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

Карти в това тесте

1. Карта 1

   Въпрос

   Which relationship gives average velocity over a time interval?

   Отговор

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

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

2. Карта 2

   Въпрос

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

   Отговор

   $n=m/M$.

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

3. Карта 3

   Въпрос

   What is the electrostatic force between two point charges?

   Отговор

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

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

4. Карта 4

   Въпрос

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

   Отговор

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. Карта 5

   Въпрос

   How are period and frequency related?

   Отговор

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. Карта 6

   Въпрос

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

   Отговор

   $q=mc\Delta T$.

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

7. Карта 7

   Въпрос

   Which relationship defines mass density?

   Отговор

   $\rho=m/V$.

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

8. Карта 8

   Въпрос

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

   Отговор

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. Карта 9

   Въпрос

   How is photon energy related to frequency and wavelength?

   Отговор

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. Карта 10

    Въпрос

    How is standard cell potential calculated from reduction potentials?

    Отговор

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

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

11. Карта 11

    Въпрос

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

    Отговор

    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. Карта 12

    Въпрос

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

    Отговор

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

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

13. Карта 13

    Въпрос

    Which relationship gives average acceleration over a time interval?

    Отговор

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

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

14. Карта 14

    Въпрос

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

    Отговор

    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. Карта 15

    Въпрос

    What electric-field magnitude does a point charge produce?

    Отговор

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

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

16. Карта 16

    Въпрос

    How do moles relate to the number of microscopic particles?

    Отговор

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

17. Карта 17

    Въпрос

    For constant acceleration, how does velocity change with time?

    Отговор

    $v=v_0+at$.

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

18. Карта 18

    Въпрос

    How is pOH defined?

    Отговор

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

19. Карта 19

    Въпрос

    How is specific gravity defined?

    Отговор

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

    It is dimensionless because it is a density ratio.

20. Карта 20

    Въпрос

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

    Отговор

    $q=C\Delta T$.

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

21. Карта 21

    Въпрос

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

    Отговор

    $c=f\lambda$.

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

22. Карта 22

    Въпрос

    Which species are omitted from a heterogeneous equilibrium expression?

    Отговор

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

23. Карта 23

    Въпрос

    What force does an electric field exert on a charge?

    Отговор

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. Карта 24

    Въпрос

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

    Отговор

    $PV=nRT$.

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

25. Карта 25

    Въпрос

    Which equation relates wave speed, frequency, and wavelength?

    Отговор

    $v=f\lambda$.

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

26. Карта 26

    Въпрос

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

    Отговор

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

    Its value changes with temperature.

27. Карта 27

    Въпрос

    What base-unit dimensions define one newton?

    Отговор

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

    A force must have dimensions of mass times acceleration.

28. Карта 28

    Въпрос

    How is cell potential related to reaction free energy?

    Отговор

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

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

29. Карта 29

    Въпрос

    For constant acceleration, how does displacement depend on time?

    Отговор

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

    Choose a positive direction first, then keep signs consistent.

30. Карта 30

    Въпрос

    How is molarity defined?

    Отговор

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

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

31. Карта 31

    Въпрос

    What electric potential does a point charge produce?

    Отговор

    $V=k_e q/r$.

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

32. Карта 32

    Въпрос

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

    Отговор

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

33. Карта 33

    Въпрос

    Which constant-acceleration equation avoids time?

    Отговор

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

    It connects speed and displacement when time is absent.

34. Карта 34

    Въпрос

    What is the general experimental rate-law form?

    Отговор

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

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

35. Карта 35

    Въпрос

    Which relationship defines pressure from a normal force?

    Отговор

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. Карта 36

    Въпрос

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

    Отговор

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

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

37. Карта 37

    Въпрос

    How is wave intensity related to transmitted power and area?

    Отговор

    $I=P/A$.

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

38. Карта 38

    Въпрос

    How is molality defined?

    Отговор

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

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

39. Карта 39

    Въпрос

    What base-unit dimensions define one joule?

    Отговор

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

    Work, energy, and heat share this unit.

40. Карта 40

    Въпрос

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

    Отговор

    $\Delta U=q+w$.

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

41. Карта 41

    Въпрос

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

    Отговор

    $n=c/v$.

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

42. Карта 42

    Въпрос

    What equation links net force and acceleration?

    Отговор

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

    The vector sum of external forces determines the acceleration.

43. Карта 43

    Въпрос

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

    Отговор

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. Карта 44

    Въпрос

    How is electric potential energy related to charge and voltage?

    Отговор

    $\Delta U=q\Delta V$.

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

45. Карта 45

    Въпрос

    How are standard cell potential and the equilibrium constant related?

    Отговор

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

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

46. Карта 46

    Въпрос

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

    Отговор

    $W=mg$.

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

47. Карта 47

    Въпрос

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

    Отговор

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

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

48. Карта 48

    Въпрос

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

    Отговор

    $P=P_0+\rho gh$.

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

49. Карта 49

    Въпрос

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

    Отговор

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

50. Карта 50

    Въпрос

    Which relationship defines electric current?

    Отговор

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

    Conventional current points in the direction positive charge would move.

51. Карта 51

    Въпрос

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

    Отговор

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

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

52. Карта 52

    Въпрос

    What equation governs refraction at a boundary?

    Отговор

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

    Angles are measured from the normal, not the surface.

53. Карта 53

    Въпрос

    How is mole fraction defined for component $i$?

    Отговор

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. Карта 54

    Въпрос

    What SI units and base dimensions define pressure?

    Отговор

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

55. Карта 55

    Въпрос

    What pressure–volume work occurs against constant external pressure?

    Отговор

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

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

56. Карта 56

    Въпрос

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

    Отговор

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

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

57. Карта 57

    Въпрос

    How large can static friction become before slipping begins?

    Отговор

    $f_s\leq\mu_sN$, 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. Карта 58

    Въпрос

    Which relationship handles dilution when solute amount is conserved?

    Отговор

    $M_1V_1=M_2V_2$.

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

59. Карта 59

    Въпрос

    What is Ohm's law for an ohmic element?

    Отговор

    $V=IR$.

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

60. Карта 60

    Въпрос

    How is the reaction quotient $Q$ constructed?

    Отговор

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

61. Карта 61

    Въпрос

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

    Отговор

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. Карта 62

    Въпрос

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

    Отговор

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

63. Карта 63

    Въпрос

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

    Отговор

    $F_1/A_1=F_2/A_2$.

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

64. Карта 64

    Въпрос

    How much charge passes through a cell carrying constant current?

    Отговор

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. Карта 65

    Въпрос

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

    Отговор

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

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

66. Карта 66

    Въпрос

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

    Отговор

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

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

67. Карта 67

    Въпрос

    How is the coulomb expressed through SI base units?

    Отговор

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

    Charge equals current multiplied by time.

68. Карта 68

    Въпрос

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    Отговор

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

69. Карта 69

    Въпрос

    How is sound intensity level in decibels defined?

    Отговор

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

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

70. Карта 70

    Въпрос

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

    Отговор

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

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

71. Карта 71

    Въпрос

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

    Отговор

    $R=\rho L/A$.

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

72. Карта 72

    Въпрос

    Which equation gives the magnitude of torque from a force?

    Отговор

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

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

73. Карта 73

    Въпрос

    How is mass percent composition calculated?

    Отговор

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

74. Карта 74

    Въпрос

    What buoyant force acts on a submerged object?

    Отговор

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

    It equals the weight of displaced fluid.

75. Карта 75

    Въпрос

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

    Отговор

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

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

76. Карта 76

    Въпрос

    What two conditions define static mechanical equilibrium?

    Отговор

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

    Both translational and rotational equilibrium are required.

77. Карта 77

    Въпрос

    How does Hess's law combine reaction enthalpies?

    Отговор

    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. Карта 78

    Въпрос

    Which equivalent forms give electrical power in a resistor?

    Отговор

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

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

79. Карта 79

    Въпрос

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

    Отговор

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

80. Карта 80

    Въпрос

    What decibel change corresponds to multiplying sound intensity by 10?

    Отговор

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

81. Карта 81

    Въпрос

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

    Отговор

    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. Карта 82

    Въпрос

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

    Отговор

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

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

83. Карта 83

    Въпрос

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

    Отговор

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

84. Карта 84

    Въпрос

    How is the volt expressed through joules and coulombs?

    Отговор

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

    Voltage is energy transferred per unit charge.

85. Карта 85

    Въпрос

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

    Отговор

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

86. Карта 86

    Въпрос

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

    Отговор

    $W=Fd\cos\theta$.

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

87. Карта 87

    Въпрос

    How is volume percent calculated for a liquid mixture?

    Отговор

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

    Use it only when the problem defines composition by volume.

88. Карта 88

    Въпрос

    How do resistors combine in series?

    Отговор

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

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

89. Карта 89

    Въпрос

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

    Отговор

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

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

90. Карта 90

    Въпрос

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

    Отговор

    $Q=Av$.

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

    

    180 карти

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

    Учете с това тесте безплатно

    Nibomo се отваря, за да започнете да учите.

91. Карта 91

    Въпрос

    How can average bond energies estimate reaction enthalpy?

    Отговор

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

    Breaking bonds costs energy; forming bonds releases it.

92. Карта 92

    Въпрос

    What is the translational kinetic energy of a point mass?

    Отговор

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. Карта 93

    Въпрос

    What ratio defines parts per million by mass?

    Отговор

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

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

94. Карта 94

    Въпрос

    How do resistors combine in parallel?

    Отговор

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

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

95. Карта 95

    Въпрос

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

    Отговор

    $K_aK_b=K_w$.

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

96. Карта 96

    Въпрос

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

    Отговор

    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. Карта 97

    Въпрос

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

    Отговор

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

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

98. Карта 98

    Въпрос

    How is lateral magnification related to image and object distances?

    Отговор

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

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

99. Карта 99

    Въпрос

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

    Отговор

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. Карта 100

     Въпрос

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

     Отговор

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

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

101. Карта 101

     Въпрос

     How does reversing a reaction change its equilibrium constant?

     Отговор

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

102. Карта 102

     Въпрос

     What does the work–energy theorem say?

     Отговор

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

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

103. Карта 103

     Въпрос

     What entropy change accompanies reversible heat transfer at constant temperature?

     Отговор

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

     Temperature must be in kelvin.

104. Карта 104

     Въпрос

     What does Kirchhoff's junction rule require?

     Отговор

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

     It follows from conservation of charge at a node.

105. Карта 105

     Въпрос

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

     Отговор

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

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

106. Карта 106

     Въпрос

     What continuity relationship applies to steady incompressible flow?

     Отговор

     $A_1v_1=A_2v_2$.

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

107. Карта 107

     Въпрос

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

     Отговор

     $m=\rho V$.

     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. Карта 108

     Въпрос

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

     Отговор

     $U_g=mgh$.

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

109. Карта 109

     Въпрос

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

     Отговор

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

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

110. Карта 110

     Въпрос

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

     Отговор

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

     Both open ends are displacement antinodes.

111. Карта 111

     Въпрос

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

     Отговор

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

     Use compatible energy units and absolute temperature.

112. Карта 112

     Въпрос

     What does Kirchhoff's loop rule require?

     Отговор

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

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

113. Карта 113

     Въпрос

     What elastic potential energy is stored in an ideal spring?

     Отговор

     $U_s=\tfrac12kx^2$.

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

114. Карта 114

     Въпрос

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

     Отговор

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

     Dividing coefficients by $n$ takes the corresponding root.

115. Карта 115

     Въпрос

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

     Отговор

     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. Карта 116

     Въпрос

     How is lens power related to focal length?

     Отговор

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

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

117. Карта 117

     Въпрос

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

     Отговор

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

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

118. Карта 118

     Въпрос

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

     Отговор

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

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

119. Карта 119

     Въпрос

     What is the Nernst equation for a cell reaction?

     Отговор

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

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

120. Карта 120

     Въпрос

     What force does an ideal spring exert?

     Отговор

     $F_s=-kx$.

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

121. Карта 121

     Въпрос

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

     Отговор

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. Карта 122

     Въпрос

     Which relationship defines capacitance?

     Отговор

     $C=Q/V$.

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

123. Карта 123

     Въпрос

     How do elemental mass percentages lead to an empirical formula?

     Отговор

     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. Карта 124

     Въпрос

     When can mechanical energy be conserved?

     Отговор

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

125. Карта 125

     Въпрос

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

     Отговор

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

126. Карта 126

     Въпрос

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

     Отговор

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

127. Карта 127

     Въпрос

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

     Отговор

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

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

128. Карта 128

     Въпрос

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

     Отговор

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

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

129. Карта 129

     Въпрос

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

     Отговор

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

     It is independent of initial concentration.

130. Карта 130

     Въпрос

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

     Отговор

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. Карта 131

     Въпрос

     How is a molecular formula obtained from an empirical formula?

     Отговор

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

132. Карта 132

     Въпрос

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

     Отговор

     $C=\kappa\varepsilon_0A/d$.

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

133. Карта 133

     Въпрос

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

     Отговор

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

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

134. Карта 134

     Въпрос

     Which relationship gives laminar flow through a cylindrical tube?

     Отговор

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

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

135. Карта 135

     Въпрос

     How do equilibrium constants combine when reactions are added?

     Отговор

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

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

136. Карта 136

     Въпрос

     Which relationship defines average power?

     Отговор

     $P=W/\Delta t$.

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

137. Карта 137

     Въпрос

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

     Отговор

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

138. Карта 138

     Въпрос

     Which equivalent forms give energy stored in a capacitor?

     Отговор

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

     Use the form matching the known variables.

139. Карта 139

     Въпрос

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

     Отговор

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

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

140. Карта 140

     Въпрос

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

     Отговор

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

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

141. Карта 141

     Въпрос

     How is percent yield calculated?

     Отговор

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

142. Карта 142

     Въпрос

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

     Отговор

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

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

143. Карта 143

     Въпрос

     What stoichiometric condition marks acid–base equivalence?

     Отговор

     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. Карта 144

     Въпрос

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

     Отговор

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

145. Карта 145

     Въпрос

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

     Отговор

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

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

146. Карта 146

     Въпрос

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

     Отговор

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

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

147. Карта 147

     Въпрос

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     Отговор

     $Re=\rho vD/\eta$.

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

148. Карта 148

     Въпрос

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

     Отговор

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

     This predicts the favorable direction under nonstandard conditions.

149. Карта 149

     Въпрос

     What is linear momentum?

     Отговор

     $\vec p=m\vec v$.

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

150. Карта 150

     Въпрос

     How do you identify the limiting reactant from available moles?

     Отговор

     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. Карта 151

     Въпрос

     How do capacitors combine in parallel?

     Отговор

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

     Parallel capacitors share voltage and their stored charges add.

152. Карта 152

     Въпрос

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

     Отговор

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

153. Карта 153

     Въпрос

     What relationship connects impulse and momentum change?

     Отговор

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

154. Карта 154

     Въпрос

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

     Отговор

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

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

155. Карта 155

     Въпрос

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

     Отговор

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

     The central maximum lies between the first minima.

156. Карта 156

     Въпрос

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

     Отговор

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

157. Карта 157

     Въпрос

     How do capacitors combine in series?

     Отговор

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

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

158. Карта 158

     Въпрос

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

     Отговор

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

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

159. Карта 159

     Въпрос

     What beat frequency is heard from two nearby tones?

     Отговор

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

     Beats arise from alternating constructive and destructive interference.

160. Карта 160

     Въпрос

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

     Отговор

     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. Карта 161

     Въпрос

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

     Отговор

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

162. Карта 162

     Въпрос

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

     Отговор

     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. Карта 163

     Въпрос

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

     Отговор

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

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

164. Карта 164

     Въпрос

     When is total linear momentum conserved?

     Отговор

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

165. Карта 165

     Въпрос

     What relationship connects absorbance and concentration in a dilute solution?

     Отговор

     $A=\varepsilon bc$.

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

166. Карта 166

     Въпрос

     What magnetic force acts on a moving charge?

     Отговор

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

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

167. Карта 167

     Въпрос

     How does the Arrhenius equation relate rate constant and temperature?

     Отговор

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

168. Карта 168

     Въпрос

     What is centripetal acceleration for uniform circular motion?

     Отговор

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

     It points toward the center even when speed is constant.

169. Карта 169

     Въпрос

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

     Отговор

     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. Карта 170

     Въпрос

     What is the maximum kinetic energy in the photoelectric effect?

     Отговор

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

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

171. Карта 171

     Въпрос

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

     Отговор

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

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

172. Карта 172

     Въпрос

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

     Отговор

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

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

173. Карта 173

     Въпрос

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

     Отговор

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

     This relation changes when a common ion is already present.

174. Карта 174

     Въпрос

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

     Отговор

     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. Карта 175

     Въпрос

     How is percent ionization of a weak acid calculated?

     Отговор

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

176. Карта 176

     Въпрос

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

     Отговор

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

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

177. Карта 177

     Въпрос

     What energy balance applies in an insulated calorimetry problem?

     Отговор

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

178. Карта 178

     Въпрос

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

     Отговор

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

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

179. Карта 179

     Въпрос

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

     Отговор

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

180. Карта 180

     Въпрос

     What net inward force is required for circular motion?

     Отговор

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

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

180 карти

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

Учете с това тесте безплатно

Nibomo се отваря, за да започнете да учите.