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

Kartice v tem kompletu

1. Kartica 1

   Vprašanje

   Which relationship gives average velocity over a time interval?

   Odgovor

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

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

2. Kartica 2

   Vprašanje

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

   Odgovor

   $n=m/M$.

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

3. Kartica 3

   Vprašanje

   What is the electrostatic force between two point charges?

   Odgovor

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

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

4. Kartica 4

   Vprašanje

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

   Odgovor

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. Kartica 5

   Vprašanje

   How are period and frequency related?

   Odgovor

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. Kartica 6

   Vprašanje

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

   Odgovor

   $q=mc\Delta T$.

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

7. Kartica 7

   Vprašanje

   Which relationship defines mass density?

   Odgovor

   $\rho=m/V$.

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

8. Kartica 8

   Vprašanje

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

   Odgovor

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. Kartica 9

   Vprašanje

   How is photon energy related to frequency and wavelength?

   Odgovor

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. Kartica 10

    Vprašanje

    How is standard cell potential calculated from reduction potentials?

    Odgovor

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

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

11. Kartica 11

    Vprašanje

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

    Odgovor

    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. Kartica 12

    Vprašanje

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

    Odgovor

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

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

13. Kartica 13

    Vprašanje

    Which relationship gives average acceleration over a time interval?

    Odgovor

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

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

14. Kartica 14

    Vprašanje

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

    Odgovor

    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. Kartica 15

    Vprašanje

    What electric-field magnitude does a point charge produce?

    Odgovor

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

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

16. Kartica 16

    Vprašanje

    How do moles relate to the number of microscopic particles?

    Odgovor

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

17. Kartica 17

    Vprašanje

    For constant acceleration, how does velocity change with time?

    Odgovor

    $v=v_0+at$.

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

18. Kartica 18

    Vprašanje

    How is pOH defined?

    Odgovor

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

19. Kartica 19

    Vprašanje

    How is specific gravity defined?

    Odgovor

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

    It is dimensionless because it is a density ratio.

20. Kartica 20

    Vprašanje

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

    Odgovor

    $q=C\Delta T$.

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

21. Kartica 21

    Vprašanje

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

    Odgovor

    $c=f\lambda$.

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

22. Kartica 22

    Vprašanje

    Which species are omitted from a heterogeneous equilibrium expression?

    Odgovor

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

23. Kartica 23

    Vprašanje

    What force does an electric field exert on a charge?

    Odgovor

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. Kartica 24

    Vprašanje

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

    Odgovor

    $PV=nRT$.

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

25. Kartica 25

    Vprašanje

    Which equation relates wave speed, frequency, and wavelength?

    Odgovor

    $v=f\lambda$.

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

26. Kartica 26

    Vprašanje

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

    Odgovor

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

    Its value changes with temperature.

27. Kartica 27

    Vprašanje

    What base-unit dimensions define one newton?

    Odgovor

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

    A force must have dimensions of mass times acceleration.

28. Kartica 28

    Vprašanje

    How is cell potential related to reaction free energy?

    Odgovor

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

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

29. Kartica 29

    Vprašanje

    For constant acceleration, how does displacement depend on time?

    Odgovor

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

    Choose a positive direction first, then keep signs consistent.

30. Kartica 30

    Vprašanje

    How is molarity defined?

    Odgovor

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

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

31. Kartica 31

    Vprašanje

    What electric potential does a point charge produce?

    Odgovor

    $V=k_e q/r$.

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

32. Kartica 32

    Vprašanje

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

    Odgovor

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

33. Kartica 33

    Vprašanje

    Which constant-acceleration equation avoids time?

    Odgovor

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

    It connects speed and displacement when time is absent.

34. Kartica 34

    Vprašanje

    What is the general experimental rate-law form?

    Odgovor

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

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

35. Kartica 35

    Vprašanje

    Which relationship defines pressure from a normal force?

    Odgovor

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. Kartica 36

    Vprašanje

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

    Odgovor

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

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

37. Kartica 37

    Vprašanje

    How is wave intensity related to transmitted power and area?

    Odgovor

    $I=P/A$.

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

38. Kartica 38

    Vprašanje

    How is molality defined?

    Odgovor

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

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

39. Kartica 39

    Vprašanje

    What base-unit dimensions define one joule?

    Odgovor

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

    Work, energy, and heat share this unit.

40. Kartica 40

    Vprašanje

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

    Odgovor

    $\Delta U=q+w$.

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

41. Kartica 41

    Vprašanje

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

    Odgovor

    $n=c/v$.

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

42. Kartica 42

    Vprašanje

    What equation links net force and acceleration?

    Odgovor

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

    The vector sum of external forces determines the acceleration.

43. Kartica 43

    Vprašanje

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

    Odgovor

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. Kartica 44

    Vprašanje

    How is electric potential energy related to charge and voltage?

    Odgovor

    $\Delta U=q\Delta V$.

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

45. Kartica 45

    Vprašanje

    How are standard cell potential and the equilibrium constant related?

    Odgovor

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

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

46. Kartica 46

    Vprašanje

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

    Odgovor

    $W=mg$.

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

47. Kartica 47

    Vprašanje

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

    Odgovor

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

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

48. Kartica 48

    Vprašanje

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

    Odgovor

    $P=P_0+\rho gh$.

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

49. Kartica 49

    Vprašanje

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

    Odgovor

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

50. Kartica 50

    Vprašanje

    Which relationship defines electric current?

    Odgovor

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

    Conventional current points in the direction positive charge would move.

51. Kartica 51

    Vprašanje

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

    Odgovor

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

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

52. Kartica 52

    Vprašanje

    What equation governs refraction at a boundary?

    Odgovor

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

    Angles are measured from the normal, not the surface.

53. Kartica 53

    Vprašanje

    How is mole fraction defined for component $i$?

    Odgovor

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. Kartica 54

    Vprašanje

    What SI units and base dimensions define pressure?

    Odgovor

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

55. Kartica 55

    Vprašanje

    What pressure–volume work occurs against constant external pressure?

    Odgovor

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

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

56. Kartica 56

    Vprašanje

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

    Odgovor

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

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

57. Kartica 57

    Vprašanje

    How large can static friction become before slipping begins?

    Odgovor

    $f_s\leq\mu_sN$, 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. Kartica 58

    Vprašanje

    Which relationship handles dilution when solute amount is conserved?

    Odgovor

    $M_1V_1=M_2V_2$.

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

59. Kartica 59

    Vprašanje

    What is Ohm's law for an ohmic element?

    Odgovor

    $V=IR$.

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

60. Kartica 60

    Vprašanje

    How is the reaction quotient $Q$ constructed?

    Odgovor

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

61. Kartica 61

    Vprašanje

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

    Odgovor

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. Kartica 62

    Vprašanje

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

    Odgovor

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

63. Kartica 63

    Vprašanje

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

    Odgovor

    $F_1/A_1=F_2/A_2$.

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

64. Kartica 64

    Vprašanje

    How much charge passes through a cell carrying constant current?

    Odgovor

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. Kartica 65

    Vprašanje

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

    Odgovor

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

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

66. Kartica 66

    Vprašanje

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

    Odgovor

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

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

67. Kartica 67

    Vprašanje

    How is the coulomb expressed through SI base units?

    Odgovor

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

    Charge equals current multiplied by time.

68. Kartica 68

    Vprašanje

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    Odgovor

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

69. Kartica 69

    Vprašanje

    How is sound intensity level in decibels defined?

    Odgovor

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

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

70. Kartica 70

    Vprašanje

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

    Odgovor

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

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

71. Kartica 71

    Vprašanje

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

    Odgovor

    $R=\rho L/A$.

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

72. Kartica 72

    Vprašanje

    Which equation gives the magnitude of torque from a force?

    Odgovor

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

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

73. Kartica 73

    Vprašanje

    How is mass percent composition calculated?

    Odgovor

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

74. Kartica 74

    Vprašanje

    What buoyant force acts on a submerged object?

    Odgovor

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

    It equals the weight of displaced fluid.

75. Kartica 75

    Vprašanje

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

    Odgovor

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

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

76. Kartica 76

    Vprašanje

    What two conditions define static mechanical equilibrium?

    Odgovor

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

    Both translational and rotational equilibrium are required.

77. Kartica 77

    Vprašanje

    How does Hess's law combine reaction enthalpies?

    Odgovor

    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. Kartica 78

    Vprašanje

    Which equivalent forms give electrical power in a resistor?

    Odgovor

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

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

79. Kartica 79

    Vprašanje

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

    Odgovor

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

80. Kartica 80

    Vprašanje

    What decibel change corresponds to multiplying sound intensity by 10?

    Odgovor

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

81. Kartica 81

    Vprašanje

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

    Odgovor

    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. Kartica 82

    Vprašanje

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

    Odgovor

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

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

83. Kartica 83

    Vprašanje

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

    Odgovor

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

84. Kartica 84

    Vprašanje

    How is the volt expressed through joules and coulombs?

    Odgovor

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

    Voltage is energy transferred per unit charge.

85. Kartica 85

    Vprašanje

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

    Odgovor

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

86. Kartica 86

    Vprašanje

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

    Odgovor

    $W=Fd\cos\theta$.

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

87. Kartica 87

    Vprašanje

    How is volume percent calculated for a liquid mixture?

    Odgovor

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

    Use it only when the problem defines composition by volume.

88. Kartica 88

    Vprašanje

    How do resistors combine in series?

    Odgovor

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

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

89. Kartica 89

    Vprašanje

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

    Odgovor

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

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

90. Kartica 90

    Vprašanje

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

    Odgovor

    $Q=Av$.

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

    

    180 kartic

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

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91. Kartica 91

    Vprašanje

    How can average bond energies estimate reaction enthalpy?

    Odgovor

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

    Breaking bonds costs energy; forming bonds releases it.

92. Kartica 92

    Vprašanje

    What is the translational kinetic energy of a point mass?

    Odgovor

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. Kartica 93

    Vprašanje

    What ratio defines parts per million by mass?

    Odgovor

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

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

94. Kartica 94

    Vprašanje

    How do resistors combine in parallel?

    Odgovor

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

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

95. Kartica 95

    Vprašanje

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

    Odgovor

    $K_aK_b=K_w$.

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

96. Kartica 96

    Vprašanje

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

    Odgovor

    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. Kartica 97

    Vprašanje

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

    Odgovor

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

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

98. Kartica 98

    Vprašanje

    How is lateral magnification related to image and object distances?

    Odgovor

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

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

99. Kartica 99

    Vprašanje

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

    Odgovor

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. Kartica 100

     Vprašanje

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

     Odgovor

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

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

101. Kartica 101

     Vprašanje

     How does reversing a reaction change its equilibrium constant?

     Odgovor

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

102. Kartica 102

     Vprašanje

     What does the work–energy theorem say?

     Odgovor

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

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

103. Kartica 103

     Vprašanje

     What entropy change accompanies reversible heat transfer at constant temperature?

     Odgovor

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

     Temperature must be in kelvin.

104. Kartica 104

     Vprašanje

     What does Kirchhoff's junction rule require?

     Odgovor

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

     It follows from conservation of charge at a node.

105. Kartica 105

     Vprašanje

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

     Odgovor

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

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

106. Kartica 106

     Vprašanje

     What continuity relationship applies to steady incompressible flow?

     Odgovor

     $A_1v_1=A_2v_2$.

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

107. Kartica 107

     Vprašanje

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

     Odgovor

     $m=\rho V$.

     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. Kartica 108

     Vprašanje

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

     Odgovor

     $U_g=mgh$.

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

109. Kartica 109

     Vprašanje

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

     Odgovor

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

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

110. Kartica 110

     Vprašanje

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

     Odgovor

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

     Both open ends are displacement antinodes.

111. Kartica 111

     Vprašanje

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

     Odgovor

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

     Use compatible energy units and absolute temperature.

112. Kartica 112

     Vprašanje

     What does Kirchhoff's loop rule require?

     Odgovor

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

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

113. Kartica 113

     Vprašanje

     What elastic potential energy is stored in an ideal spring?

     Odgovor

     $U_s=\tfrac12kx^2$.

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

114. Kartica 114

     Vprašanje

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

     Odgovor

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

     Dividing coefficients by $n$ takes the corresponding root.

115. Kartica 115

     Vprašanje

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

     Odgovor

     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. Kartica 116

     Vprašanje

     How is lens power related to focal length?

     Odgovor

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

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

117. Kartica 117

     Vprašanje

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

     Odgovor

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

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

118. Kartica 118

     Vprašanje

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

     Odgovor

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

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

119. Kartica 119

     Vprašanje

     What is the Nernst equation for a cell reaction?

     Odgovor

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

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

120. Kartica 120

     Vprašanje

     What force does an ideal spring exert?

     Odgovor

     $F_s=-kx$.

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

121. Kartica 121

     Vprašanje

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

     Odgovor

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. Kartica 122

     Vprašanje

     Which relationship defines capacitance?

     Odgovor

     $C=Q/V$.

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

123. Kartica 123

     Vprašanje

     How do elemental mass percentages lead to an empirical formula?

     Odgovor

     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. Kartica 124

     Vprašanje

     When can mechanical energy be conserved?

     Odgovor

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

125. Kartica 125

     Vprašanje

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

     Odgovor

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

126. Kartica 126

     Vprašanje

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

     Odgovor

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

127. Kartica 127

     Vprašanje

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

     Odgovor

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

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

128. Kartica 128

     Vprašanje

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

     Odgovor

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

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

129. Kartica 129

     Vprašanje

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

     Odgovor

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

     It is independent of initial concentration.

130. Kartica 130

     Vprašanje

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

     Odgovor

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. Kartica 131

     Vprašanje

     How is a molecular formula obtained from an empirical formula?

     Odgovor

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

132. Kartica 132

     Vprašanje

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

     Odgovor

     $C=\kappa\varepsilon_0A/d$.

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

133. Kartica 133

     Vprašanje

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

     Odgovor

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

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

134. Kartica 134

     Vprašanje

     Which relationship gives laminar flow through a cylindrical tube?

     Odgovor

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

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

135. Kartica 135

     Vprašanje

     How do equilibrium constants combine when reactions are added?

     Odgovor

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

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

136. Kartica 136

     Vprašanje

     Which relationship defines average power?

     Odgovor

     $P=W/\Delta t$.

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

137. Kartica 137

     Vprašanje

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

     Odgovor

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

138. Kartica 138

     Vprašanje

     Which equivalent forms give energy stored in a capacitor?

     Odgovor

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

     Use the form matching the known variables.

139. Kartica 139

     Vprašanje

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

     Odgovor

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

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

140. Kartica 140

     Vprašanje

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

     Odgovor

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

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

141. Kartica 141

     Vprašanje

     How is percent yield calculated?

     Odgovor

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

142. Kartica 142

     Vprašanje

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

     Odgovor

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

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

143. Kartica 143

     Vprašanje

     What stoichiometric condition marks acid–base equivalence?

     Odgovor

     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. Kartica 144

     Vprašanje

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

     Odgovor

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

145. Kartica 145

     Vprašanje

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

     Odgovor

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

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

146. Kartica 146

     Vprašanje

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

     Odgovor

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

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

147. Kartica 147

     Vprašanje

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     Odgovor

     $Re=\rho vD/\eta$.

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

148. Kartica 148

     Vprašanje

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

     Odgovor

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

     This predicts the favorable direction under nonstandard conditions.

149. Kartica 149

     Vprašanje

     What is linear momentum?

     Odgovor

     $\vec p=m\vec v$.

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

150. Kartica 150

     Vprašanje

     How do you identify the limiting reactant from available moles?

     Odgovor

     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. Kartica 151

     Vprašanje

     How do capacitors combine in parallel?

     Odgovor

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

     Parallel capacitors share voltage and their stored charges add.

152. Kartica 152

     Vprašanje

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

     Odgovor

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

153. Kartica 153

     Vprašanje

     What relationship connects impulse and momentum change?

     Odgovor

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

154. Kartica 154

     Vprašanje

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

     Odgovor

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

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

155. Kartica 155

     Vprašanje

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

     Odgovor

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

     The central maximum lies between the first minima.

156. Kartica 156

     Vprašanje

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

     Odgovor

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

157. Kartica 157

     Vprašanje

     How do capacitors combine in series?

     Odgovor

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

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

158. Kartica 158

     Vprašanje

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

     Odgovor

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

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

159. Kartica 159

     Vprašanje

     What beat frequency is heard from two nearby tones?

     Odgovor

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

     Beats arise from alternating constructive and destructive interference.

160. Kartica 160

     Vprašanje

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

     Odgovor

     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. Kartica 161

     Vprašanje

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

     Odgovor

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

162. Kartica 162

     Vprašanje

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

     Odgovor

     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. Kartica 163

     Vprašanje

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

     Odgovor

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

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

164. Kartica 164

     Vprašanje

     When is total linear momentum conserved?

     Odgovor

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

165. Kartica 165

     Vprašanje

     What relationship connects absorbance and concentration in a dilute solution?

     Odgovor

     $A=\varepsilon bc$.

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

166. Kartica 166

     Vprašanje

     What magnetic force acts on a moving charge?

     Odgovor

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

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

167. Kartica 167

     Vprašanje

     How does the Arrhenius equation relate rate constant and temperature?

     Odgovor

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

168. Kartica 168

     Vprašanje

     What is centripetal acceleration for uniform circular motion?

     Odgovor

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

     It points toward the center even when speed is constant.

169. Kartica 169

     Vprašanje

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

     Odgovor

     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. Kartica 170

     Vprašanje

     What is the maximum kinetic energy in the photoelectric effect?

     Odgovor

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

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

171. Kartica 171

     Vprašanje

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

     Odgovor

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

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

172. Kartica 172

     Vprašanje

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

     Odgovor

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

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

173. Kartica 173

     Vprašanje

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

     Odgovor

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

     This relation changes when a common ion is already present.

174. Kartica 174

     Vprašanje

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

     Odgovor

     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. Kartica 175

     Vprašanje

     How is percent ionization of a weak acid calculated?

     Odgovor

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

176. Kartica 176

     Vprašanje

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

     Odgovor

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

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

177. Kartica 177

     Vprašanje

     What energy balance applies in an insulated calorimetry problem?

     Odgovor

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

178. Kartica 178

     Vprašanje

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

     Odgovor

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

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

179. Kartica 179

     Vprašanje

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

     Odgovor

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

180. Kartica 180

     Vprašanje

     What net inward force is required for circular motion?

     Odgovor

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

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

180 kartic

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

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