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

اس ڈیک کے کارڈز

1. کارڈ 1

   سوال

   Which relationship gives average velocity over a time interval?

   جواب

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

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

2. کارڈ 2

   سوال

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

   جواب

   $n=m/M$.

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

3. کارڈ 3

   سوال

   What is the electrostatic force between two point charges?

   جواب

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

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

4. کارڈ 4

   سوال

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

   جواب

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. کارڈ 5

   سوال

   How are period and frequency related?

   جواب

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. کارڈ 6

   سوال

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

   جواب

   $q=mc\Delta T$.

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

7. کارڈ 7

   سوال

   Which relationship defines mass density?

   جواب

   $\rho=m/V$.

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

8. کارڈ 8

   سوال

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

   جواب

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. کارڈ 9

   سوال

   How is photon energy related to frequency and wavelength?

   جواب

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. کارڈ 10

    سوال

    How is standard cell potential calculated from reduction potentials?

    جواب

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

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

11. کارڈ 11

    سوال

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

    جواب

    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. کارڈ 12

    سوال

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

    جواب

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

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

13. کارڈ 13

    سوال

    Which relationship gives average acceleration over a time interval?

    جواب

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

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

14. کارڈ 14

    سوال

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

    جواب

    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. کارڈ 15

    سوال

    What electric-field magnitude does a point charge produce?

    جواب

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

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

16. کارڈ 16

    سوال

    How do moles relate to the number of microscopic particles?

    جواب

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

17. کارڈ 17

    سوال

    For constant acceleration, how does velocity change with time?

    جواب

    $v=v_0+at$.

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

18. کارڈ 18

    سوال

    How is pOH defined?

    جواب

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

19. کارڈ 19

    سوال

    How is specific gravity defined?

    جواب

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

    It is dimensionless because it is a density ratio.

20. کارڈ 20

    سوال

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

    جواب

    $q=C\Delta T$.

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

21. کارڈ 21

    سوال

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

    جواب

    $c=f\lambda$.

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

22. کارڈ 22

    سوال

    Which species are omitted from a heterogeneous equilibrium expression?

    جواب

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

23. کارڈ 23

    سوال

    What force does an electric field exert on a charge?

    جواب

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. کارڈ 24

    سوال

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

    جواب

    $PV=nRT$.

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

25. کارڈ 25

    سوال

    Which equation relates wave speed, frequency, and wavelength?

    جواب

    $v=f\lambda$.

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

26. کارڈ 26

    سوال

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

    جواب

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

    Its value changes with temperature.

27. کارڈ 27

    سوال

    What base-unit dimensions define one newton?

    جواب

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

    A force must have dimensions of mass times acceleration.

28. کارڈ 28

    سوال

    How is cell potential related to reaction free energy?

    جواب

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

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

29. کارڈ 29

    سوال

    For constant acceleration, how does displacement depend on time?

    جواب

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

    Choose a positive direction first, then keep signs consistent.

30. کارڈ 30

    سوال

    How is molarity defined?

    جواب

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

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

31. کارڈ 31

    سوال

    What electric potential does a point charge produce?

    جواب

    $V=k_e q/r$.

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

32. کارڈ 32

    سوال

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

    جواب

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

33. کارڈ 33

    سوال

    Which constant-acceleration equation avoids time?

    جواب

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

    It connects speed and displacement when time is absent.

34. کارڈ 34

    سوال

    What is the general experimental rate-law form?

    جواب

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

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

35. کارڈ 35

    سوال

    Which relationship defines pressure from a normal force?

    جواب

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. کارڈ 36

    سوال

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

    جواب

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

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

37. کارڈ 37

    سوال

    How is wave intensity related to transmitted power and area?

    جواب

    $I=P/A$.

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

38. کارڈ 38

    سوال

    How is molality defined?

    جواب

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

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

39. کارڈ 39

    سوال

    What base-unit dimensions define one joule?

    جواب

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

    Work, energy, and heat share this unit.

40. کارڈ 40

    سوال

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

    جواب

    $\Delta U=q+w$.

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

41. کارڈ 41

    سوال

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

    جواب

    $n=c/v$.

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

42. کارڈ 42

    سوال

    What equation links net force and acceleration?

    جواب

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

    The vector sum of external forces determines the acceleration.

43. کارڈ 43

    سوال

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

    جواب

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. کارڈ 44

    سوال

    How is electric potential energy related to charge and voltage?

    جواب

    $\Delta U=q\Delta V$.

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

45. کارڈ 45

    سوال

    How are standard cell potential and the equilibrium constant related?

    جواب

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

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

46. کارڈ 46

    سوال

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

    جواب

    $W=mg$.

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

47. کارڈ 47

    سوال

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

    جواب

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

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

48. کارڈ 48

    سوال

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

    جواب

    $P=P_0+\rho gh$.

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

49. کارڈ 49

    سوال

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

    جواب

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

50. کارڈ 50

    سوال

    Which relationship defines electric current?

    جواب

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

    Conventional current points in the direction positive charge would move.

51. کارڈ 51

    سوال

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

    جواب

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

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

52. کارڈ 52

    سوال

    What equation governs refraction at a boundary?

    جواب

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

    Angles are measured from the normal, not the surface.

53. کارڈ 53

    سوال

    How is mole fraction defined for component $i$?

    جواب

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. کارڈ 54

    سوال

    What SI units and base dimensions define pressure?

    جواب

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

55. کارڈ 55

    سوال

    What pressure–volume work occurs against constant external pressure?

    جواب

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

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

56. کارڈ 56

    سوال

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

    جواب

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

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

57. کارڈ 57

    سوال

    How large can static friction become before slipping begins?

    جواب

    $f_s\leq\mu_sN$, 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. کارڈ 58

    سوال

    Which relationship handles dilution when solute amount is conserved?

    جواب

    $M_1V_1=M_2V_2$.

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

59. کارڈ 59

    سوال

    What is Ohm's law for an ohmic element?

    جواب

    $V=IR$.

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

60. کارڈ 60

    سوال

    How is the reaction quotient $Q$ constructed?

    جواب

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

61. کارڈ 61

    سوال

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

    جواب

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. کارڈ 62

    سوال

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

    جواب

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

63. کارڈ 63

    سوال

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

    جواب

    $F_1/A_1=F_2/A_2$.

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

64. کارڈ 64

    سوال

    How much charge passes through a cell carrying constant current?

    جواب

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. کارڈ 65

    سوال

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

    جواب

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

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

66. کارڈ 66

    سوال

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

    جواب

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

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

67. کارڈ 67

    سوال

    How is the coulomb expressed through SI base units?

    جواب

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

    Charge equals current multiplied by time.

68. کارڈ 68

    سوال

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    جواب

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

69. کارڈ 69

    سوال

    How is sound intensity level in decibels defined?

    جواب

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

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

70. کارڈ 70

    سوال

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

    جواب

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

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

71. کارڈ 71

    سوال

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

    جواب

    $R=\rho L/A$.

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

72. کارڈ 72

    سوال

    Which equation gives the magnitude of torque from a force?

    جواب

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

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

73. کارڈ 73

    سوال

    How is mass percent composition calculated?

    جواب

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

74. کارڈ 74

    سوال

    What buoyant force acts on a submerged object?

    جواب

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

    It equals the weight of displaced fluid.

75. کارڈ 75

    سوال

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

    جواب

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

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

76. کارڈ 76

    سوال

    What two conditions define static mechanical equilibrium?

    جواب

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

    Both translational and rotational equilibrium are required.

77. کارڈ 77

    سوال

    How does Hess's law combine reaction enthalpies?

    جواب

    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. کارڈ 78

    سوال

    Which equivalent forms give electrical power in a resistor?

    جواب

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

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

79. کارڈ 79

    سوال

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

    جواب

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

80. کارڈ 80

    سوال

    What decibel change corresponds to multiplying sound intensity by 10?

    جواب

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

81. کارڈ 81

    سوال

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

    جواب

    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. کارڈ 82

    سوال

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

    جواب

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

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

83. کارڈ 83

    سوال

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

    جواب

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

84. کارڈ 84

    سوال

    How is the volt expressed through joules and coulombs?

    جواب

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

    Voltage is energy transferred per unit charge.

85. کارڈ 85

    سوال

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

    جواب

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

86. کارڈ 86

    سوال

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

    جواب

    $W=Fd\cos\theta$.

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

87. کارڈ 87

    سوال

    How is volume percent calculated for a liquid mixture?

    جواب

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

    Use it only when the problem defines composition by volume.

88. کارڈ 88

    سوال

    How do resistors combine in series?

    جواب

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

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

89. کارڈ 89

    سوال

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

    جواب

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

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

90. کارڈ 90

    سوال

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

    جواب

    $Q=Av$.

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

    

    180 کارڈز

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

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91. کارڈ 91

    سوال

    How can average bond energies estimate reaction enthalpy?

    جواب

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

    Breaking bonds costs energy; forming bonds releases it.

92. کارڈ 92

    سوال

    What is the translational kinetic energy of a point mass?

    جواب

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. کارڈ 93

    سوال

    What ratio defines parts per million by mass?

    جواب

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

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

94. کارڈ 94

    سوال

    How do resistors combine in parallel?

    جواب

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

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

95. کارڈ 95

    سوال

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

    جواب

    $K_aK_b=K_w$.

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

96. کارڈ 96

    سوال

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

    جواب

    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. کارڈ 97

    سوال

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

    جواب

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

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

98. کارڈ 98

    سوال

    How is lateral magnification related to image and object distances?

    جواب

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

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

99. کارڈ 99

    سوال

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

    جواب

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. کارڈ 100

     سوال

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

     جواب

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

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

101. کارڈ 101

     سوال

     How does reversing a reaction change its equilibrium constant?

     جواب

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

102. کارڈ 102

     سوال

     What does the work–energy theorem say?

     جواب

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

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

103. کارڈ 103

     سوال

     What entropy change accompanies reversible heat transfer at constant temperature?

     جواب

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

     Temperature must be in kelvin.

104. کارڈ 104

     سوال

     What does Kirchhoff's junction rule require?

     جواب

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

     It follows from conservation of charge at a node.

105. کارڈ 105

     سوال

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

     جواب

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

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

106. کارڈ 106

     سوال

     What continuity relationship applies to steady incompressible flow?

     جواب

     $A_1v_1=A_2v_2$.

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

107. کارڈ 107

     سوال

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

     جواب

     $m=\rho V$.

     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. کارڈ 108

     سوال

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

     جواب

     $U_g=mgh$.

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

109. کارڈ 109

     سوال

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

     جواب

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

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

110. کارڈ 110

     سوال

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

     جواب

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

     Both open ends are displacement antinodes.

111. کارڈ 111

     سوال

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

     جواب

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

     Use compatible energy units and absolute temperature.

112. کارڈ 112

     سوال

     What does Kirchhoff's loop rule require?

     جواب

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

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

113. کارڈ 113

     سوال

     What elastic potential energy is stored in an ideal spring?

     جواب

     $U_s=\tfrac12kx^2$.

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

114. کارڈ 114

     سوال

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

     جواب

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

     Dividing coefficients by $n$ takes the corresponding root.

115. کارڈ 115

     سوال

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

     جواب

     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. کارڈ 116

     سوال

     How is lens power related to focal length?

     جواب

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

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

117. کارڈ 117

     سوال

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

     جواب

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

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

118. کارڈ 118

     سوال

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

     جواب

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

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

119. کارڈ 119

     سوال

     What is the Nernst equation for a cell reaction?

     جواب

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

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

120. کارڈ 120

     سوال

     What force does an ideal spring exert?

     جواب

     $F_s=-kx$.

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

121. کارڈ 121

     سوال

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

     جواب

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. کارڈ 122

     سوال

     Which relationship defines capacitance?

     جواب

     $C=Q/V$.

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

123. کارڈ 123

     سوال

     How do elemental mass percentages lead to an empirical formula?

     جواب

     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. کارڈ 124

     سوال

     When can mechanical energy be conserved?

     جواب

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

125. کارڈ 125

     سوال

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

     جواب

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

126. کارڈ 126

     سوال

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

     جواب

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

127. کارڈ 127

     سوال

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

     جواب

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

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

128. کارڈ 128

     سوال

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

     جواب

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

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

129. کارڈ 129

     سوال

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

     جواب

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

     It is independent of initial concentration.

130. کارڈ 130

     سوال

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

     جواب

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. کارڈ 131

     سوال

     How is a molecular formula obtained from an empirical formula?

     جواب

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

132. کارڈ 132

     سوال

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

     جواب

     $C=\kappa\varepsilon_0A/d$.

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

133. کارڈ 133

     سوال

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

     جواب

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

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

134. کارڈ 134

     سوال

     Which relationship gives laminar flow through a cylindrical tube?

     جواب

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

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

135. کارڈ 135

     سوال

     How do equilibrium constants combine when reactions are added?

     جواب

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

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

136. کارڈ 136

     سوال

     Which relationship defines average power?

     جواب

     $P=W/\Delta t$.

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

137. کارڈ 137

     سوال

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

     جواب

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

138. کارڈ 138

     سوال

     Which equivalent forms give energy stored in a capacitor?

     جواب

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

     Use the form matching the known variables.

139. کارڈ 139

     سوال

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

     جواب

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

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

140. کارڈ 140

     سوال

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

     جواب

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

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

141. کارڈ 141

     سوال

     How is percent yield calculated?

     جواب

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

142. کارڈ 142

     سوال

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

     جواب

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

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

143. کارڈ 143

     سوال

     What stoichiometric condition marks acid–base equivalence?

     جواب

     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. کارڈ 144

     سوال

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

     جواب

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

145. کارڈ 145

     سوال

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

     جواب

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

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

146. کارڈ 146

     سوال

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

     جواب

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

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

147. کارڈ 147

     سوال

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     جواب

     $Re=\rho vD/\eta$.

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

148. کارڈ 148

     سوال

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

     جواب

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

     This predicts the favorable direction under nonstandard conditions.

149. کارڈ 149

     سوال

     What is linear momentum?

     جواب

     $\vec p=m\vec v$.

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

150. کارڈ 150

     سوال

     How do you identify the limiting reactant from available moles?

     جواب

     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. کارڈ 151

     سوال

     How do capacitors combine in parallel?

     جواب

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

     Parallel capacitors share voltage and their stored charges add.

152. کارڈ 152

     سوال

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

     جواب

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

153. کارڈ 153

     سوال

     What relationship connects impulse and momentum change?

     جواب

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

154. کارڈ 154

     سوال

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

     جواب

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

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

155. کارڈ 155

     سوال

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

     جواب

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

     The central maximum lies between the first minima.

156. کارڈ 156

     سوال

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

     جواب

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

157. کارڈ 157

     سوال

     How do capacitors combine in series?

     جواب

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

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

158. کارڈ 158

     سوال

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

     جواب

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

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

159. کارڈ 159

     سوال

     What beat frequency is heard from two nearby tones?

     جواب

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

     Beats arise from alternating constructive and destructive interference.

160. کارڈ 160

     سوال

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

     جواب

     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. کارڈ 161

     سوال

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

     جواب

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

162. کارڈ 162

     سوال

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

     جواب

     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. کارڈ 163

     سوال

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

     جواب

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

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

164. کارڈ 164

     سوال

     When is total linear momentum conserved?

     جواب

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

165. کارڈ 165

     سوال

     What relationship connects absorbance and concentration in a dilute solution?

     جواب

     $A=\varepsilon bc$.

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

166. کارڈ 166

     سوال

     What magnetic force acts on a moving charge?

     جواب

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

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

167. کارڈ 167

     سوال

     How does the Arrhenius equation relate rate constant and temperature?

     جواب

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

168. کارڈ 168

     سوال

     What is centripetal acceleration for uniform circular motion?

     جواب

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

     It points toward the center even when speed is constant.

169. کارڈ 169

     سوال

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

     جواب

     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. کارڈ 170

     سوال

     What is the maximum kinetic energy in the photoelectric effect?

     جواب

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

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

171. کارڈ 171

     سوال

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

     جواب

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

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

172. کارڈ 172

     سوال

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

     جواب

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

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

173. کارڈ 173

     سوال

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

     جواب

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

     This relation changes when a common ion is already present.

174. کارڈ 174

     سوال

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

     جواب

     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. کارڈ 175

     سوال

     How is percent ionization of a weak acid calculated?

     جواب

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

176. کارڈ 176

     سوال

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

     جواب

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

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

177. کارڈ 177

     سوال

     What energy balance applies in an insulated calorimetry problem?

     جواب

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

178. کارڈ 178

     سوال

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

     جواب

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

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

179. کارڈ 179

     سوال

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

     جواب

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

180. کارڈ 180

     سوال

     What net inward force is required for circular motion?

     جواب

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

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

180 کارڈز

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

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