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

Amakhadi akuleli qoqo

1. Ikhadi 1

   Umbuzo

   Which relationship gives average velocity over a time interval?

   Impendulo

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

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

2. Ikhadi 2

   Umbuzo

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

   Impendulo

   $n=m/M$.

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

3. Ikhadi 3

   Umbuzo

   What is the electrostatic force between two point charges?

   Impendulo

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

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

4. Ikhadi 4

   Umbuzo

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

   Impendulo

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. Ikhadi 5

   Umbuzo

   How are period and frequency related?

   Impendulo

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. Ikhadi 6

   Umbuzo

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

   Impendulo

   $q=mc\Delta T$.

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

7. Ikhadi 7

   Umbuzo

   Which relationship defines mass density?

   Impendulo

   $\rho=m/V$.

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

8. Ikhadi 8

   Umbuzo

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

   Impendulo

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. Ikhadi 9

   Umbuzo

   How is photon energy related to frequency and wavelength?

   Impendulo

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. Ikhadi 10

    Umbuzo

    How is standard cell potential calculated from reduction potentials?

    Impendulo

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

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

11. Ikhadi 11

    Umbuzo

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

    Impendulo

    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. Ikhadi 12

    Umbuzo

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

    Impendulo

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

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

13. Ikhadi 13

    Umbuzo

    Which relationship gives average acceleration over a time interval?

    Impendulo

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

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

14. Ikhadi 14

    Umbuzo

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

    Impendulo

    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. Ikhadi 15

    Umbuzo

    What electric-field magnitude does a point charge produce?

    Impendulo

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

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

16. Ikhadi 16

    Umbuzo

    How do moles relate to the number of microscopic particles?

    Impendulo

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

17. Ikhadi 17

    Umbuzo

    For constant acceleration, how does velocity change with time?

    Impendulo

    $v=v_0+at$.

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

18. Ikhadi 18

    Umbuzo

    How is pOH defined?

    Impendulo

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

19. Ikhadi 19

    Umbuzo

    How is specific gravity defined?

    Impendulo

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

    It is dimensionless because it is a density ratio.

20. Ikhadi 20

    Umbuzo

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

    Impendulo

    $q=C\Delta T$.

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

21. Ikhadi 21

    Umbuzo

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

    Impendulo

    $c=f\lambda$.

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

22. Ikhadi 22

    Umbuzo

    Which species are omitted from a heterogeneous equilibrium expression?

    Impendulo

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

23. Ikhadi 23

    Umbuzo

    What force does an electric field exert on a charge?

    Impendulo

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. Ikhadi 24

    Umbuzo

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

    Impendulo

    $PV=nRT$.

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

25. Ikhadi 25

    Umbuzo

    Which equation relates wave speed, frequency, and wavelength?

    Impendulo

    $v=f\lambda$.

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

26. Ikhadi 26

    Umbuzo

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

    Impendulo

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

    Its value changes with temperature.

27. Ikhadi 27

    Umbuzo

    What base-unit dimensions define one newton?

    Impendulo

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

    A force must have dimensions of mass times acceleration.

28. Ikhadi 28

    Umbuzo

    How is cell potential related to reaction free energy?

    Impendulo

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

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

29. Ikhadi 29

    Umbuzo

    For constant acceleration, how does displacement depend on time?

    Impendulo

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

    Choose a positive direction first, then keep signs consistent.

30. Ikhadi 30

    Umbuzo

    How is molarity defined?

    Impendulo

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

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

31. Ikhadi 31

    Umbuzo

    What electric potential does a point charge produce?

    Impendulo

    $V=k_e q/r$.

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

32. Ikhadi 32

    Umbuzo

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

    Impendulo

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

33. Ikhadi 33

    Umbuzo

    Which constant-acceleration equation avoids time?

    Impendulo

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

    It connects speed and displacement when time is absent.

34. Ikhadi 34

    Umbuzo

    What is the general experimental rate-law form?

    Impendulo

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

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

35. Ikhadi 35

    Umbuzo

    Which relationship defines pressure from a normal force?

    Impendulo

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. Ikhadi 36

    Umbuzo

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

    Impendulo

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

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

37. Ikhadi 37

    Umbuzo

    How is wave intensity related to transmitted power and area?

    Impendulo

    $I=P/A$.

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

38. Ikhadi 38

    Umbuzo

    How is molality defined?

    Impendulo

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

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

39. Ikhadi 39

    Umbuzo

    What base-unit dimensions define one joule?

    Impendulo

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

    Work, energy, and heat share this unit.

40. Ikhadi 40

    Umbuzo

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

    Impendulo

    $\Delta U=q+w$.

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

41. Ikhadi 41

    Umbuzo

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

    Impendulo

    $n=c/v$.

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

42. Ikhadi 42

    Umbuzo

    What equation links net force and acceleration?

    Impendulo

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

    The vector sum of external forces determines the acceleration.

43. Ikhadi 43

    Umbuzo

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

    Impendulo

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. Ikhadi 44

    Umbuzo

    How is electric potential energy related to charge and voltage?

    Impendulo

    $\Delta U=q\Delta V$.

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

45. Ikhadi 45

    Umbuzo

    How are standard cell potential and the equilibrium constant related?

    Impendulo

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

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

46. Ikhadi 46

    Umbuzo

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

    Impendulo

    $W=mg$.

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

47. Ikhadi 47

    Umbuzo

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

    Impendulo

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

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

48. Ikhadi 48

    Umbuzo

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

    Impendulo

    $P=P_0+\rho gh$.

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

49. Ikhadi 49

    Umbuzo

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

    Impendulo

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

50. Ikhadi 50

    Umbuzo

    Which relationship defines electric current?

    Impendulo

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

    Conventional current points in the direction positive charge would move.

51. Ikhadi 51

    Umbuzo

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

    Impendulo

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

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

52. Ikhadi 52

    Umbuzo

    What equation governs refraction at a boundary?

    Impendulo

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

    Angles are measured from the normal, not the surface.

53. Ikhadi 53

    Umbuzo

    How is mole fraction defined for component $i$?

    Impendulo

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. Ikhadi 54

    Umbuzo

    What SI units and base dimensions define pressure?

    Impendulo

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

55. Ikhadi 55

    Umbuzo

    What pressure–volume work occurs against constant external pressure?

    Impendulo

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

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

56. Ikhadi 56

    Umbuzo

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

    Impendulo

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

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

57. Ikhadi 57

    Umbuzo

    How large can static friction become before slipping begins?

    Impendulo

    $f_s\leq\mu_sN$, 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. Ikhadi 58

    Umbuzo

    Which relationship handles dilution when solute amount is conserved?

    Impendulo

    $M_1V_1=M_2V_2$.

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

59. Ikhadi 59

    Umbuzo

    What is Ohm's law for an ohmic element?

    Impendulo

    $V=IR$.

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

60. Ikhadi 60

    Umbuzo

    How is the reaction quotient $Q$ constructed?

    Impendulo

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

61. Ikhadi 61

    Umbuzo

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

    Impendulo

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. Ikhadi 62

    Umbuzo

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

    Impendulo

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

63. Ikhadi 63

    Umbuzo

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

    Impendulo

    $F_1/A_1=F_2/A_2$.

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

64. Ikhadi 64

    Umbuzo

    How much charge passes through a cell carrying constant current?

    Impendulo

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. Ikhadi 65

    Umbuzo

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

    Impendulo

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

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

66. Ikhadi 66

    Umbuzo

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

    Impendulo

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

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

67. Ikhadi 67

    Umbuzo

    How is the coulomb expressed through SI base units?

    Impendulo

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

    Charge equals current multiplied by time.

68. Ikhadi 68

    Umbuzo

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    Impendulo

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

69. Ikhadi 69

    Umbuzo

    How is sound intensity level in decibels defined?

    Impendulo

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

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

70. Ikhadi 70

    Umbuzo

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

    Impendulo

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

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

71. Ikhadi 71

    Umbuzo

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

    Impendulo

    $R=\rho L/A$.

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

72. Ikhadi 72

    Umbuzo

    Which equation gives the magnitude of torque from a force?

    Impendulo

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

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

73. Ikhadi 73

    Umbuzo

    How is mass percent composition calculated?

    Impendulo

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

74. Ikhadi 74

    Umbuzo

    What buoyant force acts on a submerged object?

    Impendulo

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

    It equals the weight of displaced fluid.

75. Ikhadi 75

    Umbuzo

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

    Impendulo

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

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

76. Ikhadi 76

    Umbuzo

    What two conditions define static mechanical equilibrium?

    Impendulo

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

    Both translational and rotational equilibrium are required.

77. Ikhadi 77

    Umbuzo

    How does Hess's law combine reaction enthalpies?

    Impendulo

    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. Ikhadi 78

    Umbuzo

    Which equivalent forms give electrical power in a resistor?

    Impendulo

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

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

79. Ikhadi 79

    Umbuzo

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

    Impendulo

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

80. Ikhadi 80

    Umbuzo

    What decibel change corresponds to multiplying sound intensity by 10?

    Impendulo

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

81. Ikhadi 81

    Umbuzo

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

    Impendulo

    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. Ikhadi 82

    Umbuzo

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

    Impendulo

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

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

83. Ikhadi 83

    Umbuzo

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

    Impendulo

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

84. Ikhadi 84

    Umbuzo

    How is the volt expressed through joules and coulombs?

    Impendulo

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

    Voltage is energy transferred per unit charge.

85. Ikhadi 85

    Umbuzo

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

    Impendulo

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

86. Ikhadi 86

    Umbuzo

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

    Impendulo

    $W=Fd\cos\theta$.

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

87. Ikhadi 87

    Umbuzo

    How is volume percent calculated for a liquid mixture?

    Impendulo

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

    Use it only when the problem defines composition by volume.

88. Ikhadi 88

    Umbuzo

    How do resistors combine in series?

    Impendulo

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

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

89. Ikhadi 89

    Umbuzo

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

    Impendulo

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

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

90. Ikhadi 90

    Umbuzo

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

    Impendulo

    $Q=Av$.

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

    

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

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91. Ikhadi 91

    Umbuzo

    How can average bond energies estimate reaction enthalpy?

    Impendulo

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

    Breaking bonds costs energy; forming bonds releases it.

92. Ikhadi 92

    Umbuzo

    What is the translational kinetic energy of a point mass?

    Impendulo

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. Ikhadi 93

    Umbuzo

    What ratio defines parts per million by mass?

    Impendulo

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

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

94. Ikhadi 94

    Umbuzo

    How do resistors combine in parallel?

    Impendulo

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

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

95. Ikhadi 95

    Umbuzo

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

    Impendulo

    $K_aK_b=K_w$.

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

96. Ikhadi 96

    Umbuzo

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

    Impendulo

    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. Ikhadi 97

    Umbuzo

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

    Impendulo

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

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

98. Ikhadi 98

    Umbuzo

    How is lateral magnification related to image and object distances?

    Impendulo

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

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

99. Ikhadi 99

    Umbuzo

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

    Impendulo

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. Ikhadi 100

     Umbuzo

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

     Impendulo

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

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

101. Ikhadi 101

     Umbuzo

     How does reversing a reaction change its equilibrium constant?

     Impendulo

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

102. Ikhadi 102

     Umbuzo

     What does the work–energy theorem say?

     Impendulo

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

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

103. Ikhadi 103

     Umbuzo

     What entropy change accompanies reversible heat transfer at constant temperature?

     Impendulo

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

     Temperature must be in kelvin.

104. Ikhadi 104

     Umbuzo

     What does Kirchhoff's junction rule require?

     Impendulo

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

     It follows from conservation of charge at a node.

105. Ikhadi 105

     Umbuzo

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

     Impendulo

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

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

106. Ikhadi 106

     Umbuzo

     What continuity relationship applies to steady incompressible flow?

     Impendulo

     $A_1v_1=A_2v_2$.

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

107. Ikhadi 107

     Umbuzo

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

     Impendulo

     $m=\rho V$.

     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. Ikhadi 108

     Umbuzo

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

     Impendulo

     $U_g=mgh$.

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

109. Ikhadi 109

     Umbuzo

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

     Impendulo

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

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

110. Ikhadi 110

     Umbuzo

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

     Impendulo

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

     Both open ends are displacement antinodes.

111. Ikhadi 111

     Umbuzo

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

     Impendulo

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

     Use compatible energy units and absolute temperature.

112. Ikhadi 112

     Umbuzo

     What does Kirchhoff's loop rule require?

     Impendulo

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

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

113. Ikhadi 113

     Umbuzo

     What elastic potential energy is stored in an ideal spring?

     Impendulo

     $U_s=\tfrac12kx^2$.

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

114. Ikhadi 114

     Umbuzo

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

     Impendulo

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

     Dividing coefficients by $n$ takes the corresponding root.

115. Ikhadi 115

     Umbuzo

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

     Impendulo

     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. Ikhadi 116

     Umbuzo

     How is lens power related to focal length?

     Impendulo

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

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

117. Ikhadi 117

     Umbuzo

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

     Impendulo

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

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

118. Ikhadi 118

     Umbuzo

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

     Impendulo

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

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

119. Ikhadi 119

     Umbuzo

     What is the Nernst equation for a cell reaction?

     Impendulo

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

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

120. Ikhadi 120

     Umbuzo

     What force does an ideal spring exert?

     Impendulo

     $F_s=-kx$.

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

121. Ikhadi 121

     Umbuzo

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

     Impendulo

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. Ikhadi 122

     Umbuzo

     Which relationship defines capacitance?

     Impendulo

     $C=Q/V$.

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

123. Ikhadi 123

     Umbuzo

     How do elemental mass percentages lead to an empirical formula?

     Impendulo

     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. Ikhadi 124

     Umbuzo

     When can mechanical energy be conserved?

     Impendulo

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

125. Ikhadi 125

     Umbuzo

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

     Impendulo

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

126. Ikhadi 126

     Umbuzo

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

     Impendulo

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

127. Ikhadi 127

     Umbuzo

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

     Impendulo

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

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

128. Ikhadi 128

     Umbuzo

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

     Impendulo

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

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

129. Ikhadi 129

     Umbuzo

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

     Impendulo

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

     It is independent of initial concentration.

130. Ikhadi 130

     Umbuzo

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

     Impendulo

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. Ikhadi 131

     Umbuzo

     How is a molecular formula obtained from an empirical formula?

     Impendulo

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

132. Ikhadi 132

     Umbuzo

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

     Impendulo

     $C=\kappa\varepsilon_0A/d$.

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

133. Ikhadi 133

     Umbuzo

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

     Impendulo

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

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

134. Ikhadi 134

     Umbuzo

     Which relationship gives laminar flow through a cylindrical tube?

     Impendulo

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

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

135. Ikhadi 135

     Umbuzo

     How do equilibrium constants combine when reactions are added?

     Impendulo

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

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

136. Ikhadi 136

     Umbuzo

     Which relationship defines average power?

     Impendulo

     $P=W/\Delta t$.

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

137. Ikhadi 137

     Umbuzo

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

     Impendulo

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

138. Ikhadi 138

     Umbuzo

     Which equivalent forms give energy stored in a capacitor?

     Impendulo

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

     Use the form matching the known variables.

139. Ikhadi 139

     Umbuzo

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

     Impendulo

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

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

140. Ikhadi 140

     Umbuzo

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

     Impendulo

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

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

141. Ikhadi 141

     Umbuzo

     How is percent yield calculated?

     Impendulo

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

142. Ikhadi 142

     Umbuzo

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

     Impendulo

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

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

143. Ikhadi 143

     Umbuzo

     What stoichiometric condition marks acid–base equivalence?

     Impendulo

     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. Ikhadi 144

     Umbuzo

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

     Impendulo

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

145. Ikhadi 145

     Umbuzo

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

     Impendulo

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

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

146. Ikhadi 146

     Umbuzo

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

     Impendulo

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

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

147. Ikhadi 147

     Umbuzo

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     Impendulo

     $Re=\rho vD/\eta$.

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

148. Ikhadi 148

     Umbuzo

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

     Impendulo

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

     This predicts the favorable direction under nonstandard conditions.

149. Ikhadi 149

     Umbuzo

     What is linear momentum?

     Impendulo

     $\vec p=m\vec v$.

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

150. Ikhadi 150

     Umbuzo

     How do you identify the limiting reactant from available moles?

     Impendulo

     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. Ikhadi 151

     Umbuzo

     How do capacitors combine in parallel?

     Impendulo

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

     Parallel capacitors share voltage and their stored charges add.

152. Ikhadi 152

     Umbuzo

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

     Impendulo

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

153. Ikhadi 153

     Umbuzo

     What relationship connects impulse and momentum change?

     Impendulo

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

154. Ikhadi 154

     Umbuzo

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

     Impendulo

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

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

155. Ikhadi 155

     Umbuzo

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

     Impendulo

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

     The central maximum lies between the first minima.

156. Ikhadi 156

     Umbuzo

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

     Impendulo

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

157. Ikhadi 157

     Umbuzo

     How do capacitors combine in series?

     Impendulo

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

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

158. Ikhadi 158

     Umbuzo

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

     Impendulo

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

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

159. Ikhadi 159

     Umbuzo

     What beat frequency is heard from two nearby tones?

     Impendulo

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

     Beats arise from alternating constructive and destructive interference.

160. Ikhadi 160

     Umbuzo

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

     Impendulo

     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. Ikhadi 161

     Umbuzo

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

     Impendulo

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

162. Ikhadi 162

     Umbuzo

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

     Impendulo

     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. Ikhadi 163

     Umbuzo

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

     Impendulo

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

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

164. Ikhadi 164

     Umbuzo

     When is total linear momentum conserved?

     Impendulo

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

165. Ikhadi 165

     Umbuzo

     What relationship connects absorbance and concentration in a dilute solution?

     Impendulo

     $A=\varepsilon bc$.

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

166. Ikhadi 166

     Umbuzo

     What magnetic force acts on a moving charge?

     Impendulo

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

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

167. Ikhadi 167

     Umbuzo

     How does the Arrhenius equation relate rate constant and temperature?

     Impendulo

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

168. Ikhadi 168

     Umbuzo

     What is centripetal acceleration for uniform circular motion?

     Impendulo

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

     It points toward the center even when speed is constant.

169. Ikhadi 169

     Umbuzo

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

     Impendulo

     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. Ikhadi 170

     Umbuzo

     What is the maximum kinetic energy in the photoelectric effect?

     Impendulo

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

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

171. Ikhadi 171

     Umbuzo

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

     Impendulo

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

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

172. Ikhadi 172

     Umbuzo

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

     Impendulo

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

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

173. Ikhadi 173

     Umbuzo

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

     Impendulo

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

     This relation changes when a common ion is already present.

174. Ikhadi 174

     Umbuzo

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

     Impendulo

     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. Ikhadi 175

     Umbuzo

     How is percent ionization of a weak acid calculated?

     Impendulo

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

176. Ikhadi 176

     Umbuzo

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

     Impendulo

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

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

177. Ikhadi 177

     Umbuzo

     What energy balance applies in an insulated calorimetry problem?

     Impendulo

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

178. Ikhadi 178

     Umbuzo

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

     Impendulo

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

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

179. Ikhadi 179

     Umbuzo

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

     Impendulo

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

180. Ikhadi 180

     Umbuzo

     What net inward force is required for circular motion?

     Impendulo

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

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

amakhadi angu-180

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

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