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%`?