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

Kadi za fungu hili

1. Kadi namba 1

   Swali

   Which relationship gives average velocity over a time interval?

   Jibu

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

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

2. Kadi namba 2

   Swali

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

   Jibu

   $n=m/M$.

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

3. Kadi namba 3

   Swali

   What is the electrostatic force between two point charges?

   Jibu

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

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

4. Kadi namba 4

   Swali

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

   Jibu

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. Kadi namba 5

   Swali

   How are period and frequency related?

   Jibu

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. Kadi namba 6

   Swali

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

   Jibu

   $q=mc\Delta T$.

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

7. Kadi namba 7

   Swali

   Which relationship defines mass density?

   Jibu

   $\rho=m/V$.

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

8. Kadi namba 8

   Swali

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

   Jibu

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. Kadi namba 9

   Swali

   How is photon energy related to frequency and wavelength?

   Jibu

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. Kadi namba 10

    Swali

    How is standard cell potential calculated from reduction potentials?

    Jibu

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

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

11. Kadi namba 11

    Swali

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

    Jibu

    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. Kadi namba 12

    Swali

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

    Jibu

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

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

13. Kadi namba 13

    Swali

    Which relationship gives average acceleration over a time interval?

    Jibu

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

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

14. Kadi namba 14

    Swali

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

    Jibu

    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. Kadi namba 15

    Swali

    What electric-field magnitude does a point charge produce?

    Jibu

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

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

16. Kadi namba 16

    Swali

    How do moles relate to the number of microscopic particles?

    Jibu

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

17. Kadi namba 17

    Swali

    For constant acceleration, how does velocity change with time?

    Jibu

    $v=v_0+at$.

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

18. Kadi namba 18

    Swali

    How is pOH defined?

    Jibu

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

19. Kadi namba 19

    Swali

    How is specific gravity defined?

    Jibu

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

    It is dimensionless because it is a density ratio.

20. Kadi namba 20

    Swali

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

    Jibu

    $q=C\Delta T$.

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

21. Kadi namba 21

    Swali

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

    Jibu

    $c=f\lambda$.

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

22. Kadi namba 22

    Swali

    Which species are omitted from a heterogeneous equilibrium expression?

    Jibu

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

23. Kadi namba 23

    Swali

    What force does an electric field exert on a charge?

    Jibu

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. Kadi namba 24

    Swali

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

    Jibu

    $PV=nRT$.

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

25. Kadi namba 25

    Swali

    Which equation relates wave speed, frequency, and wavelength?

    Jibu

    $v=f\lambda$.

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

26. Kadi namba 26

    Swali

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

    Jibu

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

    Its value changes with temperature.

27. Kadi namba 27

    Swali

    What base-unit dimensions define one newton?

    Jibu

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

    A force must have dimensions of mass times acceleration.

28. Kadi namba 28

    Swali

    How is cell potential related to reaction free energy?

    Jibu

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

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

29. Kadi namba 29

    Swali

    For constant acceleration, how does displacement depend on time?

    Jibu

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

    Choose a positive direction first, then keep signs consistent.

30. Kadi namba 30

    Swali

    How is molarity defined?

    Jibu

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

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

31. Kadi namba 31

    Swali

    What electric potential does a point charge produce?

    Jibu

    $V=k_e q/r$.

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

32. Kadi namba 32

    Swali

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

    Jibu

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

33. Kadi namba 33

    Swali

    Which constant-acceleration equation avoids time?

    Jibu

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

    It connects speed and displacement when time is absent.

34. Kadi namba 34

    Swali

    What is the general experimental rate-law form?

    Jibu

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

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

35. Kadi namba 35

    Swali

    Which relationship defines pressure from a normal force?

    Jibu

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. Kadi namba 36

    Swali

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

    Jibu

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

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

37. Kadi namba 37

    Swali

    How is wave intensity related to transmitted power and area?

    Jibu

    $I=P/A$.

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

38. Kadi namba 38

    Swali

    How is molality defined?

    Jibu

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

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

39. Kadi namba 39

    Swali

    What base-unit dimensions define one joule?

    Jibu

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

    Work, energy, and heat share this unit.

40. Kadi namba 40

    Swali

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

    Jibu

    $\Delta U=q+w$.

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

41. Kadi namba 41

    Swali

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

    Jibu

    $n=c/v$.

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

42. Kadi namba 42

    Swali

    What equation links net force and acceleration?

    Jibu

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

    The vector sum of external forces determines the acceleration.

43. Kadi namba 43

    Swali

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

    Jibu

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. Kadi namba 44

    Swali

    How is electric potential energy related to charge and voltage?

    Jibu

    $\Delta U=q\Delta V$.

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

45. Kadi namba 45

    Swali

    How are standard cell potential and the equilibrium constant related?

    Jibu

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

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

46. Kadi namba 46

    Swali

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

    Jibu

    $W=mg$.

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

47. Kadi namba 47

    Swali

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

    Jibu

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

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

48. Kadi namba 48

    Swali

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

    Jibu

    $P=P_0+\rho gh$.

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

49. Kadi namba 49

    Swali

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

    Jibu

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

50. Kadi namba 50

    Swali

    Which relationship defines electric current?

    Jibu

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

    Conventional current points in the direction positive charge would move.

51. Kadi namba 51

    Swali

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

    Jibu

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

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

52. Kadi namba 52

    Swali

    What equation governs refraction at a boundary?

    Jibu

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

    Angles are measured from the normal, not the surface.

53. Kadi namba 53

    Swali

    How is mole fraction defined for component $i$?

    Jibu

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. Kadi namba 54

    Swali

    What SI units and base dimensions define pressure?

    Jibu

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

55. Kadi namba 55

    Swali

    What pressure–volume work occurs against constant external pressure?

    Jibu

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

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

56. Kadi namba 56

    Swali

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

    Jibu

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

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

57. Kadi namba 57

    Swali

    How large can static friction become before slipping begins?

    Jibu

    $f_s\leq\mu_sN$, 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. Kadi namba 58

    Swali

    Which relationship handles dilution when solute amount is conserved?

    Jibu

    $M_1V_1=M_2V_2$.

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

59. Kadi namba 59

    Swali

    What is Ohm's law for an ohmic element?

    Jibu

    $V=IR$.

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

60. Kadi namba 60

    Swali

    How is the reaction quotient $Q$ constructed?

    Jibu

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

61. Kadi namba 61

    Swali

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

    Jibu

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. Kadi namba 62

    Swali

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

    Jibu

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

63. Kadi namba 63

    Swali

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

    Jibu

    $F_1/A_1=F_2/A_2$.

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

64. Kadi namba 64

    Swali

    How much charge passes through a cell carrying constant current?

    Jibu

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. Kadi namba 65

    Swali

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

    Jibu

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

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

66. Kadi namba 66

    Swali

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

    Jibu

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

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

67. Kadi namba 67

    Swali

    How is the coulomb expressed through SI base units?

    Jibu

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

    Charge equals current multiplied by time.

68. Kadi namba 68

    Swali

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    Jibu

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

69. Kadi namba 69

    Swali

    How is sound intensity level in decibels defined?

    Jibu

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

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

70. Kadi namba 70

    Swali

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

    Jibu

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

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

71. Kadi namba 71

    Swali

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

    Jibu

    $R=\rho L/A$.

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

72. Kadi namba 72

    Swali

    Which equation gives the magnitude of torque from a force?

    Jibu

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

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

73. Kadi namba 73

    Swali

    How is mass percent composition calculated?

    Jibu

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

74. Kadi namba 74

    Swali

    What buoyant force acts on a submerged object?

    Jibu

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

    It equals the weight of displaced fluid.

75. Kadi namba 75

    Swali

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

    Jibu

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

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

76. Kadi namba 76

    Swali

    What two conditions define static mechanical equilibrium?

    Jibu

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

    Both translational and rotational equilibrium are required.

77. Kadi namba 77

    Swali

    How does Hess's law combine reaction enthalpies?

    Jibu

    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. Kadi namba 78

    Swali

    Which equivalent forms give electrical power in a resistor?

    Jibu

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

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

79. Kadi namba 79

    Swali

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

    Jibu

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

80. Kadi namba 80

    Swali

    What decibel change corresponds to multiplying sound intensity by 10?

    Jibu

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

81. Kadi namba 81

    Swali

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

    Jibu

    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. Kadi namba 82

    Swali

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

    Jibu

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

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

83. Kadi namba 83

    Swali

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

    Jibu

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

84. Kadi namba 84

    Swali

    How is the volt expressed through joules and coulombs?

    Jibu

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

    Voltage is energy transferred per unit charge.

85. Kadi namba 85

    Swali

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

    Jibu

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

86. Kadi namba 86

    Swali

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

    Jibu

    $W=Fd\cos\theta$.

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

87. Kadi namba 87

    Swali

    How is volume percent calculated for a liquid mixture?

    Jibu

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

    Use it only when the problem defines composition by volume.

88. Kadi namba 88

    Swali

    How do resistors combine in series?

    Jibu

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

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

89. Kadi namba 89

    Swali

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

    Jibu

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

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

90. Kadi namba 90

    Swali

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

    Jibu

    $Q=Av$.

    $Q$ 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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    Nibomo itafunguka ili uanze kusoma.

91. Kadi namba 91

    Swali

    How can average bond energies estimate reaction enthalpy?

    Jibu

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

    Breaking bonds costs energy; forming bonds releases it.

92. Kadi namba 92

    Swali

    What is the translational kinetic energy of a point mass?

    Jibu

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. Kadi namba 93

    Swali

    What ratio defines parts per million by mass?

    Jibu

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

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

94. Kadi namba 94

    Swali

    How do resistors combine in parallel?

    Jibu

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

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

95. Kadi namba 95

    Swali

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

    Jibu

    $K_aK_b=K_w$.

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

96. Kadi namba 96

    Swali

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

    Jibu

    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. Kadi namba 97

    Swali

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

    Jibu

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

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

98. Kadi namba 98

    Swali

    How is lateral magnification related to image and object distances?

    Jibu

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

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

99. Kadi namba 99

    Swali

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

    Jibu

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. Kadi namba 100

     Swali

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

     Jibu

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

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

101. Kadi namba 101

     Swali

     How does reversing a reaction change its equilibrium constant?

     Jibu

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

102. Kadi namba 102

     Swali

     What does the work–energy theorem say?

     Jibu

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

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

103. Kadi namba 103

     Swali

     What entropy change accompanies reversible heat transfer at constant temperature?

     Jibu

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

     Temperature must be in kelvin.

104. Kadi namba 104

     Swali

     What does Kirchhoff's junction rule require?

     Jibu

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

     It follows from conservation of charge at a node.

105. Kadi namba 105

     Swali

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

     Jibu

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

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

106. Kadi namba 106

     Swali

     What continuity relationship applies to steady incompressible flow?

     Jibu

     $A_1v_1=A_2v_2$.

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

107. Kadi namba 107

     Swali

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

     Jibu

     $m=\rho V$.

     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. Kadi namba 108

     Swali

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

     Jibu

     $U_g=mgh$.

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

109. Kadi namba 109

     Swali

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

     Jibu

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

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

110. Kadi namba 110

     Swali

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

     Jibu

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

     Both open ends are displacement antinodes.

111. Kadi namba 111

     Swali

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

     Jibu

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

     Use compatible energy units and absolute temperature.

112. Kadi namba 112

     Swali

     What does Kirchhoff's loop rule require?

     Jibu

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

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

113. Kadi namba 113

     Swali

     What elastic potential energy is stored in an ideal spring?

     Jibu

     $U_s=\tfrac12kx^2$.

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

114. Kadi namba 114

     Swali

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

     Jibu

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

     Dividing coefficients by $n$ takes the corresponding root.

115. Kadi namba 115

     Swali

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

     Jibu

     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. Kadi namba 116

     Swali

     How is lens power related to focal length?

     Jibu

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

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

117. Kadi namba 117

     Swali

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

     Jibu

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

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

118. Kadi namba 118

     Swali

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

     Jibu

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

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

119. Kadi namba 119

     Swali

     What is the Nernst equation for a cell reaction?

     Jibu

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

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

120. Kadi namba 120

     Swali

     What force does an ideal spring exert?

     Jibu

     $F_s=-kx$.

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

121. Kadi namba 121

     Swali

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

     Jibu

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. Kadi namba 122

     Swali

     Which relationship defines capacitance?

     Jibu

     $C=Q/V$.

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

123. Kadi namba 123

     Swali

     How do elemental mass percentages lead to an empirical formula?

     Jibu

     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. Kadi namba 124

     Swali

     When can mechanical energy be conserved?

     Jibu

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

125. Kadi namba 125

     Swali

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

     Jibu

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

126. Kadi namba 126

     Swali

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

     Jibu

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

127. Kadi namba 127

     Swali

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

     Jibu

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

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

128. Kadi namba 128

     Swali

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

     Jibu

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

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

129. Kadi namba 129

     Swali

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

     Jibu

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

     It is independent of initial concentration.

130. Kadi namba 130

     Swali

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

     Jibu

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. Kadi namba 131

     Swali

     How is a molecular formula obtained from an empirical formula?

     Jibu

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

132. Kadi namba 132

     Swali

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

     Jibu

     $C=\kappa\varepsilon_0A/d$.

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

133. Kadi namba 133

     Swali

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

     Jibu

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

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

134. Kadi namba 134

     Swali

     Which relationship gives laminar flow through a cylindrical tube?

     Jibu

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

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

135. Kadi namba 135

     Swali

     How do equilibrium constants combine when reactions are added?

     Jibu

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

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

136. Kadi namba 136

     Swali

     Which relationship defines average power?

     Jibu

     $P=W/\Delta t$.

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

137. Kadi namba 137

     Swali

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

     Jibu

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

138. Kadi namba 138

     Swali

     Which equivalent forms give energy stored in a capacitor?

     Jibu

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

     Use the form matching the known variables.

139. Kadi namba 139

     Swali

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

     Jibu

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

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

140. Kadi namba 140

     Swali

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

     Jibu

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

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

141. Kadi namba 141

     Swali

     How is percent yield calculated?

     Jibu

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

142. Kadi namba 142

     Swali

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

     Jibu

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

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

143. Kadi namba 143

     Swali

     What stoichiometric condition marks acid–base equivalence?

     Jibu

     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. Kadi namba 144

     Swali

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

     Jibu

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

145. Kadi namba 145

     Swali

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

     Jibu

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

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

146. Kadi namba 146

     Swali

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

     Jibu

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

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

147. Kadi namba 147

     Swali

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     Jibu

     $Re=\rho vD/\eta$.

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

148. Kadi namba 148

     Swali

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

     Jibu

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

     This predicts the favorable direction under nonstandard conditions.

149. Kadi namba 149

     Swali

     What is linear momentum?

     Jibu

     $\vec p=m\vec v$.

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

150. Kadi namba 150

     Swali

     How do you identify the limiting reactant from available moles?

     Jibu

     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. Kadi namba 151

     Swali

     How do capacitors combine in parallel?

     Jibu

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

     Parallel capacitors share voltage and their stored charges add.

152. Kadi namba 152

     Swali

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

     Jibu

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

153. Kadi namba 153

     Swali

     What relationship connects impulse and momentum change?

     Jibu

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

154. Kadi namba 154

     Swali

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

     Jibu

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

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

155. Kadi namba 155

     Swali

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

     Jibu

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

     The central maximum lies between the first minima.

156. Kadi namba 156

     Swali

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

     Jibu

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

157. Kadi namba 157

     Swali

     How do capacitors combine in series?

     Jibu

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

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

158. Kadi namba 158

     Swali

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

     Jibu

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

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

159. Kadi namba 159

     Swali

     What beat frequency is heard from two nearby tones?

     Jibu

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

     Beats arise from alternating constructive and destructive interference.

160. Kadi namba 160

     Swali

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

     Jibu

     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. Kadi namba 161

     Swali

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

     Jibu

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

162. Kadi namba 162

     Swali

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

     Jibu

     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. Kadi namba 163

     Swali

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

     Jibu

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

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

164. Kadi namba 164

     Swali

     When is total linear momentum conserved?

     Jibu

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

165. Kadi namba 165

     Swali

     What relationship connects absorbance and concentration in a dilute solution?

     Jibu

     $A=\varepsilon bc$.

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

166. Kadi namba 166

     Swali

     What magnetic force acts on a moving charge?

     Jibu

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

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

167. Kadi namba 167

     Swali

     How does the Arrhenius equation relate rate constant and temperature?

     Jibu

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

168. Kadi namba 168

     Swali

     What is centripetal acceleration for uniform circular motion?

     Jibu

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

     It points toward the center even when speed is constant.

169. Kadi namba 169

     Swali

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

     Jibu

     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. Kadi namba 170

     Swali

     What is the maximum kinetic energy in the photoelectric effect?

     Jibu

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

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

171. Kadi namba 171

     Swali

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

     Jibu

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

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

172. Kadi namba 172

     Swali

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

     Jibu

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

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

173. Kadi namba 173

     Swali

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

     Jibu

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

     This relation changes when a common ion is already present.

174. Kadi namba 174

     Swali

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

     Jibu

     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. Kadi namba 175

     Swali

     How is percent ionization of a weak acid calculated?

     Jibu

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

176. Kadi namba 176

     Swali

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

     Jibu

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

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

177. Kadi namba 177

     Swali

     What energy balance applies in an insulated calorimetry problem?

     Jibu

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

178. Kadi namba 178

     Swali

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

     Jibu

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

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

179. Kadi namba 179

     Swali

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

     Jibu

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

180. Kadi namba 180

     Swali

     What net inward force is required for circular motion?

     Jibu

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

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

kadi 180

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

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