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

Fișele din acest pachet

1. Fișa 1

   Întrebare

   Which relationship gives average velocity over a time interval?

   Răspuns

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

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

2. Fișa 2

   Întrebare

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

   Răspuns

   $n=m/M$.

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

3. Fișa 3

   Întrebare

   What is the electrostatic force between two point charges?

   Răspuns

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

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

4. Fișa 4

   Întrebare

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

   Răspuns

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. Fișa 5

   Întrebare

   How are period and frequency related?

   Răspuns

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. Fișa 6

   Întrebare

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

   Răspuns

   $q=mc\Delta T$.

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

7. Fișa 7

   Întrebare

   Which relationship defines mass density?

   Răspuns

   $\rho=m/V$.

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

8. Fișa 8

   Întrebare

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

   Răspuns

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. Fișa 9

   Întrebare

   How is photon energy related to frequency and wavelength?

   Răspuns

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. Fișa 10

    Întrebare

    How is standard cell potential calculated from reduction potentials?

    Răspuns

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

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

11. Fișa 11

    Întrebare

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

    Răspuns

    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. Fișa 12

    Întrebare

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

    Răspuns

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

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

13. Fișa 13

    Întrebare

    Which relationship gives average acceleration over a time interval?

    Răspuns

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

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

14. Fișa 14

    Întrebare

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

    Răspuns

    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. Fișa 15

    Întrebare

    What electric-field magnitude does a point charge produce?

    Răspuns

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

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

16. Fișa 16

    Întrebare

    How do moles relate to the number of microscopic particles?

    Răspuns

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

17. Fișa 17

    Întrebare

    For constant acceleration, how does velocity change with time?

    Răspuns

    $v=v_0+at$.

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

18. Fișa 18

    Întrebare

    How is pOH defined?

    Răspuns

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

19. Fișa 19

    Întrebare

    How is specific gravity defined?

    Răspuns

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

    It is dimensionless because it is a density ratio.

20. Fișa 20

    Întrebare

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

    Răspuns

    $q=C\Delta T$.

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

21. Fișa 21

    Întrebare

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

    Răspuns

    $c=f\lambda$.

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

22. Fișa 22

    Întrebare

    Which species are omitted from a heterogeneous equilibrium expression?

    Răspuns

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

23. Fișa 23

    Întrebare

    What force does an electric field exert on a charge?

    Răspuns

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. Fișa 24

    Întrebare

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

    Răspuns

    $PV=nRT$.

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

25. Fișa 25

    Întrebare

    Which equation relates wave speed, frequency, and wavelength?

    Răspuns

    $v=f\lambda$.

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

26. Fișa 26

    Întrebare

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

    Răspuns

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

    Its value changes with temperature.

27. Fișa 27

    Întrebare

    What base-unit dimensions define one newton?

    Răspuns

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

    A force must have dimensions of mass times acceleration.

28. Fișa 28

    Întrebare

    How is cell potential related to reaction free energy?

    Răspuns

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

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

29. Fișa 29

    Întrebare

    For constant acceleration, how does displacement depend on time?

    Răspuns

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

    Choose a positive direction first, then keep signs consistent.

30. Fișa 30

    Întrebare

    How is molarity defined?

    Răspuns

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

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

31. Fișa 31

    Întrebare

    What electric potential does a point charge produce?

    Răspuns

    $V=k_e q/r$.

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

32. Fișa 32

    Întrebare

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

    Răspuns

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

33. Fișa 33

    Întrebare

    Which constant-acceleration equation avoids time?

    Răspuns

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

    It connects speed and displacement when time is absent.

34. Fișa 34

    Întrebare

    What is the general experimental rate-law form?

    Răspuns

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

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

35. Fișa 35

    Întrebare

    Which relationship defines pressure from a normal force?

    Răspuns

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. Fișa 36

    Întrebare

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

    Răspuns

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

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

37. Fișa 37

    Întrebare

    How is wave intensity related to transmitted power and area?

    Răspuns

    $I=P/A$.

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

38. Fișa 38

    Întrebare

    How is molality defined?

    Răspuns

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

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

39. Fișa 39

    Întrebare

    What base-unit dimensions define one joule?

    Răspuns

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

    Work, energy, and heat share this unit.

40. Fișa 40

    Întrebare

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

    Răspuns

    $\Delta U=q+w$.

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

41. Fișa 41

    Întrebare

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

    Răspuns

    $n=c/v$.

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

42. Fișa 42

    Întrebare

    What equation links net force and acceleration?

    Răspuns

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

    The vector sum of external forces determines the acceleration.

43. Fișa 43

    Întrebare

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

    Răspuns

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. Fișa 44

    Întrebare

    How is electric potential energy related to charge and voltage?

    Răspuns

    $\Delta U=q\Delta V$.

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

45. Fișa 45

    Întrebare

    How are standard cell potential and the equilibrium constant related?

    Răspuns

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

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

46. Fișa 46

    Întrebare

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

    Răspuns

    $W=mg$.

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

47. Fișa 47

    Întrebare

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

    Răspuns

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

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

48. Fișa 48

    Întrebare

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

    Răspuns

    $P=P_0+\rho gh$.

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

49. Fișa 49

    Întrebare

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

    Răspuns

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

50. Fișa 50

    Întrebare

    Which relationship defines electric current?

    Răspuns

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

    Conventional current points in the direction positive charge would move.

51. Fișa 51

    Întrebare

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

    Răspuns

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

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

52. Fișa 52

    Întrebare

    What equation governs refraction at a boundary?

    Răspuns

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

    Angles are measured from the normal, not the surface.

53. Fișa 53

    Întrebare

    How is mole fraction defined for component $i$?

    Răspuns

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. Fișa 54

    Întrebare

    What SI units and base dimensions define pressure?

    Răspuns

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

55. Fișa 55

    Întrebare

    What pressure–volume work occurs against constant external pressure?

    Răspuns

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

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

56. Fișa 56

    Întrebare

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

    Răspuns

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

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

57. Fișa 57

    Întrebare

    How large can static friction become before slipping begins?

    Răspuns

    $f_s\leq\mu_sN$, 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. Fișa 58

    Întrebare

    Which relationship handles dilution when solute amount is conserved?

    Răspuns

    $M_1V_1=M_2V_2$.

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

59. Fișa 59

    Întrebare

    What is Ohm's law for an ohmic element?

    Răspuns

    $V=IR$.

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

60. Fișa 60

    Întrebare

    How is the reaction quotient $Q$ constructed?

    Răspuns

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

61. Fișa 61

    Întrebare

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

    Răspuns

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. Fișa 62

    Întrebare

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

    Răspuns

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

63. Fișa 63

    Întrebare

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

    Răspuns

    $F_1/A_1=F_2/A_2$.

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

64. Fișa 64

    Întrebare

    How much charge passes through a cell carrying constant current?

    Răspuns

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. Fișa 65

    Întrebare

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

    Răspuns

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

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

66. Fișa 66

    Întrebare

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

    Răspuns

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

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

67. Fișa 67

    Întrebare

    How is the coulomb expressed through SI base units?

    Răspuns

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

    Charge equals current multiplied by time.

68. Fișa 68

    Întrebare

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    Răspuns

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

69. Fișa 69

    Întrebare

    How is sound intensity level in decibels defined?

    Răspuns

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

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

70. Fișa 70

    Întrebare

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

    Răspuns

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

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

71. Fișa 71

    Întrebare

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

    Răspuns

    $R=\rho L/A$.

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

72. Fișa 72

    Întrebare

    Which equation gives the magnitude of torque from a force?

    Răspuns

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

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

73. Fișa 73

    Întrebare

    How is mass percent composition calculated?

    Răspuns

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

74. Fișa 74

    Întrebare

    What buoyant force acts on a submerged object?

    Răspuns

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

    It equals the weight of displaced fluid.

75. Fișa 75

    Întrebare

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

    Răspuns

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

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

76. Fișa 76

    Întrebare

    What two conditions define static mechanical equilibrium?

    Răspuns

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

    Both translational and rotational equilibrium are required.

77. Fișa 77

    Întrebare

    How does Hess's law combine reaction enthalpies?

    Răspuns

    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. Fișa 78

    Întrebare

    Which equivalent forms give electrical power in a resistor?

    Răspuns

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

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

79. Fișa 79

    Întrebare

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

    Răspuns

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

80. Fișa 80

    Întrebare

    What decibel change corresponds to multiplying sound intensity by 10?

    Răspuns

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

81. Fișa 81

    Întrebare

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

    Răspuns

    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. Fișa 82

    Întrebare

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

    Răspuns

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

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

83. Fișa 83

    Întrebare

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

    Răspuns

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

84. Fișa 84

    Întrebare

    How is the volt expressed through joules and coulombs?

    Răspuns

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

    Voltage is energy transferred per unit charge.

85. Fișa 85

    Întrebare

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

    Răspuns

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

86. Fișa 86

    Întrebare

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

    Răspuns

    $W=Fd\cos\theta$.

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

87. Fișa 87

    Întrebare

    How is volume percent calculated for a liquid mixture?

    Răspuns

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

    Use it only when the problem defines composition by volume.

88. Fișa 88

    Întrebare

    How do resistors combine in series?

    Răspuns

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

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

89. Fișa 89

    Întrebare

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

    Răspuns

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

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

90. Fișa 90

    Întrebare

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

    Răspuns

    $Q=Av$.

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

    

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91. Fișa 91

    Întrebare

    How can average bond energies estimate reaction enthalpy?

    Răspuns

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

    Breaking bonds costs energy; forming bonds releases it.

92. Fișa 92

    Întrebare

    What is the translational kinetic energy of a point mass?

    Răspuns

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. Fișa 93

    Întrebare

    What ratio defines parts per million by mass?

    Răspuns

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

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

94. Fișa 94

    Întrebare

    How do resistors combine in parallel?

    Răspuns

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

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

95. Fișa 95

    Întrebare

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

    Răspuns

    $K_aK_b=K_w$.

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

96. Fișa 96

    Întrebare

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

    Răspuns

    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. Fișa 97

    Întrebare

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

    Răspuns

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

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

98. Fișa 98

    Întrebare

    How is lateral magnification related to image and object distances?

    Răspuns

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

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

99. Fișa 99

    Întrebare

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

    Răspuns

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. Fișa 100

     Întrebare

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

     Răspuns

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

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

101. Fișa 101

     Întrebare

     How does reversing a reaction change its equilibrium constant?

     Răspuns

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

102. Fișa 102

     Întrebare

     What does the work–energy theorem say?

     Răspuns

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

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

103. Fișa 103

     Întrebare

     What entropy change accompanies reversible heat transfer at constant temperature?

     Răspuns

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

     Temperature must be in kelvin.

104. Fișa 104

     Întrebare

     What does Kirchhoff's junction rule require?

     Răspuns

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

     It follows from conservation of charge at a node.

105. Fișa 105

     Întrebare

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

     Răspuns

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

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

106. Fișa 106

     Întrebare

     What continuity relationship applies to steady incompressible flow?

     Răspuns

     $A_1v_1=A_2v_2$.

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

107. Fișa 107

     Întrebare

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

     Răspuns

     $m=\rho V$.

     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. Fișa 108

     Întrebare

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

     Răspuns

     $U_g=mgh$.

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

109. Fișa 109

     Întrebare

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

     Răspuns

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

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

110. Fișa 110

     Întrebare

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

     Răspuns

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

     Both open ends are displacement antinodes.

111. Fișa 111

     Întrebare

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

     Răspuns

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

     Use compatible energy units and absolute temperature.

112. Fișa 112

     Întrebare

     What does Kirchhoff's loop rule require?

     Răspuns

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

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

113. Fișa 113

     Întrebare

     What elastic potential energy is stored in an ideal spring?

     Răspuns

     $U_s=\tfrac12kx^2$.

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

114. Fișa 114

     Întrebare

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

     Răspuns

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

     Dividing coefficients by $n$ takes the corresponding root.

115. Fișa 115

     Întrebare

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

     Răspuns

     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. Fișa 116

     Întrebare

     How is lens power related to focal length?

     Răspuns

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

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

117. Fișa 117

     Întrebare

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

     Răspuns

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

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

118. Fișa 118

     Întrebare

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

     Răspuns

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

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

119. Fișa 119

     Întrebare

     What is the Nernst equation for a cell reaction?

     Răspuns

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

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

120. Fișa 120

     Întrebare

     What force does an ideal spring exert?

     Răspuns

     $F_s=-kx$.

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

121. Fișa 121

     Întrebare

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

     Răspuns

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. Fișa 122

     Întrebare

     Which relationship defines capacitance?

     Răspuns

     $C=Q/V$.

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

123. Fișa 123

     Întrebare

     How do elemental mass percentages lead to an empirical formula?

     Răspuns

     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. Fișa 124

     Întrebare

     When can mechanical energy be conserved?

     Răspuns

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

125. Fișa 125

     Întrebare

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

     Răspuns

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

126. Fișa 126

     Întrebare

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

     Răspuns

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

127. Fișa 127

     Întrebare

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

     Răspuns

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

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

128. Fișa 128

     Întrebare

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

     Răspuns

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

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

129. Fișa 129

     Întrebare

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

     Răspuns

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

     It is independent of initial concentration.

130. Fișa 130

     Întrebare

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

     Răspuns

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. Fișa 131

     Întrebare

     How is a molecular formula obtained from an empirical formula?

     Răspuns

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

132. Fișa 132

     Întrebare

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

     Răspuns

     $C=\kappa\varepsilon_0A/d$.

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

133. Fișa 133

     Întrebare

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

     Răspuns

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

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

134. Fișa 134

     Întrebare

     Which relationship gives laminar flow through a cylindrical tube?

     Răspuns

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

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

135. Fișa 135

     Întrebare

     How do equilibrium constants combine when reactions are added?

     Răspuns

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

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

136. Fișa 136

     Întrebare

     Which relationship defines average power?

     Răspuns

     $P=W/\Delta t$.

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

137. Fișa 137

     Întrebare

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

     Răspuns

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

138. Fișa 138

     Întrebare

     Which equivalent forms give energy stored in a capacitor?

     Răspuns

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

     Use the form matching the known variables.

139. Fișa 139

     Întrebare

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

     Răspuns

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

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

140. Fișa 140

     Întrebare

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

     Răspuns

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

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

141. Fișa 141

     Întrebare

     How is percent yield calculated?

     Răspuns

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

142. Fișa 142

     Întrebare

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

     Răspuns

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

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

143. Fișa 143

     Întrebare

     What stoichiometric condition marks acid–base equivalence?

     Răspuns

     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. Fișa 144

     Întrebare

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

     Răspuns

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

145. Fișa 145

     Întrebare

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

     Răspuns

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

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

146. Fișa 146

     Întrebare

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

     Răspuns

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

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

147. Fișa 147

     Întrebare

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     Răspuns

     $Re=\rho vD/\eta$.

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

148. Fișa 148

     Întrebare

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

     Răspuns

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

     This predicts the favorable direction under nonstandard conditions.

149. Fișa 149

     Întrebare

     What is linear momentum?

     Răspuns

     $\vec p=m\vec v$.

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

150. Fișa 150

     Întrebare

     How do you identify the limiting reactant from available moles?

     Răspuns

     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. Fișa 151

     Întrebare

     How do capacitors combine in parallel?

     Răspuns

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

     Parallel capacitors share voltage and their stored charges add.

152. Fișa 152

     Întrebare

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

     Răspuns

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

153. Fișa 153

     Întrebare

     What relationship connects impulse and momentum change?

     Răspuns

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

154. Fișa 154

     Întrebare

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

     Răspuns

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

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

155. Fișa 155

     Întrebare

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

     Răspuns

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

     The central maximum lies between the first minima.

156. Fișa 156

     Întrebare

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

     Răspuns

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

157. Fișa 157

     Întrebare

     How do capacitors combine in series?

     Răspuns

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

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

158. Fișa 158

     Întrebare

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

     Răspuns

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

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

159. Fișa 159

     Întrebare

     What beat frequency is heard from two nearby tones?

     Răspuns

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

     Beats arise from alternating constructive and destructive interference.

160. Fișa 160

     Întrebare

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

     Răspuns

     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. Fișa 161

     Întrebare

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

     Răspuns

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

162. Fișa 162

     Întrebare

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

     Răspuns

     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. Fișa 163

     Întrebare

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

     Răspuns

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

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

164. Fișa 164

     Întrebare

     When is total linear momentum conserved?

     Răspuns

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

165. Fișa 165

     Întrebare

     What relationship connects absorbance and concentration in a dilute solution?

     Răspuns

     $A=\varepsilon bc$.

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

166. Fișa 166

     Întrebare

     What magnetic force acts on a moving charge?

     Răspuns

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

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

167. Fișa 167

     Întrebare

     How does the Arrhenius equation relate rate constant and temperature?

     Răspuns

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

168. Fișa 168

     Întrebare

     What is centripetal acceleration for uniform circular motion?

     Răspuns

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

     It points toward the center even when speed is constant.

169. Fișa 169

     Întrebare

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

     Răspuns

     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. Fișa 170

     Întrebare

     What is the maximum kinetic energy in the photoelectric effect?

     Răspuns

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

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

171. Fișa 171

     Întrebare

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

     Răspuns

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

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

172. Fișa 172

     Întrebare

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

     Răspuns

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

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

173. Fișa 173

     Întrebare

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

     Răspuns

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

     This relation changes when a common ion is already present.

174. Fișa 174

     Întrebare

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

     Răspuns

     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. Fișa 175

     Întrebare

     How is percent ionization of a weak acid calculated?

     Răspuns

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

176. Fișa 176

     Întrebare

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

     Răspuns

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

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

177. Fișa 177

     Întrebare

     What energy balance applies in an insulated calorimetry problem?

     Răspuns

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

178. Fișa 178

     Întrebare

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

     Răspuns

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

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

179. Fișa 179

     Întrebare

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

     Răspuns

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

180. Fișa 180

     Întrebare

     What net inward force is required for circular motion?

     Răspuns

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

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

180 de fișe

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

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