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

Κάρτες σε αυτήν τη δέσμη

1. Κάρτα 1

   Ερώτηση

   Which relationship gives average velocity over a time interval?

   Απάντηση

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

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

2. Κάρτα 2

   Ερώτηση

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

   Απάντηση

   $n=m/M$.

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

3. Κάρτα 3

   Ερώτηση

   What is the electrostatic force between two point charges?

   Απάντηση

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

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

4. Κάρτα 4

   Ερώτηση

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

   Απάντηση

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. Κάρτα 5

   Ερώτηση

   How are period and frequency related?

   Απάντηση

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. Κάρτα 6

   Ερώτηση

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

   Απάντηση

   $q=mc\Delta T$.

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

7. Κάρτα 7

   Ερώτηση

   Which relationship defines mass density?

   Απάντηση

   $\rho=m/V$.

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

8. Κάρτα 8

   Ερώτηση

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

   Απάντηση

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. Κάρτα 9

   Ερώτηση

   How is photon energy related to frequency and wavelength?

   Απάντηση

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. Κάρτα 10

    Ερώτηση

    How is standard cell potential calculated from reduction potentials?

    Απάντηση

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

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

11. Κάρτα 11

    Ερώτηση

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

    Απάντηση

    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. Κάρτα 12

    Ερώτηση

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

    Απάντηση

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

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

13. Κάρτα 13

    Ερώτηση

    Which relationship gives average acceleration over a time interval?

    Απάντηση

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

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

14. Κάρτα 14

    Ερώτηση

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

    Απάντηση

    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. Κάρτα 15

    Ερώτηση

    What electric-field magnitude does a point charge produce?

    Απάντηση

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

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

16. Κάρτα 16

    Ερώτηση

    How do moles relate to the number of microscopic particles?

    Απάντηση

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

17. Κάρτα 17

    Ερώτηση

    For constant acceleration, how does velocity change with time?

    Απάντηση

    $v=v_0+at$.

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

18. Κάρτα 18

    Ερώτηση

    How is pOH defined?

    Απάντηση

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

19. Κάρτα 19

    Ερώτηση

    How is specific gravity defined?

    Απάντηση

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

    It is dimensionless because it is a density ratio.

20. Κάρτα 20

    Ερώτηση

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

    Απάντηση

    $q=C\Delta T$.

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

21. Κάρτα 21

    Ερώτηση

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

    Απάντηση

    $c=f\lambda$.

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

22. Κάρτα 22

    Ερώτηση

    Which species are omitted from a heterogeneous equilibrium expression?

    Απάντηση

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

23. Κάρτα 23

    Ερώτηση

    What force does an electric field exert on a charge?

    Απάντηση

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. Κάρτα 24

    Ερώτηση

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

    Απάντηση

    $PV=nRT$.

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

25. Κάρτα 25

    Ερώτηση

    Which equation relates wave speed, frequency, and wavelength?

    Απάντηση

    $v=f\lambda$.

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

26. Κάρτα 26

    Ερώτηση

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

    Απάντηση

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

    Its value changes with temperature.

27. Κάρτα 27

    Ερώτηση

    What base-unit dimensions define one newton?

    Απάντηση

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

    A force must have dimensions of mass times acceleration.

28. Κάρτα 28

    Ερώτηση

    How is cell potential related to reaction free energy?

    Απάντηση

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

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

29. Κάρτα 29

    Ερώτηση

    For constant acceleration, how does displacement depend on time?

    Απάντηση

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

    Choose a positive direction first, then keep signs consistent.

30. Κάρτα 30

    Ερώτηση

    How is molarity defined?

    Απάντηση

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

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

31. Κάρτα 31

    Ερώτηση

    What electric potential does a point charge produce?

    Απάντηση

    $V=k_e q/r$.

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

32. Κάρτα 32

    Ερώτηση

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

    Απάντηση

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

33. Κάρτα 33

    Ερώτηση

    Which constant-acceleration equation avoids time?

    Απάντηση

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

    It connects speed and displacement when time is absent.

34. Κάρτα 34

    Ερώτηση

    What is the general experimental rate-law form?

    Απάντηση

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

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

35. Κάρτα 35

    Ερώτηση

    Which relationship defines pressure from a normal force?

    Απάντηση

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. Κάρτα 36

    Ερώτηση

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

    Απάντηση

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

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

37. Κάρτα 37

    Ερώτηση

    How is wave intensity related to transmitted power and area?

    Απάντηση

    $I=P/A$.

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

38. Κάρτα 38

    Ερώτηση

    How is molality defined?

    Απάντηση

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

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

39. Κάρτα 39

    Ερώτηση

    What base-unit dimensions define one joule?

    Απάντηση

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

    Work, energy, and heat share this unit.

40. Κάρτα 40

    Ερώτηση

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

    Απάντηση

    $\Delta U=q+w$.

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

41. Κάρτα 41

    Ερώτηση

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

    Απάντηση

    $n=c/v$.

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

42. Κάρτα 42

    Ερώτηση

    What equation links net force and acceleration?

    Απάντηση

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

    The vector sum of external forces determines the acceleration.

43. Κάρτα 43

    Ερώτηση

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

    Απάντηση

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. Κάρτα 44

    Ερώτηση

    How is electric potential energy related to charge and voltage?

    Απάντηση

    $\Delta U=q\Delta V$.

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

45. Κάρτα 45

    Ερώτηση

    How are standard cell potential and the equilibrium constant related?

    Απάντηση

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

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

46. Κάρτα 46

    Ερώτηση

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

    Απάντηση

    $W=mg$.

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

47. Κάρτα 47

    Ερώτηση

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

    Απάντηση

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

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

48. Κάρτα 48

    Ερώτηση

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

    Απάντηση

    $P=P_0+\rho gh$.

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

49. Κάρτα 49

    Ερώτηση

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

    Απάντηση

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

50. Κάρτα 50

    Ερώτηση

    Which relationship defines electric current?

    Απάντηση

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

    Conventional current points in the direction positive charge would move.

51. Κάρτα 51

    Ερώτηση

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

    Απάντηση

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

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

52. Κάρτα 52

    Ερώτηση

    What equation governs refraction at a boundary?

    Απάντηση

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

    Angles are measured from the normal, not the surface.

53. Κάρτα 53

    Ερώτηση

    How is mole fraction defined for component $i$?

    Απάντηση

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. Κάρτα 54

    Ερώτηση

    What SI units and base dimensions define pressure?

    Απάντηση

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

55. Κάρτα 55

    Ερώτηση

    What pressure–volume work occurs against constant external pressure?

    Απάντηση

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

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

56. Κάρτα 56

    Ερώτηση

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

    Απάντηση

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

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

57. Κάρτα 57

    Ερώτηση

    How large can static friction become before slipping begins?

    Απάντηση

    $f_s\leq\mu_sN$, 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. Κάρτα 58

    Ερώτηση

    Which relationship handles dilution when solute amount is conserved?

    Απάντηση

    $M_1V_1=M_2V_2$.

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

59. Κάρτα 59

    Ερώτηση

    What is Ohm's law for an ohmic element?

    Απάντηση

    $V=IR$.

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

60. Κάρτα 60

    Ερώτηση

    How is the reaction quotient $Q$ constructed?

    Απάντηση

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

61. Κάρτα 61

    Ερώτηση

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

    Απάντηση

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. Κάρτα 62

    Ερώτηση

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

    Απάντηση

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

63. Κάρτα 63

    Ερώτηση

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

    Απάντηση

    $F_1/A_1=F_2/A_2$.

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

64. Κάρτα 64

    Ερώτηση

    How much charge passes through a cell carrying constant current?

    Απάντηση

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. Κάρτα 65

    Ερώτηση

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

    Απάντηση

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

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

66. Κάρτα 66

    Ερώτηση

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

    Απάντηση

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

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

67. Κάρτα 67

    Ερώτηση

    How is the coulomb expressed through SI base units?

    Απάντηση

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

    Charge equals current multiplied by time.

68. Κάρτα 68

    Ερώτηση

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    Απάντηση

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

69. Κάρτα 69

    Ερώτηση

    How is sound intensity level in decibels defined?

    Απάντηση

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

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

70. Κάρτα 70

    Ερώτηση

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

    Απάντηση

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

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

71. Κάρτα 71

    Ερώτηση

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

    Απάντηση

    $R=\rho L/A$.

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

72. Κάρτα 72

    Ερώτηση

    Which equation gives the magnitude of torque from a force?

    Απάντηση

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

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

73. Κάρτα 73

    Ερώτηση

    How is mass percent composition calculated?

    Απάντηση

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

74. Κάρτα 74

    Ερώτηση

    What buoyant force acts on a submerged object?

    Απάντηση

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

    It equals the weight of displaced fluid.

75. Κάρτα 75

    Ερώτηση

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

    Απάντηση

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

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

76. Κάρτα 76

    Ερώτηση

    What two conditions define static mechanical equilibrium?

    Απάντηση

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

    Both translational and rotational equilibrium are required.

77. Κάρτα 77

    Ερώτηση

    How does Hess's law combine reaction enthalpies?

    Απάντηση

    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. Κάρτα 78

    Ερώτηση

    Which equivalent forms give electrical power in a resistor?

    Απάντηση

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

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

79. Κάρτα 79

    Ερώτηση

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

    Απάντηση

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

80. Κάρτα 80

    Ερώτηση

    What decibel change corresponds to multiplying sound intensity by 10?

    Απάντηση

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

81. Κάρτα 81

    Ερώτηση

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

    Απάντηση

    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. Κάρτα 82

    Ερώτηση

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

    Απάντηση

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

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

83. Κάρτα 83

    Ερώτηση

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

    Απάντηση

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

84. Κάρτα 84

    Ερώτηση

    How is the volt expressed through joules and coulombs?

    Απάντηση

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

    Voltage is energy transferred per unit charge.

85. Κάρτα 85

    Ερώτηση

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

    Απάντηση

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

86. Κάρτα 86

    Ερώτηση

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

    Απάντηση

    $W=Fd\cos\theta$.

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

87. Κάρτα 87

    Ερώτηση

    How is volume percent calculated for a liquid mixture?

    Απάντηση

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

    Use it only when the problem defines composition by volume.

88. Κάρτα 88

    Ερώτηση

    How do resistors combine in series?

    Απάντηση

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

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

89. Κάρτα 89

    Ερώτηση

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

    Απάντηση

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

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

90. Κάρτα 90

    Ερώτηση

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

    Απάντηση

    $Q=Av$.

    $Q$ 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. Κάρτα 91

    Ερώτηση

    How can average bond energies estimate reaction enthalpy?

    Απάντηση

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

    Breaking bonds costs energy; forming bonds releases it.

92. Κάρτα 92

    Ερώτηση

    What is the translational kinetic energy of a point mass?

    Απάντηση

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. Κάρτα 93

    Ερώτηση

    What ratio defines parts per million by mass?

    Απάντηση

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

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

94. Κάρτα 94

    Ερώτηση

    How do resistors combine in parallel?

    Απάντηση

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

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

95. Κάρτα 95

    Ερώτηση

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

    Απάντηση

    $K_aK_b=K_w$.

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

96. Κάρτα 96

    Ερώτηση

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

    Απάντηση

    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. Κάρτα 97

    Ερώτηση

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

    Απάντηση

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

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

98. Κάρτα 98

    Ερώτηση

    How is lateral magnification related to image and object distances?

    Απάντηση

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

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

99. Κάρτα 99

    Ερώτηση

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

    Απάντηση

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. Κάρτα 100

     Ερώτηση

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

     Απάντηση

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

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

101. Κάρτα 101

     Ερώτηση

     How does reversing a reaction change its equilibrium constant?

     Απάντηση

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

102. Κάρτα 102

     Ερώτηση

     What does the work–energy theorem say?

     Απάντηση

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

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

103. Κάρτα 103

     Ερώτηση

     What entropy change accompanies reversible heat transfer at constant temperature?

     Απάντηση

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

     Temperature must be in kelvin.

104. Κάρτα 104

     Ερώτηση

     What does Kirchhoff's junction rule require?

     Απάντηση

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

     It follows from conservation of charge at a node.

105. Κάρτα 105

     Ερώτηση

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

     Απάντηση

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

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

106. Κάρτα 106

     Ερώτηση

     What continuity relationship applies to steady incompressible flow?

     Απάντηση

     $A_1v_1=A_2v_2$.

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

107. Κάρτα 107

     Ερώτηση

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

     Απάντηση

     $m=\rho V$.

     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. Κάρτα 108

     Ερώτηση

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

     Απάντηση

     $U_g=mgh$.

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

109. Κάρτα 109

     Ερώτηση

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

     Απάντηση

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

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

110. Κάρτα 110

     Ερώτηση

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

     Απάντηση

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

     Both open ends are displacement antinodes.

111. Κάρτα 111

     Ερώτηση

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

     Απάντηση

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

     Use compatible energy units and absolute temperature.

112. Κάρτα 112

     Ερώτηση

     What does Kirchhoff's loop rule require?

     Απάντηση

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

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

113. Κάρτα 113

     Ερώτηση

     What elastic potential energy is stored in an ideal spring?

     Απάντηση

     $U_s=\tfrac12kx^2$.

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

114. Κάρτα 114

     Ερώτηση

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

     Απάντηση

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

     Dividing coefficients by $n$ takes the corresponding root.

115. Κάρτα 115

     Ερώτηση

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

     Απάντηση

     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. Κάρτα 116

     Ερώτηση

     How is lens power related to focal length?

     Απάντηση

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

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

117. Κάρτα 117

     Ερώτηση

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

     Απάντηση

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

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

118. Κάρτα 118

     Ερώτηση

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

     Απάντηση

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

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

119. Κάρτα 119

     Ερώτηση

     What is the Nernst equation for a cell reaction?

     Απάντηση

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

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

120. Κάρτα 120

     Ερώτηση

     What force does an ideal spring exert?

     Απάντηση

     $F_s=-kx$.

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

121. Κάρτα 121

     Ερώτηση

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

     Απάντηση

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. Κάρτα 122

     Ερώτηση

     Which relationship defines capacitance?

     Απάντηση

     $C=Q/V$.

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

123. Κάρτα 123

     Ερώτηση

     How do elemental mass percentages lead to an empirical formula?

     Απάντηση

     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. Κάρτα 124

     Ερώτηση

     When can mechanical energy be conserved?

     Απάντηση

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

125. Κάρτα 125

     Ερώτηση

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

     Απάντηση

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

126. Κάρτα 126

     Ερώτηση

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

     Απάντηση

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

127. Κάρτα 127

     Ερώτηση

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

     Απάντηση

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

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

128. Κάρτα 128

     Ερώτηση

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

     Απάντηση

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

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

129. Κάρτα 129

     Ερώτηση

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

     Απάντηση

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

     It is independent of initial concentration.

130. Κάρτα 130

     Ερώτηση

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

     Απάντηση

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. Κάρτα 131

     Ερώτηση

     How is a molecular formula obtained from an empirical formula?

     Απάντηση

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

132. Κάρτα 132

     Ερώτηση

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

     Απάντηση

     $C=\kappa\varepsilon_0A/d$.

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

133. Κάρτα 133

     Ερώτηση

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

     Απάντηση

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

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

134. Κάρτα 134

     Ερώτηση

     Which relationship gives laminar flow through a cylindrical tube?

     Απάντηση

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

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

135. Κάρτα 135

     Ερώτηση

     How do equilibrium constants combine when reactions are added?

     Απάντηση

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

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

136. Κάρτα 136

     Ερώτηση

     Which relationship defines average power?

     Απάντηση

     $P=W/\Delta t$.

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

137. Κάρτα 137

     Ερώτηση

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

     Απάντηση

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

138. Κάρτα 138

     Ερώτηση

     Which equivalent forms give energy stored in a capacitor?

     Απάντηση

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

     Use the form matching the known variables.

139. Κάρτα 139

     Ερώτηση

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

     Απάντηση

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

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

140. Κάρτα 140

     Ερώτηση

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

     Απάντηση

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

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

141. Κάρτα 141

     Ερώτηση

     How is percent yield calculated?

     Απάντηση

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

142. Κάρτα 142

     Ερώτηση

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

     Απάντηση

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

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

143. Κάρτα 143

     Ερώτηση

     What stoichiometric condition marks acid–base equivalence?

     Απάντηση

     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. Κάρτα 144

     Ερώτηση

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

     Απάντηση

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

145. Κάρτα 145

     Ερώτηση

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

     Απάντηση

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

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

146. Κάρτα 146

     Ερώτηση

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

     Απάντηση

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

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

147. Κάρτα 147

     Ερώτηση

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     Απάντηση

     $Re=\rho vD/\eta$.

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

148. Κάρτα 148

     Ερώτηση

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

     Απάντηση

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

     This predicts the favorable direction under nonstandard conditions.

149. Κάρτα 149

     Ερώτηση

     What is linear momentum?

     Απάντηση

     $\vec p=m\vec v$.

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

150. Κάρτα 150

     Ερώτηση

     How do you identify the limiting reactant from available moles?

     Απάντηση

     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. Κάρτα 151

     Ερώτηση

     How do capacitors combine in parallel?

     Απάντηση

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

     Parallel capacitors share voltage and their stored charges add.

152. Κάρτα 152

     Ερώτηση

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

     Απάντηση

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

153. Κάρτα 153

     Ερώτηση

     What relationship connects impulse and momentum change?

     Απάντηση

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

154. Κάρτα 154

     Ερώτηση

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

     Απάντηση

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

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

155. Κάρτα 155

     Ερώτηση

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

     Απάντηση

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

     The central maximum lies between the first minima.

156. Κάρτα 156

     Ερώτηση

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

     Απάντηση

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

157. Κάρτα 157

     Ερώτηση

     How do capacitors combine in series?

     Απάντηση

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

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

158. Κάρτα 158

     Ερώτηση

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

     Απάντηση

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

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

159. Κάρτα 159

     Ερώτηση

     What beat frequency is heard from two nearby tones?

     Απάντηση

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

     Beats arise from alternating constructive and destructive interference.

160. Κάρτα 160

     Ερώτηση

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

     Απάντηση

     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. Κάρτα 161

     Ερώτηση

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

     Απάντηση

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

162. Κάρτα 162

     Ερώτηση

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

     Απάντηση

     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. Κάρτα 163

     Ερώτηση

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

     Απάντηση

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

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

164. Κάρτα 164

     Ερώτηση

     When is total linear momentum conserved?

     Απάντηση

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

165. Κάρτα 165

     Ερώτηση

     What relationship connects absorbance and concentration in a dilute solution?

     Απάντηση

     $A=\varepsilon bc$.

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

166. Κάρτα 166

     Ερώτηση

     What magnetic force acts on a moving charge?

     Απάντηση

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

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

167. Κάρτα 167

     Ερώτηση

     How does the Arrhenius equation relate rate constant and temperature?

     Απάντηση

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

168. Κάρτα 168

     Ερώτηση

     What is centripetal acceleration for uniform circular motion?

     Απάντηση

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

     It points toward the center even when speed is constant.

169. Κάρτα 169

     Ερώτηση

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

     Απάντηση

     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. Κάρτα 170

     Ερώτηση

     What is the maximum kinetic energy in the photoelectric effect?

     Απάντηση

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

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

171. Κάρτα 171

     Ερώτηση

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

     Απάντηση

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

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

172. Κάρτα 172

     Ερώτηση

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

     Απάντηση

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

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

173. Κάρτα 173

     Ερώτηση

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

     Απάντηση

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

     This relation changes when a common ion is already present.

174. Κάρτα 174

     Ερώτηση

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

     Απάντηση

     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. Κάρτα 175

     Ερώτηση

     How is percent ionization of a weak acid calculated?

     Απάντηση

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

176. Κάρτα 176

     Ερώτηση

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

     Απάντηση

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

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

177. Κάρτα 177

     Ερώτηση

     What energy balance applies in an insulated calorimetry problem?

     Απάντηση

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

178. Κάρτα 178

     Ερώτηση

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

     Απάντηση

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

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

179. Κάρτα 179

     Ερώτηση

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

     Απάντηση

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

180. Κάρτα 180

     Ερώτηση

     What net inward force is required for circular motion?

     Απάντηση

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

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

180 κάρτες

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

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