Questions asked by Truong-Son N.

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• How to do this equilibrium derivation? (I'll post an answer showing the problem)
  
• What makes the classical dipole moment for water different than its experimental result? I used #r = 0.958# angstroms, #A_(HOH) = 104.4776^o#, and #q_(OH) = -0.52672 a.u.#, where #a.u. = # electron-charge. My result was #1.484 D#, compared to #1.85 D#.
  
• Any chance second-semester/year Organic Chemistry topic categories can be added? e.g. Grignard Reactions, Benzene Sub/Elim Rxns, Robinson Annulation, etc.?
  
• What is the overall charge of the Pro-Met-Phe-Ser-Glu-Leu polypeptide at pH #7.2#? I've drawn it, and I think it's #-1#, but I'm not 100% sure.
  
• When using Greater Than symbol to indent, the content that goes after it cannot be commented on or marked helpful/confusing?
  
• Is there a way to write #rightleftharpoons# with something above and below, while still keeping #rightleftharpoons# on the same line as the rest of the text? This would be useful for equilibrium reactions and kinetics.
  
• Writing [content]|_(a)^(b) gives a Math Processing Error?
  
• What is a dilation, or scaling around a point?
  
• What are all the relevant extensive and intensive thermodynamic quantities?
  
• Browser compatibility --- Can't answer questions when using Internet Explorer?
  
• How many isomers of [insert straight-chained alkane here] exist?
  
• What happened to the "Unanswered questions" button, the ability to sort questions according to "Conceptual" vs. "Practice", etc. on the Subject pages?
  
• Ordered lists can't be commented on or rated?
  
• When is the aspartate mechanism used for transferring oxaloacetate from the mitochondrion to the cytosol?
  
• Is there a systematic way to determine the number of numbers between 10 and, say, 50, divisible by their units digits?
  
• What are the roles of each member of the SHD catalytic triad? How does the mechanism work?
  
• How do you find the #LU# factorization for #tildeA = [(1,0),(-3,1)]# such that #tildeL# is unit diagonal?
  
• How do you use symmetry-adapted linear combinations to explain water's molecular bonding?
  
• How do you efficiently show that for the vector space #V# where #f(x)# is continuous on #[0,15]# and #W# where #f(x)# is differentiable on #[0,15]#, #W# is a subspace in #V#, i.e. #W sube V#?
  
• Suppose there was a basis for and a certain number of dimensions for subspace #W# in #RR^4#. Why is the number of dimensions #2#?
  
• What is the difference between the trans influence and trans effect on square-planar transition metal complex substitution/interchange reactions? So is the trans influence defined under the trans effect or alongside, or both?
  
• What's the visual and mathematical difference between a vector projection of #a# onto #b# and an orthogonal projection of #a# onto #b#? Are they just different ways to say the same thing?
  
• What is an Abelian group, from a linear/abstract algebra perspective?
  
• Have we ever used #""^56 "Co"# for any interesting industrial purpose(s)? Cite any sources you may find on this.
  
• Find the matrix #A# for the linear transformation #T# relative to the bases #B = {1,x,x^2}# and #B' = {1,x,x^2,x^3}# such that #T(vecx) = Avecx#?
  
• What is going on with the alkyl migration step in the Schmidt reaction mechanism on a ketone?
  
• Prove quantitatively that for infinitesimally small #Deltax#, #(Deltax)/x ~~ Delta(lnx)#?
  
• How do I calculate the new pressure of liquid water using its isothermal compressibility #kappa# and expansion coefficient #alpha#?
  
• Without using Wolfram Alpha, evaluate #log_10(y) = -138.265#? The answer is not #0#.
  
• How do you find the infinite sum of a p series? EX: #1/n^2#
  
• How do you write position and momentum in terms of the raising and lowering operators?
  
• Prove that for an ideal-gas reaction, #(dlnK_C^@)/(dT) = (DeltaU^@)/(RT^2)#?
  
• A certain gas mixture is held at #395^@ "C"# has the following initial partial pressures: #P_(Cl_2) = 351.4#, #P_(CO) = 342.0#, #P_(COCl_2) = 0#, all in #"torr"#. Find #K_P^@#?
  
• Using #psi_0 = ((2c)/(pi))^("1/4")e^(-cx^2)# as the normalized ground-state wave function, find #c#, and the trial energy #E_phi# such that #E_phi = (<< phi_0 | hatH | phi_0 >>)/(<< phi_0 | phi_0 >>) >= E_0#, where #E_0# is the exact ground-state energy?
  
• Despite the large difference in electronegativity between #"Si"# and #"F"#, #"SiF"_4# has a boiling point lower than that of #"NH"_3# (#-86^@ "C"#, vs. #-33^@ "C"#). Why is that? Could it be due to the symmetry? Hydrogen-bonding?
  
• Use the Debye-Huckel equation to evaluate #gamma_(pm)# for a #"0.0200 mol/kg"# #"HCl"# solution, with methanol as the solvent, at #25^@ "C"# and #"1 atm"#?
  
• How would I determine all the possible term symbols for an #s^1p^2# electron configuration (such as first-excited-state boron)?
  
• Will there ever be a feature to export PDFs of scratchpads (including all the cool MathJax going on)?
  
• What is #int 9/(x^2sqrt(4x+1))dx#?
  
• Is there a systematic way to determine an integrating factor #mu(x,y)# of the form #x^n y^m#, given a not-necessarily-exact differential equation?
  
• For the nonhomogeneous equation, using the method of undetermined coefficients, the solution I got for #(d^2y)/(dx^2) - 5(dy)/(dx) + 6y = xe^x# is #y = (xe^x)/2 + (3e^x)/4#, but along the way I got two solutions for #A_1#?
  
• How would I convert kinetic energy for one particle in six dimensions (x, y, z, and their time derivatives) from Cartesian to spherical coordinates? Note: #dotq = (delq)/(delt)#, and this is from a 1962 Statistical Mechanics textbook by Norman Davidson.
  
• For the unit vector #hattheta#, geometrically show that #hattheta = -sinthetahati + costhetahatj#? Essentially, converting from cartesian to polar, how would I determine the unit vector for #vectheta# in terms of #theta#, #hati#, and #hatj#?
  
• If I had #N# fermions, how could I determine the number of ways I can place these into #g# distinguishable containers? For example, how could I determine how many ways I could place #54# electrons into #54# #p# orbitals?
  
• Suppose you have #"500.0 mL"# of #"0.200 M"# acetic acid (#K_a = 1.8 xx 10^(-5)#). To make a #"pH"# #4.50# buffer, how many #"mL"# of #"3.0 M"# #"NaOH"# must be added?
  
• What trigonometric identity was used to get from #sin((kpix)/L)[A_kcos((kpict)/L) + B_ksin((kpict)/L)]# to #E_ksin((kpix)/L)cos[(kpic)/L(t-t_k)]#? What is the relationship between the pair of constants #E_k# and #t_k#, and the pair #A_k# and #B_k#?
  
• How do I verify the percent composition of #"MgSO"_4cdotx"H"_2"O"# in this Epsom Salt package and solve for #x#?
  
• Given the distribution of #N# particles in #n# systems, #t = prod_N prod_i (n!)/(n_(N_i)!)#, and the following constraints, derive the grand canonical partition function and the distribution law for the grand ensemble?
  
• Is there an error in this question: Show that #((del^2Q)/(delbeta^2))_V = bar(E^2) - barE^2# (the variance of the energy)? #beta# is only a function of temperature #T#, not a function of volume #V#. #E# is a function of only #V#.
  
• How could I compare a SYSTEM of linear second-order partial differential equations with two different functions within them to the heat equation? Please also provide a reference that I can cite in my paper.
  
• Given internal coordinates of a molecule (say, #"CCl"_3"Br"#), its relevant bond length(s), and bond angle(s), how do you calculate the moments of inertia in each direction? #r_(C-Br) = "1.91 Å"#, #r_(C-Cl) = "1.77 Å"#, #/_ClCBr = 109.4bar(66)^@#
  
• #y(x,t) = Ce^(iomegax//c)e^(-iomegat) = Ce^(ialpha)#, where #alpha = (2pix)/lambda - 2pi nut#... Show that for standing waves, #y(x,t) = Asin((npix)/L)sin(2pin nu_0 t + delta)#? You may want to note the boundary conditions of a vibrating guitar string.
  
• Could someone elaborate on orthogonal polynomials?
  
• How do I truncate this infinite series by choosing an odd #l#?
  
• How do I calculate the Fourier Transform of #a/(2pi) 1/(a^2 + x^2)#?
  
• How do you show that #lim_(r->oo) e^(ircostheta - rsintheta) = 0#?
  
• How do I use this proved result for the Dirac Delta function to evaluate the following integral involving a Dirac Delta function of a function?
  
• Why does a Gaussian wave packet take on the minimum value of the Heisenberg Uncertainty Principle?
  
• Conceptually, why does a Fourier transform connect the wave function in a position representation to its representation in the momentum representation?
  
• How do you use spherical Bessel functions of the first and second kind to solve the following ordinary differential equation?
  
• What could the #""^(n)"Pr"# mean in #""^(n)"PrNH"_2#?
  
• How do you generalize #Delta(PV)# from #d(PV)#?
  
• Calculate for the first-excited state #psi_1(x)# of the simple harmonic oscillator the value of the Heisenberg Uncertainty relation?
  
• How can we prove that #|m_l| <= l#, i.e. that the magnetic quantum number can be no bigger than #l#, and no more negative than #-l#?
  
• How do we know that the atomic orbital angular momentum magnitude is #sqrt(l(l+1))ℏ#, where #ℏ = h//2pi#?
  
• Why is there a discrepancy in the force constants of #"HBr"# vs. #"HCl"#?
  
• A #"100.00-mL"# solution containing #"0.500 M"# #"NH"_3# and #"0.500 M"# #"NH"_4^+# (#"pK"_a = 9.26#) had #"NaOH"# added to it, and increased to a #"pH"# of #10.26#. If #"20.45 mL"# of #"NaOH"# was added, what was its molarity at the time of addition?
  
• What is the internal energy for an isothermal process?
  
• What is the van't Hoff factor for a binary ionic compound #"MX"# for which ion pairing has led to a percent dissociation of #50%#?