts on a moving charge?

     Відповідь

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

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

167. Картка 167

     Питання

     How does the Arrhenius equation relate rate constant and temperature?

     Відповідь

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

168. Картка 168

     Питання

     What is centripetal acceleration for uniform circular motion?

     Відповідь

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

     It points toward the center even when speed is constant.

169. Картка 169

     Питання

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

     Відповідь

     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. Картка 170

     Питання

     What is the maximum kinetic energy in the photoelectric effect?

     Відповідь

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

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

171. Картка 171

     Питання

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

     Відповідь

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

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

172. Картка 172

     Питання

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

     Відповідь

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

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

173. Картка 173

     Питання

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

     Відповідь

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

     This relation changes when a common ion is already present.

174. Картка 174

     Питання

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

     Відповідь

     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. Картка 175

     Питання

     How is percent ionization of a weak acid calculated?

     Відповідь

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

176. Картка 176

     Питання

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

     Відповідь

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

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

177. Картка 177

     Питання

     What energy balance applies in an insulated calorimetry problem?

     Відповідь

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

178. Картка 178

     Питання

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

     Відповідь

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

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

179. Картка 179

     Питання

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

     Відповідь

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

180. Картка 180

     Питання

     What net inward force is required for circular motion?

     Відповідь

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

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

180 карток

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

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