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

کارت‌های این دسته

1. کارت ۱

   پرسش

   Which relationship gives average velocity over a time interval?

   پاسخ

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

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

2. کارت ۲

   پرسش

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

   پاسخ

   $n=m/M$.

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

3. کارت ۳

   پرسش

   What is the electrostatic force between two point charges?

   پاسخ

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

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

4. کارت ۴

   پرسش

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

   پاسخ

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. کارت ۵

   پرسش

   How are period and frequency related?

   پاسخ

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. کارت ۶

   پرسش

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

   پاسخ

   $q=mc\Delta T$.

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

7. کارت ۷

   پرسش

   Which relationship defines mass density?

   پاسخ

   $\rho=m/V$.

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

8. کارت ۸

   پرسش

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

   پاسخ

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. کارت ۹

   پرسش

   How is photon energy related to frequency and wavelength?

   پاسخ

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. کارت ۱۰

    پرسش

    How is standard cell potential calculated from reduction potentials?

    پاسخ

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

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

11. کارت ۱۱

    پرسش

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

    پاسخ

    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. کارت ۱۲

    پرسش

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

    پاسخ

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

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

13. کارت ۱۳

    پرسش

    Which relationship gives average acceleration over a time interval?

    پاسخ

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

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

14. کارت ۱۴

    پرسش

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

    پاسخ

    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. کارت ۱۵

    پرسش

    What electric-field magnitude does a point charge produce?

    پاسخ

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

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

16. کارت ۱۶

    پرسش

    How do moles relate to the number of microscopic particles?

    پاسخ

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

17. کارت ۱۷

    پرسش

    For constant acceleration, how does velocity change with time?

    پاسخ

    $v=v_0+at$.

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

18. کارت ۱۸

    پرسش

    How is pOH defined?

    پاسخ

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

19. کارت ۱۹

    پرسش

    How is specific gravity defined?

    پاسخ

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

    It is dimensionless because it is a density ratio.

20. کارت ۲۰

    پرسش

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

    پاسخ

    $q=C\Delta T$.

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

21. کارت ۲۱

    پرسش

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

    پاسخ

    $c=f\lambda$.

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

22. کارت ۲۲

    پرسش

    Which species are omitted from a heterogeneous equilibrium expression?

    پاسخ

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

23. کارت ۲۳

    پرسش

    What force does an electric field exert on a charge?

    پاسخ

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. کارت ۲۴

    پرسش

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

    پاسخ

    $PV=nRT$.

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

25. کارت ۲۵

    پرسش

    Which equation relates wave speed, frequency, and wavelength?

    پاسخ

    $v=f\lambda$.

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

26. کارت ۲۶

    پرسش

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

    پاسخ

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

    Its value changes with temperature.

27. کارت ۲۷

    پرسش

    What base-unit dimensions define one newton?

    پاسخ

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

    A force must have dimensions of mass times acceleration.

28. کارت ۲۸

    پرسش

    How is cell potential related to reaction free energy?

    پاسخ

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

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

29. کارت ۲۹

    پرسش

    For constant acceleration, how does displacement depend on time?

    پاسخ

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

    Choose a positive direction first, then keep signs consistent.

30. کارت ۳۰

    پرسش

    How is molarity defined?

    پاسخ

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

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

31. کارت ۳۱

    پرسش

    What electric potential does a point charge produce?

    پاسخ

    $V=k_e q/r$.

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

32. کارت ۳۲

    پرسش

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

    پاسخ

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

33. کارت ۳۳

    پرسش

    Which constant-acceleration equation avoids time?

    پاسخ

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

    It connects speed and displacement when time is absent.

34. کارت ۳۴

    پرسش

    What is the general experimental rate-law form?

    پاسخ

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

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

35. کارت ۳۵

    پرسش

    Which relationship defines pressure from a normal force?

    پاسخ

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. کارت ۳۶

    پرسش

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

    پاسخ

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

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

37. کارت ۳۷

    پرسش

    How is wave intensity related to transmitted power and area?

    پاسخ

    $I=P/A$.

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

38. کارت ۳۸

    پرسش

    How is molality defined?

    پاسخ

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

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

39. کارت ۳۹

    پرسش

    What base-unit dimensions define one joule?

    پاسخ

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

    Work, energy, and heat share this unit.

40. کارت ۴۰

    پرسش

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

    پاسخ

    $\Delta U=q+w$.

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

41. کارت ۴۱

    پرسش

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

    پاسخ

    $n=c/v$.

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

42. کارت ۴۲

    پرسش

    What equation links net force and acceleration?

    پاسخ

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

    The vector sum of external forces determines the acceleration.

43. کارت ۴۳

    پرسش

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

    پاسخ

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. کارت ۴۴

    پرسش

    How is electric potential energy related to charge and voltage?

    پاسخ

    $\Delta U=q\Delta V$.

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

45. کارت ۴۵

    پرسش

    How are standard cell potential and the equilibrium constant related?

    پاسخ

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

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

46. کارت ۴۶

    پرسش

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

    پاسخ

    $W=mg$.

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

47. کارت ۴۷

    پرسش

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

    پاسخ

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

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

48. کارت ۴۸

    پرسش

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

    پاسخ

    $P=P_0+\rho gh$.

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

49. کارت ۴۹

    پرسش

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

    پاسخ

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

50. کارت ۵۰

    پرسش

    Which relationship defines electric current?

    پاسخ

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

    Conventional current points in the direction positive charge would move.

51. کارت ۵۱

    پرسش

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

    پاسخ

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

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

52. کارت ۵۲

    پرسش

    What equation governs refraction at a boundary?

    پاسخ

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

    Angles are measured from the normal, not the surface.

53. کارت ۵۳

    پرسش

    How is mole fraction defined for component $i$?

    پاسخ

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. کارت ۵۴

    پرسش

    What SI units and base dimensions define pressure?

    پاسخ

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

55. کارت ۵۵

    پرسش

    What pressure–volume work occurs against constant external pressure?

    پاسخ

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

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

56. کارت ۵۶

    پرسش

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

    پاسخ

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

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

57. کارت ۵۷

    پرسش

    How large can static friction become before slipping begins?

    پاسخ

    $f_s\leq\mu_sN$, 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. کارت ۵۸

    پرسش

    Which relationship handles dilution when solute amount is conserved?

    پاسخ

    $M_1V_1=M_2V_2$.

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

59. کارت ۵۹

    پرسش

    What is Ohm's law for an ohmic element?

    پاسخ

    $V=IR$.

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

60. کارت ۶۰

    پرسش

    How is the reaction quotient $Q$ constructed?

    پاسخ

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

61. کارت ۶۱

    پرسش

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

    پاسخ

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. کارت ۶۲

    پرسش

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

    پاسخ

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

63. کارت ۶۳

    پرسش

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

    پاسخ

    $F_1/A_1=F_2/A_2$.

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

64. کارت ۶۴

    پرسش

    How much charge passes through a cell carrying constant current?

    پاسخ

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. کارت ۶۵

    پرسش

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

    پاسخ

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

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

66. کارت ۶۶

    پرسش

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

    پاسخ

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

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

67. کارت ۶۷

    پرسش

    How is the coulomb expressed through SI base units?

    پاسخ

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

    Charge equals current multiplied by time.

68. کارت ۶۸

    پرسش

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    پاسخ

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

69. کارت ۶۹

    پرسش

    How is sound intensity level in decibels defined?

    پاسخ

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

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

70. کارت ۷۰

    پرسش

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

    پاسخ

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

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

71. کارت ۷۱

    پرسش

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

    پاسخ

    $R=\rho L/A$.

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

72. کارت ۷۲

    پرسش

    Which equation gives the magnitude of torque from a force?

    پاسخ

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

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

73. کارت ۷۳

    پرسش

    How is mass percent composition calculated?

    پاسخ

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

74. کارت ۷۴

    پرسش

    What buoyant force acts on a submerged object?

    پاسخ

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

    It equals the weight of displaced fluid.

75. کارت ۷۵

    پرسش

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

    پاسخ

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

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

76. کارت ۷۶

    پرسش

    What two conditions define static mechanical equilibrium?

    پاسخ

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

    Both translational and rotational equilibrium are required.

77. کارت ۷۷

    پرسش

    How does Hess's law combine reaction enthalpies?

    پاسخ

    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. کارت ۷۸

    پرسش

    Which equivalent forms give electrical power in a resistor?

    پاسخ

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

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

79. کارت ۷۹

    پرسش

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

    پاسخ

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

80. کارت ۸۰

    پرسش

    What decibel change corresponds to multiplying sound intensity by 10?

    پاسخ

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

81. کارت ۸۱

    پرسش

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

    پاسخ

    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. کارت ۸۲

    پرسش

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

    پاسخ

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

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

83. کارت ۸۳

    پرسش

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

    پاسخ

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

84. کارت ۸۴

    پرسش

    How is the volt expressed through joules and coulombs?

    پاسخ

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

    Voltage is energy transferred per unit charge.

85. کارت ۸۵

    پرسش

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

    پاسخ

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

86. کارت ۸۶

    پرسش

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

    پاسخ

    $W=Fd\cos\theta$.

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

87. کارت ۸۷

    پرسش

    How is volume percent calculated for a liquid mixture?

    پاسخ

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

    Use it only when the problem defines composition by volume.

88. کارت ۸۸

    پرسش

    How do resistors combine in series?

    پاسخ

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

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

89. کارت ۸۹

    پرسش

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

    پاسخ

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

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

90. کارت ۹۰

    پرسش

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

    پاسخ

    $Q=Av$.

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

    

    ۱۸۰ کارت

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

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91. کارت ۹۱

    پرسش

    How can average bond energies estimate reaction enthalpy?

    پاسخ

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

    Breaking bonds costs energy; forming bonds releases it.

92. کارت ۹۲

    پرسش

    What is the translational kinetic energy of a point mass?

    پاسخ

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. کارت ۹۳

    پرسش

    What ratio defines parts per million by mass?

    پاسخ

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

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

94. کارت ۹۴

    پرسش

    How do resistors combine in parallel?

    پاسخ

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

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

95. کارت ۹۵

    پرسش

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

    پاسخ

    $K_aK_b=K_w$.

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

96. کارت ۹۶

    پرسش

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

    پاسخ

    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. کارت ۹۷

    پرسش

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

    پاسخ

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

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

98. کارت ۹۸

    پرسش

    How is lateral magnification related to image and object distances?

    پاسخ

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

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

99. کارت ۹۹

    پرسش

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

    پاسخ

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. کارت ۱۰۰

     پرسش

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

     پاسخ

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

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

101. کارت ۱۰۱

     پرسش

     How does reversing a reaction change its equilibrium constant?

     پاسخ

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

102. کارت ۱۰۲

     پرسش

     What does the work–energy theorem say?

     پاسخ

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

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

103. کارت ۱۰۳

     پرسش

     What entropy change accompanies reversible heat transfer at constant temperature?

     پاسخ

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

     Temperature must be in kelvin.

104. کارت ۱۰۴

     پرسش

     What does Kirchhoff's junction rule require?

     پاسخ

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

     It follows from conservation of charge at a node.

105. کارت ۱۰۵

     پرسش

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

     پاسخ

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

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

106. کارت ۱۰۶

     پرسش

     What continuity relationship applies to steady incompressible flow?

     پاسخ

     $A_1v_1=A_2v_2$.

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

107. کارت ۱۰۷

     پرسش

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

     پاسخ

     $m=\rho V$.

     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. کارت ۱۰۸

     پرسش

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

     پاسخ

     $U_g=mgh$.

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

109. کارت ۱۰۹

     پرسش

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

     پاسخ

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

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

110. کارت ۱۱۰

     پرسش

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

     پاسخ

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

     Both open ends are displacement antinodes.

111. کارت ۱۱۱

     پرسش

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

     پاسخ

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

     Use compatible energy units and absolute temperature.

112. کارت ۱۱۲

     پرسش

     What does Kirchhoff's loop rule require?

     پاسخ

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

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

113. کارت ۱۱۳

     پرسش

     What elastic potential energy is stored in an ideal spring?

     پاسخ

     $U_s=\tfrac12kx^2$.

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

114. کارت ۱۱۴

     پرسش

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

     پاسخ

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

     Dividing coefficients by $n$ takes the corresponding root.

115. کارت ۱۱۵

     پرسش

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

     پاسخ

     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. کارت ۱۱۶

     پرسش

     How is lens power related to focal length?

     پاسخ

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

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

117. کارت ۱۱۷

     پرسش

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

     پاسخ

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

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

118. کارت ۱۱۸

     پرسش

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

     پاسخ

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

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

119. کارت ۱۱۹

     پرسش

     What is the Nernst equation for a cell reaction?

     پاسخ

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

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

120. کارت ۱۲۰

     پرسش

     What force does an ideal spring exert?

     پاسخ

     $F_s=-kx$.

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

121. کارت ۱۲۱

     پرسش

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

     پاسخ

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. کارت ۱۲۲

     پرسش

     Which relationship defines capacitance?

     پاسخ

     $C=Q/V$.

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

123. کارت ۱۲۳

     پرسش

     How do elemental mass percentages lead to an empirical formula?

     پاسخ

     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. کارت ۱۲۴

     پرسش

     When can mechanical energy be conserved?

     پاسخ

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

125. کارت ۱۲۵

     پرسش

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

     پاسخ

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

126. کارت ۱۲۶

     پرسش

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

     پاسخ

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

127. کارت ۱۲۷

     پرسش

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

     پاسخ

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

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

128. کارت ۱۲۸

     پرسش

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

     پاسخ

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

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

129. کارت ۱۲۹

     پرسش

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

     پاسخ

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

     It is independent of initial concentration.

130. کارت ۱۳۰

     پرسش

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

     پاسخ

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. کارت ۱۳۱

     پرسش

     How is a molecular formula obtained from an empirical formula?

     پاسخ

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

132. کارت ۱۳۲

     پرسش

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

     پاسخ

     $C=\kappa\varepsilon_0A/d$.

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

133. کارت ۱۳۳

     پرسش

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

     پاسخ

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

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

134. کارت ۱۳۴

     پرسش

     Which relationship gives laminar flow through a cylindrical tube?

     پاسخ

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

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

135. کارت ۱۳۵

     پرسش

     How do equilibrium constants combine when reactions are added?

     پاسخ

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

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

136. کارت ۱۳۶

     پرسش

     Which relationship defines average power?

     پاسخ

     $P=W/\Delta t$.

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

137. کارت ۱۳۷

     پرسش

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

     پاسخ

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

138. کارت ۱۳۸

     پرسش

     Which equivalent forms give energy stored in a capacitor?

     پاسخ

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

     Use the form matching the known variables.

139. کارت ۱۳۹

     پرسش

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

     پاسخ

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

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

140. کارت ۱۴۰

     پرسش

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

     پاسخ

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

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

141. کارت ۱۴۱

     پرسش

     How is percent yield calculated?

     پاسخ

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

142. کارت ۱۴۲

     پرسش

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

     پاسخ

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

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

143. کارت ۱۴۳

     پرسش

     What stoichiometric condition marks acid–base equivalence?

     پاسخ

     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. کارت ۱۴۴

     پرسش

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

     پاسخ

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

145. کارت ۱۴۵

     پرسش

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

     پاسخ

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

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

146. کارت ۱۴۶

     پرسش

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

     پاسخ

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

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

147. کارت ۱۴۷

     پرسش

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     پاسخ

     $Re=\rho vD/\eta$.

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

148. کارت ۱۴۸

     پرسش

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

     پاسخ

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

     This predicts the favorable direction under nonstandard conditions.

149. کارت ۱۴۹

     پرسش

     What is linear momentum?

     پاسخ

     $\vec p=m\vec v$.

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

150. کارت ۱۵۰

     پرسش

     How do you identify the limiting reactant from available moles?

     پاسخ

     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. کارت ۱۵۱

     پرسش

     How do capacitors combine in parallel?

     پاسخ

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

     Parallel capacitors share voltage and their stored charges add.

152. کارت ۱۵۲

     پرسش

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

     پاسخ

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

153. کارت ۱۵۳

     پرسش

     What relationship connects impulse and momentum change?

     پاسخ

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

154. کارت ۱۵۴

     پرسش

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

     پاسخ

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

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

155. کارت ۱۵۵

     پرسش

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

     پاسخ

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

     The central maximum lies between the first minima.

156. کارت ۱۵۶

     پرسش

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

     پاسخ

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

157. کارت ۱۵۷

     پرسش

     How do capacitors combine in series?

     پاسخ

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

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

158. کارت ۱۵۸

     پرسش

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

     پاسخ

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

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

159. کارت ۱۵۹

     پرسش

     What beat frequency is heard from two nearby tones?

     پاسخ

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

     Beats arise from alternating constructive and destructive interference.

160. کارت ۱۶۰

     پرسش

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

     پاسخ

     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. کارت ۱۶۱

     پرسش

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

     پاسخ

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

162. کارت ۱۶۲

     پرسش

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

     پاسخ

     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. کارت ۱۶۳

     پرسش

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

     پاسخ

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

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

164. کارت ۱۶۴

     پرسش

     When is total linear momentum conserved?

     پاسخ

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

165. کارت ۱۶۵

     پرسش

     What relationship connects absorbance and concentration in a dilute solution?

     پاسخ

     $A=\varepsilon bc$.

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

166. کارت ۱۶۶

     پرسش

     What magnetic force acts on a moving charge?

     پاسخ

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

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

167. کارت ۱۶۷

     پرسش

     How does the Arrhenius equation relate rate constant and temperature?

     پاسخ

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

168. کارت ۱۶۸

     پرسش

     What is centripetal acceleration for uniform circular motion?

     پاسخ

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

     It points toward the center even when speed is constant.

169. کارت ۱۶۹

     پرسش

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

     پاسخ

     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. کارت ۱۷۰

     پرسش

     What is the maximum kinetic energy in the photoelectric effect?

     پاسخ

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

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

171. کارت ۱۷۱

     پرسش

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

     پاسخ

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

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

172. کارت ۱۷۲

     پرسش

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

     پاسخ

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

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

173. کارت ۱۷۳

     پرسش

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

     پاسخ

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

     This relation changes when a common ion is already present.

174. کارت ۱۷۴

     پرسش

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

     پاسخ

     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. کارت ۱۷۵

     پرسش

     How is percent ionization of a weak acid calculated?

     پاسخ

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

176. کارت ۱۷۶

     پرسش

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

     پاسخ

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

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

177. کارت ۱۷۷

     پرسش

     What energy balance applies in an insulated calorimetry problem?

     پاسخ

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

178. کارت ۱۷۸

     پرسش

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

     پاسخ

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

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

179. کارت ۱۷۹

     پرسش

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

     پاسخ

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

180. کارت ۱۸۰

     پرسش

     What net inward force is required for circular motion?

     پاسخ

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

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

۱۸۰ کارت

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

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