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

بطاقات هذه الرزمة

1. البطاقة ١

   السؤال

   Which relationship gives average velocity over a time interval?

   الإجابة

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

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

2. البطاقة ٢

   السؤال

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

   الإجابة

   $n=m/M$.

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

3. البطاقة ٣

   السؤال

   What is the electrostatic force between two point charges?

   الإجابة

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

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

4. البطاقة ٤

   السؤال

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

   الإجابة

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

   The bracket approximation uses molar concentration for sufficiently dilute solutions.

5. البطاقة ٥

   السؤال

   How are period and frequency related?

   الإجابة

   $f=1/T$.

   Frequency is in hertz and period is in seconds.

6. البطاقة ٦

   السؤال

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

   الإجابة

   $q=mc\Delta T$.

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

7. البطاقة ٧

   السؤال

   Which relationship defines mass density?

   الإجابة

   $\rho=m/V$.

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

8. البطاقة ٨

   السؤال

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

   الإجابة

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

   Use equilibrium concentrations and stoichiometric coefficients as exponents.

9. البطاقة ٩

   السؤال

   How is photon energy related to frequency and wavelength?

   الإجابة

   $E=hf=hc/\lambda$.

   Higher frequency and shorter wavelength mean greater photon energy.

10. البطاقة ١٠

    السؤال

    How is standard cell potential calculated from reduction potentials?

    الإجابة

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

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

11. البطاقة ١١

    السؤال

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

    الإجابة

    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. البطاقة ١٢

    السؤال

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

    الإجابة

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

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

13. البطاقة ١٣

    السؤال

    Which relationship gives average acceleration over a time interval?

    الإجابة

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

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

14. البطاقة ١٤

    السؤال

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

    الإجابة

    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. البطاقة ١٥

    السؤال

    What electric-field magnitude does a point charge produce?

    الإجابة

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

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

16. البطاقة ١٦

    السؤال

    How do moles relate to the number of microscopic particles?

    الإجابة

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

17. البطاقة ١٧

    السؤال

    For constant acceleration, how does velocity change with time?

    الإجابة

    $v=v_0+at$.

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

18. البطاقة ١٨

    السؤال

    How is pOH defined?

    الإجابة

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

19. البطاقة ١٩

    السؤال

    How is specific gravity defined?

    الإجابة

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

    It is dimensionless because it is a density ratio.

20. البطاقة ٢٠

    السؤال

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

    الإجابة

    $q=C\Delta T$.

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

21. البطاقة ٢١

    السؤال

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

    الإجابة

    $c=f\lambda$.

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

22. البطاقة ٢٢

    السؤال

    Which species are omitted from a heterogeneous equilibrium expression?

    الإجابة

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

23. البطاقة ٢٣

    السؤال

    What force does an electric field exert on a charge?

    الإجابة

    $\vec F=q\vec E$.

    A negative charge feels force opposite the field direction.

24. البطاقة ٢٤

    السؤال

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

    الإجابة

    $PV=nRT$.

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

25. البطاقة ٢٥

    السؤال

    Which equation relates wave speed, frequency, and wavelength?

    الإجابة

    $v=f\lambda$.

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

26. البطاقة ٢٦

    السؤال

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

    الإجابة

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

    Its value changes with temperature.

27. البطاقة ٢٧

    السؤال

    What base-unit dimensions define one newton?

    الإجابة

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

    A force must have dimensions of mass times acceleration.

28. البطاقة ٢٨

    السؤال

    How is cell potential related to reaction free energy?

    الإجابة

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

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

29. البطاقة ٢٩

    السؤال

    For constant acceleration, how does displacement depend on time?

    الإجابة

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

    Choose a positive direction first, then keep signs consistent.

30. البطاقة ٣٠

    السؤال

    How is molarity defined?

    الإجابة

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

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

31. البطاقة ٣١

    السؤال

    What electric potential does a point charge produce?

    الإجابة

    $V=k_e q/r$.

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

32. البطاقة ٣٢

    السؤال

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

    الإجابة

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

33. البطاقة ٣٣

    السؤال

    Which constant-acceleration equation avoids time?

    الإجابة

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

    It connects speed and displacement when time is absent.

34. البطاقة ٣٤

    السؤال

    What is the general experimental rate-law form?

    الإجابة

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

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

35. البطاقة ٣٥

    السؤال

    Which relationship defines pressure from a normal force?

    الإجابة

    $P=F_\perp/A$.

    Pressure is scalar and measured in pascals.

36. البطاقة ٣٦

    السؤال

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

    الإجابة

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

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

37. البطاقة ٣٧

    السؤال

    How is wave intensity related to transmitted power and area?

    الإجابة

    $I=P/A$.

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

38. البطاقة ٣٨

    السؤال

    How is molality defined?

    الإجابة

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

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

39. البطاقة ٣٩

    السؤال

    What base-unit dimensions define one joule?

    الإجابة

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

    Work, energy, and heat share this unit.

40. البطاقة ٤٠

    السؤال

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

    الإجابة

    $\Delta U=q+w$.

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

41. البطاقة ٤١

    السؤال

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

    الإجابة

    $n=c/v$.

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

42. البطاقة ٤٢

    السؤال

    What equation links net force and acceleration?

    الإجابة

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

    The vector sum of external forces determines the acceleration.

43. البطاقة ٤٣

    السؤال

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

    الإجابة

    $P_1V_1/T_1=P_2V_2/T_2$.

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

44. البطاقة ٤٤

    السؤال

    How is electric potential energy related to charge and voltage?

    الإجابة

    $\Delta U=q\Delta V$.

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

45. البطاقة ٤٥

    السؤال

    How are standard cell potential and the equilibrium constant related?

    الإجابة

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

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

46. البطاقة ٤٦

    السؤال

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

    الإجابة

    $W=mg$.

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

47. البطاقة ٤٧

    السؤال

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

    الإجابة

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

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

48. البطاقة ٤٨

    السؤال

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

    الإجابة

    $P=P_0+\rho gh$.

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

49. البطاقة ٤٩

    السؤال

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

    الإجابة

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

50. البطاقة ٥٠

    السؤال

    Which relationship defines electric current?

    الإجابة

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

    Conventional current points in the direction positive charge would move.

51. البطاقة ٥١

    السؤال

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

    الإجابة

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

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

52. البطاقة ٥٢

    السؤال

    What equation governs refraction at a boundary?

    الإجابة

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

    Angles are measured from the normal, not the surface.

53. البطاقة ٥٣

    السؤال

    How is mole fraction defined for component $i$?

    الإجابة

    $X_i=n_i/\sum_jn_j$.

    Mole fractions are dimensionless and sum to 1.

54. البطاقة ٥٤

    السؤال

    What SI units and base dimensions define pressure?

    الإجابة

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

55. البطاقة ٥٥

    السؤال

    What pressure–volume work occurs against constant external pressure?

    الإجابة

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

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

56. البطاقة ٥٦

    السؤال

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

    الإجابة

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

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

57. البطاقة ٥٧

    السؤال

    How large can static friction become before slipping begins?

    الإجابة

    $f_s\leq\mu_sN$, 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. البطاقة ٥٨

    السؤال

    Which relationship handles dilution when solute amount is conserved?

    الإجابة

    $M_1V_1=M_2V_2$.

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

59. البطاقة ٥٩

    السؤال

    What is Ohm's law for an ohmic element?

    الإجابة

    $V=IR$.

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

60. البطاقة ٦٠

    السؤال

    How is the reaction quotient $Q$ constructed?

    الإجابة

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

61. البطاقة ٦١

    السؤال

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

    الإجابة

    $f_k=\mu_kN$.

    The force points opposite the relative sliding motion.

62. البطاقة ٦٢

    السؤال

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

    الإجابة

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

63. البطاقة ٦٣

    السؤال

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

    الإجابة

    $F_1/A_1=F_2/A_2$.

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

64. البطاقة ٦٤

    السؤال

    How much charge passes through a cell carrying constant current?

    الإجابة

    $Q=It$.

    Use amperes and seconds to obtain coulombs.

65. البطاقة ٦٥

    السؤال

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

    الإجابة

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

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

66. البطاقة ٦٦

    السؤال

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

    الإجابة

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

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

67. البطاقة ٦٧

    السؤال

    How is the coulomb expressed through SI base units?

    الإجابة

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

    Charge equals current multiplied by time.

68. البطاقة ٦٨

    السؤال

    How is standard reaction enthalpy obtained from standard formation enthalpies?

    الإجابة

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

69. البطاقة ٦٩

    السؤال

    How is sound intensity level in decibels defined?

    الإجابة

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

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

70. البطاقة ٧٠

    السؤال

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

    الإجابة

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

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

71. البطاقة ٧١

    السؤال

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

    الإجابة

    $R=\rho L/A$.

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

72. البطاقة ٧٢

    السؤال

    Which equation gives the magnitude of torque from a force?

    الإجابة

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

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

73. البطاقة ٧٣

    السؤال

    How is mass percent composition calculated?

    الإجابة

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

74. البطاقة ٧٤

    السؤال

    What buoyant force acts on a submerged object?

    الإجابة

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

    It equals the weight of displaced fluid.

75. البطاقة ٧٥

    السؤال

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

    الإجابة

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

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

76. البطاقة ٧٦

    السؤال

    What two conditions define static mechanical equilibrium?

    الإجابة

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

    Both translational and rotational equilibrium are required.

77. البطاقة ٧٧

    السؤال

    How does Hess's law combine reaction enthalpies?

    الإجابة

    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. البطاقة ٧٨

    السؤال

    Which equivalent forms give electrical power in a resistor?

    الإجابة

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

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

79. البطاقة ٧٩

    السؤال

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

    الإجابة

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

80. البطاقة ٨٠

    السؤال

    What decibel change corresponds to multiplying sound intensity by 10?

    الإجابة

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

81. البطاقة ٨١

    السؤال

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

    الإجابة

    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. البطاقة ٨٢

    السؤال

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

    الإجابة

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

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

83. البطاقة ٨٣

    السؤال

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

    الإجابة

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

84. البطاقة ٨٤

    السؤال

    How is the volt expressed through joules and coulombs?

    الإجابة

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

    Voltage is energy transferred per unit charge.

85. البطاقة ٨٥

    السؤال

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

    الإجابة

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

86. البطاقة ٨٦

    السؤال

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

    الإجابة

    $W=Fd\cos\theta$.

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

87. البطاقة ٨٧

    السؤال

    How is volume percent calculated for a liquid mixture?

    الإجابة

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

    Use it only when the problem defines composition by volume.

88. البطاقة ٨٨

    السؤال

    How do resistors combine in series?

    الإجابة

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

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

89. البطاقة ٨٩

    السؤال

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

    الإجابة

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

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

90. البطاقة ٩٠

    السؤال

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

    الإجابة

    $Q=Av$.

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

    

    ١٨٠ بطاقة

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91. البطاقة ٩١

    السؤال

    How can average bond energies estimate reaction enthalpy?

    الإجابة

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

    Breaking bonds costs energy; forming bonds releases it.

92. البطاقة ٩٢

    السؤال

    What is the translational kinetic energy of a point mass?

    الإجابة

    $K=\tfrac12mv^2$.

    Kinetic energy is a scalar measured in joules.

93. البطاقة ٩٣

    السؤال

    What ratio defines parts per million by mass?

    الإجابة

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

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

94. البطاقة ٩٤

    السؤال

    How do resistors combine in parallel?

    الإجابة

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

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

95. البطاقة ٩٥

    السؤال

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

    الإجابة

    $K_aK_b=K_w$.

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

96. البطاقة ٩٦

    السؤال

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

    الإجابة

    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. البطاقة ٩٧

    السؤال

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

    الإجابة

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

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

98. البطاقة ٩٨

    السؤال

    How is lateral magnification related to image and object distances?

    الإجابة

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

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

99. البطاقة ٩٩

    السؤال

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

    الإجابة

    $\overline{K}=\tfrac32RT$.

    It depends only on absolute temperature, not molecular identity.

100. البطاقة ١٠٠

     السؤال

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

     الإجابة

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

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

101. البطاقة ١٠١

     السؤال

     How does reversing a reaction change its equilibrium constant?

     الإجابة

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

102. البطاقة ١٠٢

     السؤال

     What does the work–energy theorem say?

     الإجابة

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

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

103. البطاقة ١٠٣

     السؤال

     What entropy change accompanies reversible heat transfer at constant temperature?

     الإجابة

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

     Temperature must be in kelvin.

104. البطاقة ١٠٤

     السؤال

     What does Kirchhoff's junction rule require?

     الإجابة

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

     It follows from conservation of charge at a node.

105. البطاقة ١٠٥

     السؤال

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

     الإجابة

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

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

106. البطاقة ١٠٦

     السؤال

     What continuity relationship applies to steady incompressible flow?

     الإجابة

     $A_1v_1=A_2v_2$.

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

107. البطاقة ١٠٧

     السؤال

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

     الإجابة

     $m=\rho V$.

     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. البطاقة ١٠٨

     السؤال

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

     الإجابة

     $U_g=mgh$.

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

109. البطاقة ١٠٩

     السؤال

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

     الإجابة

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

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

110. البطاقة ١١٠

     السؤال

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

     الإجابة

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

     Both open ends are displacement antinodes.

111. البطاقة ١١١

     السؤال

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

     الإجابة

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

     Use compatible energy units and absolute temperature.

112. البطاقة ١١٢

     السؤال

     What does Kirchhoff's loop rule require?

     الإجابة

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

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

113. البطاقة ١١٣

     السؤال

     What elastic potential energy is stored in an ideal spring?

     الإجابة

     $U_s=\tfrac12kx^2$.

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

114. البطاقة ١١٤

     السؤال

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

     الإجابة

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

     Dividing coefficients by $n$ takes the corresponding root.

115. البطاقة ١١٥

     السؤال

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

     الإجابة

     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. البطاقة ١١٦

     السؤال

     How is lens power related to focal length?

     الإجابة

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

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

117. البطاقة ١١٧

     السؤال

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

     الإجابة

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

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

118. البطاقة ١١٨

     السؤال

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

     الإجابة

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

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

119. البطاقة ١١٩

     السؤال

     What is the Nernst equation for a cell reaction?

     الإجابة

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

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

120. البطاقة ١٢٠

     السؤال

     What force does an ideal spring exert?

     الإجابة

     $F_s=-kx$.

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

121. البطاقة ١٢١

     السؤال

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

     الإجابة

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

     This is Henderson–Hasselbalch solved for the composition ratio.

122. البطاقة ١٢٢

     السؤال

     Which relationship defines capacitance?

     الإجابة

     $C=Q/V$.

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

123. البطاقة ١٢٣

     السؤال

     How do elemental mass percentages lead to an empirical formula?

     الإجابة

     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. البطاقة ١٢٤

     السؤال

     When can mechanical energy be conserved?

     الإجابة

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

125. البطاقة ١٢٥

     السؤال

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

     الإجابة

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

126. البطاقة ١٢٦

     السؤال

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

     الإجابة

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

127. البطاقة ١٢٧

     السؤال

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

     الإجابة

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

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

128. البطاقة ١٢٨

     السؤال

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

     الإجابة

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

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

129. البطاقة ١٢٩

     السؤال

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

     الإجابة

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

     It is independent of initial concentration.

130. البطاقة ١٣٠

     السؤال

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

     الإجابة

     $f=R/2$.

     This paraxial approximation applies to rays near the principal axis.

131. البطاقة ١٣١

     السؤال

     How is a molecular formula obtained from an empirical formula?

     الإجابة

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

132. البطاقة ١٣٢

     السؤال

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

     الإجابة

     $C=\kappa\varepsilon_0A/d$.

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

133. البطاقة ١٣٣

     السؤال

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

     الإجابة

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

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

134. البطاقة ١٣٤

     السؤال

     Which relationship gives laminar flow through a cylindrical tube?

     الإجابة

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

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

135. البطاقة ١٣٥

     السؤال

     How do equilibrium constants combine when reactions are added?

     الإجابة

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

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

136. البطاقة ١٣٦

     السؤال

     Which relationship defines average power?

     الإجابة

     $P=W/\Delta t$.

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

137. البطاقة ١٣٧

     السؤال

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

     الإجابة

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

138. البطاقة ١٣٨

     السؤال

     Which equivalent forms give energy stored in a capacitor?

     الإجابة

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

     Use the form matching the known variables.

139. البطاقة ١٣٩

     السؤال

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

     الإجابة

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

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

140. البطاقة ١٤٠

     السؤال

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

     الإجابة

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

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

141. البطاقة ١٤١

     السؤال

     How is percent yield calculated?

     الإجابة

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

142. البطاقة ١٤٢

     السؤال

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

     الإجابة

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

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

143. البطاقة ١٤٣

     السؤال

     What stoichiometric condition marks acid–base equivalence?

     الإجابة

     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. البطاقة ١٤٤

     السؤال

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

     الإجابة

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

145. البطاقة ١٤٥

     السؤال

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

     الإجابة

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

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

146. البطاقة ١٤٦

     السؤال

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

     الإجابة

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

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

147. البطاقة ١٤٧

     السؤال

     What dimensionless quantity helps predict laminar versus turbulent pipe flow?

     الإجابة

     $Re=\rho vD/\eta$.

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

148. البطاقة ١٤٨

     السؤال

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

     الإجابة

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

     This predicts the favorable direction under nonstandard conditions.

149. البطاقة ١٤٩

     السؤال

     What is linear momentum?

     الإجابة

     $\vec p=m\vec v$.

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

150. البطاقة ١٥٠

     السؤال

     How do you identify the limiting reactant from available moles?

     الإجابة

     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. البطاقة ١٥١

     السؤال

     How do capacitors combine in parallel?

     الإجابة

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

     Parallel capacitors share voltage and their stored charges add.

152. البطاقة ١٥٢

     السؤال

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

     الإجابة

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

153. البطاقة ١٥٣

     السؤال

     What relationship connects impulse and momentum change?

     الإجابة

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

154. البطاقة ١٥٤

     السؤال

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

     الإجابة

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

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

155. البطاقة ١٥٥

     السؤال

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

     الإجابة

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

     The central maximum lies between the first minima.

156. البطاقة ١٥٦

     السؤال

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

     الإجابة

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

157. البطاقة ١٥٧

     السؤال

     How do capacitors combine in series?

     الإجابة

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

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

158. البطاقة ١٥٨

     السؤال

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

     الإجابة

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

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

159. البطاقة ١٥٩

     السؤال

     What beat frequency is heard from two nearby tones?

     الإجابة

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

     Beats arise from alternating constructive and destructive interference.

160. البطاقة ١٦٠

     السؤال

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

     الإجابة

     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. البطاقة ١٦١

     السؤال

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

     الإجابة

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

162. البطاقة ١٦٢

     السؤال

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

     الإجابة

     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. البطاقة ١٦٣

     السؤال

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

     الإجابة

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

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

164. البطاقة ١٦٤

     السؤال

     When is total linear momentum conserved?

     الإجابة

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

165. البطاقة ١٦٥

     السؤال

     What relationship connects absorbance and concentration in a dilute solution?

     الإجابة

     $A=\varepsilon bc$.

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

166. البطاقة ١٦٦

     السؤال

     What magnetic force acts on a moving charge?

     الإجابة

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

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

167. البطاقة ١٦٧

     السؤال

     How does the Arrhenius equation relate rate constant and temperature?

     الإجابة

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

168. البطاقة ١٦٨

     السؤال

     What is centripetal acceleration for uniform circular motion?

     الإجابة

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

     It points toward the center even when speed is constant.

169. البطاقة ١٦٩

     السؤال

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

     الإجابة

     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. البطاقة ١٧٠

     السؤال

     What is the maximum kinetic energy in the photoelectric effect?

     الإجابة

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

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

171. البطاقة ١٧١

     السؤال

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

     الإجابة

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

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

172. البطاقة ١٧٢

     السؤال

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

     الإجابة

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

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

173. البطاقة ١٧٣

     السؤال

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

     الإجابة

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

     This relation changes when a common ion is already present.

174. البطاقة ١٧٤

     السؤال

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

     الإجابة

     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. البطاقة ١٧٥

     السؤال

     How is percent ionization of a weak acid calculated?

     الإجابة

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

176. البطاقة ١٧٦

     السؤال

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

     الإجابة

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

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

177. البطاقة ١٧٧

     السؤال

     What energy balance applies in an insulated calorimetry problem?

     الإجابة

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

178. البطاقة ١٧٨

     السؤال

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

     الإجابة

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

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

179. البطاقة ١٧٩

     السؤال

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

     الإجابة

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

180. البطاقة ١٨٠

     السؤال

     What net inward force is required for circular motion?

     الإجابة

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

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

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

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