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

הכרטיסים בחפיסה הזו

1. כרטיס 1

   שאלה

   Which relationship gives average velocity over a time interval?

   תשובה

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

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

2. כרטיס 2

   שאלה

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

   תשובה

   $n=m/M$.

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

3. כרטיס 3

   שאלה

   What is the electrostatic force between two point charges?

   תשובה

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

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

4. כרטיס 4

   שאלה

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

   תשובה

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. כרטיס 5

   שאלה

   How are period and frequency related?

   תשובה

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. כרטיס 6

   שאלה

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

   תשובה

   $q=mc\Delta T$.

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

7. כרטיס 7

   שאלה

   Which relationship defines mass density?

   תשובה

   $\rho=m/V$.

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

8. כרטיס 8

   שאלה

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

   תשובה

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. כרטיס 9

   שאלה

   How is photon energy related to frequency and wavelength?

   תשובה

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. כרטיס 10

    שאלה

    How is standard cell potential calculated from reduction potentials?

    תשובה

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

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

11. כרטיס 11

    שאלה

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

    תשובה

    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. כרטיס 12

    שאלה

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

    תשובה

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

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

13. כרטיס 13

    שאלה

    Which relationship gives average acceleration over a time interval?

    תשובה

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

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

14. כרטיס 14

    שאלה

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

    תשובה

    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. כרטיס 15

    שאלה

    What electric-field magnitude does a point charge produce?

    תשובה

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

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

16. כרטיס 16

    שאלה

    How do moles relate to the number of microscopic particles?

    תשובה

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

17. כרטיס 17

    שאלה

    For constant acceleration, how does velocity change with time?

    תשובה

    $v=v_0+at$.

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

18. כרטיס 18

    שאלה

    How is pOH defined?

    תשובה

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

19. כרטיס 19

    שאלה

    How is specific gravity defined?

    תשובה

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

    It is dimensionless because it is a density ratio.

20. כרטיס 20

    שאלה

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

    תשובה

    $q=C\Delta T$.

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

21. כרטיס 21

    שאלה

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

    תשובה

    $c=f\lambda$.

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

22. כרטיס 22

    שאלה

    Which species are omitted from a heterogeneous equilibrium expression?

    תשובה

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

23. כרטיס 23

    שאלה

    What force does an electric field exert on a charge?

    תשובה

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. כרטיס 24

    שאלה

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

    תשובה

    $PV=nRT$.

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

25. כרטיס 25

    שאלה

    Which equation relates wave speed, frequency, and wavelength?

    תשובה

    $v=f\lambda$.

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

26. כרטיס 26

    שאלה

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

    תשובה

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

    Its value changes with temperature.

27. כרטיס 27

    שאלה

    What base-unit dimensions define one newton?

    תשובה

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

    A force must have dimensions of mass times acceleration.

28. כרטיס 28

    שאלה

    How is cell potential related to reaction free energy?

    תשובה

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

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

29. כרטיס 29

    שאלה

    For constant acceleration, how does displacement depend on time?

    תשובה

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

    Choose a positive direction first, then keep signs consistent.

30. כרטיס 30

    שאלה

    How is molarity defined?

    תשובה

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

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

31. כרטיס 31

    שאלה

    What electric potential does a point charge produce?

    תשובה

    $V=k_e q/r$.

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

32. כרטיס 32

    שאלה

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

    תשובה

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

33. כרטיס 33

    שאלה

    Which constant-acceleration equation avoids time?

    תשובה

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

    It connects speed and displacement when time is absent.

34. כרטיס 34

    שאלה

    What is the general experimental rate-law form?

    תשובה

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

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

35. כרטיס 35

    שאלה

    Which relationship defines pressure from a normal force?

    תשובה

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. כרטיס 36

    שאלה

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

    תשובה

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

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

37. כרטיס 37

    שאלה

    How is wave intensity related to transmitted power and area?

    תשובה

    $I=P/A$.

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

38. כרטיס 38

    שאלה

    How is molality defined?

    תשובה

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

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

39. כרטיס 39

    שאלה

    What base-unit dimensions define one joule?

    תשובה

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

    Work, energy, and heat share this unit.

40. כרטיס 40

    שאלה

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

    תשובה

    $\Delta U=q+w$.

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

41. כרטיס 41

    שאלה

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

    תשובה

    $n=c/v$.

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

42. כרטיס 42

    שאלה

    What equation links net force and acceleration?

    תשובה

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

    The vector sum of external forces determines the acceleration.

43. כרטיס 43

    שאלה

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

    תשובה

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. כרטיס 44

    שאלה

    How is electric potential energy related to charge and voltage?

    תשובה

    $\Delta U=q\Delta V$.

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

45. כרטיס 45

    שאלה

    How are standard cell potential and the equilibrium constant related?

    תשובה

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

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

46. כרטיס 46

    שאלה

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

    תשובה

    $W=mg$.

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

47. כרטיס 47

    שאלה

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

    תשובה

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

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

48. כרטיס 48

    שאלה

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

    תשובה

    $P=P_0+\rho gh$.

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

49. כרטיס 49

    שאלה

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

    תשובה

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

50. כרטיס 50

    שאלה

    Which relationship defines electric current?

    תשובה

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

    Conventional current points in the direction positive charge would move.

51. כרטיס 51

    שאלה

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

    תשובה

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

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

52. כרטיס 52

    שאלה

    What equation governs refraction at a boundary?

    תשובה

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

    Angles are measured from the normal, not the surface.

53. כרטיס 53

    שאלה

    How is mole fraction defined for component $i$?

    תשובה

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. כרטיס 54

    שאלה

    What SI units and base dimensions define pressure?

    תשובה

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

55. כרטיס 55

    שאלה

    What pressure–volume work occurs against constant external pressure?

    תשובה

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

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

56. כרטיס 56

    שאלה

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

    תשובה

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

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

57. כרטיס 57

    שאלה

    How large can static friction become before slipping begins?

    תשובה

    $f_s\leq\mu_sN$, 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. כרטיס 58

    שאלה

    Which relationship handles dilution when solute amount is conserved?

    תשובה

    $M_1V_1=M_2V_2$.

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

59. כרטיס 59

    שאלה

    What is Ohm's law for an ohmic element?

    תשובה

    $V=IR$.

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

60. כרטיס 60

    שאלה

    How is the reaction quotient $Q$ constructed?

    תשובה

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

61. כרטיס 61

    שאלה

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

    תשובה

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. כרטיס 62

    שאלה

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

    תשובה

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

63. כרטיס 63

    שאלה

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

    תשובה

    $F_1/A_1=F_2/A_2$.

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

64. כרטיס 64

    שאלה

    How much charge passes through a cell carrying constant current?

    תשובה

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. כרטיס 65

    שאלה

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

    תשובה

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

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

66. כרטיס 66

    שאלה

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

    תשובה

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

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

67. כרטיס 67

    שאלה

    How is the coulomb expressed through SI base units?

    תשובה

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

    Charge equals current multiplied by time.

68. כרטיס 68

    שאלה

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    תשובה

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

69. כרטיס 69

    שאלה

    How is sound intensity level in decibels defined?

    תשובה

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

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

70. כרטיס 70

    שאלה

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

    תשובה

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

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

71. כרטיס 71

    שאלה

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

    תשובה

    $R=\rho L/A$.

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

72. כרטיס 72

    שאלה

    Which equation gives the magnitude of torque from a force?

    תשובה

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

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

73. כרטיס 73

    שאלה

    How is mass percent composition calculated?

    תשובה

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

74. כרטיס 74

    שאלה

    What buoyant force acts on a submerged object?

    תשובה

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

    It equals the weight of displaced fluid.

75. כרטיס 75

    שאלה

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

    תשובה

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

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

76. כרטיס 76

    שאלה

    What two conditions define static mechanical equilibrium?

    תשובה

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

    Both translational and rotational equilibrium are required.

77. כרטיס 77

    שאלה

    How does Hess's law combine reaction enthalpies?

    תשובה

    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. כרטיס 78

    שאלה

    Which equivalent forms give electrical power in a resistor?

    תשובה

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

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

79. כרטיס 79

    שאלה

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

    תשובה

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

80. כרטיס 80

    שאלה

    What decibel change corresponds to multiplying sound intensity by 10?

    תשובה

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

81. כרטיס 81

    שאלה

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

    תשובה

    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. כרטיס 82

    שאלה

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

    תשובה

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

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

83. כרטיס 83

    שאלה

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

    תשובה

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

84. כרטיס 84

    שאלה

    How is the volt expressed through joules and coulombs?

    תשובה

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

    Voltage is energy transferred per unit charge.

85. כרטיס 85

    שאלה

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

    תשובה

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

86. כרטיס 86

    שאלה

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

    תשובה

    $W=Fd\cos\theta$.

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

87. כרטיס 87

    שאלה

    How is volume percent calculated for a liquid mixture?

    תשובה

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

    Use it only when the problem defines composition by volume.

88. כרטיס 88

    שאלה

    How do resistors combine in series?

    תשובה

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

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

89. כרטיס 89

    שאלה

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

    תשובה

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

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

90. כרטיס 90

    שאלה

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

    תשובה

    $Q=Av$.

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

    

    180 כרטיסים

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

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91. כרטיס 91

    שאלה

    How can average bond energies estimate reaction enthalpy?

    תשובה

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

    Breaking bonds costs energy; forming bonds releases it.

92. כרטיס 92

    שאלה

    What is the translational kinetic energy of a point mass?

    תשובה

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. כרטיס 93

    שאלה

    What ratio defines parts per million by mass?

    תשובה

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

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

94. כרטיס 94

    שאלה

    How do resistors combine in parallel?

    תשובה

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

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

95. כרטיס 95

    שאלה

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

    תשובה

    $K_aK_b=K_w$.

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

96. כרטיס 96

    שאלה

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

    תשובה

    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. כרטיס 97

    שאלה

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

    תשובה

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

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

98. כרטיס 98

    שאלה

    How is lateral magnification related to image and object distances?

    תשובה

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

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

99. כרטיס 99

    שאלה

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

    תשובה

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. כרטיס 100

     שאלה

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

     תשובה

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

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

101. כרטיס 101

     שאלה

     How does reversing a reaction change its equilibrium constant?

     תשובה

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

102. כרטיס 102

     שאלה

     What does the work–energy theorem say?

     תשובה

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

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

103. כרטיס 103

     שאלה

     What entropy change accompanies reversible heat transfer at constant temperature?

     תשובה

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

     Temperature must be in kelvin.

104. כרטיס 104

     שאלה

     What does Kirchhoff's junction rule require?

     תשובה

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

     It follows from conservation of charge at a node.

105. כרטיס 105

     שאלה

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

     תשובה

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

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

106. כרטיס 106

     שאלה

     What continuity relationship applies to steady incompressible flow?

     תשובה

     $A_1v_1=A_2v_2$.

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

107. כרטיס 107

     שאלה

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

     תשובה

     $m=\rho V$.

     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. כרטיס 108

     שאלה

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

     תשובה

     $U_g=mgh$.

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

109. כרטיס 109

     שאלה

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

     תשובה

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

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

110. כרטיס 110

     שאלה

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

     תשובה

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

     Both open ends are displacement antinodes.

111. כרטיס 111

     שאלה

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

     תשובה

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

     Use compatible energy units and absolute temperature.

112. כרטיס 112

     שאלה

     What does Kirchhoff's loop rule require?

     תשובה

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

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

113. כרטיס 113

     שאלה

     What elastic potential energy is stored in an ideal spring?

     תשובה

     $U_s=\tfrac12kx^2$.

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

114. כרטיס 114

     שאלה

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

     תשובה

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

     Dividing coefficients by $n$ takes the corresponding root.

115. כרטיס 115

     שאלה

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

     תשובה

     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. כרטיס 116

     שאלה

     How is lens power related to focal length?

     תשובה

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

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

117. כרטיס 117

     שאלה

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

     תשובה

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

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

118. כרטיס 118

     שאלה

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

     תשובה

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

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

119. כרטיס 119

     שאלה

     What is the Nernst equation for a cell reaction?

     תשובה

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

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

120. כרטיס 120

     שאלה

     What force does an ideal spring exert?

     תשובה

     $F_s=-kx$.

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

121. כרטיס 121

     שאלה

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

     תשובה

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. כרטיס 122

     שאלה

     Which relationship defines capacitance?

     תשובה

     $C=Q/V$.

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

123. כרטיס 123

     שאלה

     How do elemental mass percentages lead to an empirical formula?

     תשובה

     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. כרטיס 124

     שאלה

     When can mechanical energy be conserved?

     תשובה

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

125. כרטיס 125

     שאלה

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

     תשובה

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

126. כרטיס 126

     שאלה

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

     תשובה

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

127. כרטיס 127

     שאלה

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

     תשובה

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

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

128. כרטיס 128

     שאלה

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

     תשובה

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

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

129. כרטיס 129

     שאלה

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

     תשובה

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

     It is independent of initial concentration.

130. כרטיס 130

     שאלה

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

     תשובה

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. כרטיס 131

     שאלה

     How is a molecular formula obtained from an empirical formula?

     תשובה

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

132. כרטיס 132

     שאלה

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

     תשובה

     $C=\kappa\varepsilon_0A/d$.

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

133. כרטיס 133

     שאלה

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

     תשובה

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

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

134. כרטיס 134

     שאלה

     Which relationship gives laminar flow through a cylindrical tube?

     תשובה

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

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

135. כרטיס 135

     שאלה

     How do equilibrium constants combine when reactions are added?

     תשובה

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

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

136. כרטיס 136

     שאלה

     Which relationship defines average power?

     תשובה

     $P=W/\Delta t$.

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

137. כרטיס 137

     שאלה

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

     תשובה

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

138. כרטיס 138

     שאלה

     Which equivalent forms give energy stored in a capacitor?

     תשובה

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

     Use the form matching the known variables.

139. כרטיס 139

     שאלה

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

     תשובה

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

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

140. כרטיס 140

     שאלה

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

     תשובה

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

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

141. כרטיס 141

     שאלה

     How is percent yield calculated?

     תשובה

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

142. כרטיס 142

     שאלה

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

     תשובה

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

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

143. כרטיס 143

     שאלה

     What stoichiometric condition marks acid–base equivalence?

     תשובה

     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. כרטיס 144

     שאלה

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

     תשובה

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

145. כרטיס 145

     שאלה

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

     תשובה

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

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

146. כרטיס 146

     שאלה

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

     תשובה

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

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

147. כרטיס 147

     שאלה

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     תשובה

     $Re=\rho vD/\eta$.

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

148. כרטיס 148

     שאלה

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

     תשובה

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

     This predicts the favorable direction under nonstandard conditions.

149. כרטיס 149

     שאלה

     What is linear momentum?

     תשובה

     $\vec p=m\vec v$.

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

150. כרטיס 150

     שאלה

     How do you identify the limiting reactant from available moles?

     תשובה

     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. כרטיס 151

     שאלה

     How do capacitors combine in parallel?

     תשובה

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

     Parallel capacitors share voltage and their stored charges add.

152. כרטיס 152

     שאלה

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

     תשובה

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

153. כרטיס 153

     שאלה

     What relationship connects impulse and momentum change?

     תשובה

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

154. כרטיס 154

     שאלה

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

     תשובה

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

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

155. כרטיס 155

     שאלה

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

     תשובה

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

     The central maximum lies between the first minima.

156. כרטיס 156

     שאלה

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

     תשובה

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

157. כרטיס 157

     שאלה

     How do capacitors combine in series?

     תשובה

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

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

158. כרטיס 158

     שאלה

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

     תשובה

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

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

159. כרטיס 159

     שאלה

     What beat frequency is heard from two nearby tones?

     תשובה

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

     Beats arise from alternating constructive and destructive interference.

160. כרטיס 160

     שאלה

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

     תשובה

     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. כרטיס 161

     שאלה

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

     תשובה

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

162. כרטיס 162

     שאלה

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

     תשובה

     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. כרטיס 163

     שאלה

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

     תשובה

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

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

164. כרטיס 164

     שאלה

     When is total linear momentum conserved?

     תשובה

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

165. כרטיס 165

     שאלה

     What relationship connects absorbance and concentration in a dilute solution?

     תשובה

     $A=\varepsilon bc$.

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

166. כרטיס 166

     שאלה

     What magnetic force acts on a moving charge?

     תשובה

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

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

167. כרטיס 167

     שאלה

     How does the Arrhenius equation relate rate constant and temperature?

     תשובה

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

168. כרטיס 168

     שאלה

     What is centripetal acceleration for uniform circular motion?

     תשובה

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

     It points toward the center even when speed is constant.

169. כרטיס 169

     שאלה

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

     תשובה

     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. כרטיס 170

     שאלה

     What is the maximum kinetic energy in the photoelectric effect?

     תשובה

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

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

171. כרטיס 171

     שאלה

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

     תשובה

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

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

172. כרטיס 172

     שאלה

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

     תשובה

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

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

173. כרטיס 173

     שאלה

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

     תשובה

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

     This relation changes when a common ion is already present.

174. כרטיס 174

     שאלה

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

     תשובה

     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. כרטיס 175

     שאלה

     How is percent ionization of a weak acid calculated?

     תשובה

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

176. כרטיס 176

     שאלה

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

     תשובה

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

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

177. כרטיס 177

     שאלה

     What energy balance applies in an insulated calorimetry problem?

     תשובה

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

178. כרטיס 178

     שאלה

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

     תשובה

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

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

179. כרטיס 179

     שאלה

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

     תשובה

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

180. כרטיס 180

     שאלה

     What net inward force is required for circular motion?

     תשובה

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

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

180 כרטיסים

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

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