New answers tagged physical-chemistry
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Anatase and rutile phases form in $\ce{TiO2},$ the presence of cationic dopants or impurities significantly affect the transformation kinetics and phase stability [1].
It should be noted that anatase is metastable at all temperatures and pressures.
References
Hanaor, D. A. H.; Sorrell, C. C. Review of the Anatase to Rutile Phase Transformation. J Mater Sci ...
1
I will try to add another point to the discussion which is statistics. Quantum mechanics is a non deterministic theory which can only make assumptions about expectation values and probabilities of obtaining a special value. In general your wave functions or vectors correspond to states while the projection of one wave function onto another (aka the scalar ...
1
The temperature at which NOx is in equilibrium with its liquid and vapor phase at 1 atm is about –84 °C. Does that mean NOx exists as a liquid at that temperature? What about it's vapor phase then, because it's vapor and liquid phase should be at equilibrium, right?
Yes, the vapor and liquid can coexist, provided P and T are on the coexistence (!) line (as ...
2
The more volatile compound forms greater vapour portion, compared to its portion in the distilled liquid.
It forms e.g. 15% molar fraction of vapour, if there is 10% molar fraction in liquid.
In case of deviation from the Raoult law, when there is interaction between compounds, an azeotrope with minimal ( ethanol-water ) or maximal ( nitric acid water ) ...
0
Your book must have wrong solution
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Let me start by saying that this is a very difficult question to answer because it's not very hard to come up with pathological cases which I will address at the end. Also, as you point out, it is somewhat non-trivial to calculate $r_0$ from theory and also somewhat non-trivial to determine $r_e$ from experiment. That being said, I think I have a good first ...
2
After some thought, it is probably worthwhile to actually write an answer rather than a short, fairly useless comment.
Lets look at the Cu-Ni phase diagram, as calculated using the CALPHAD parameters given in the paper referenced in many of the pictures below (X.J. Liu et al., J. Electronic Materials 37(2) 210-217 (2008)).
Overall:
This looks a lot like ...
1
I like and dislike the question. I assume this is from your Indian university entrance exams. The good part is that it is tricky, the sad part is that the concept of equivalents is so outdated that any North American student will barely recognize it. They should abolish teaching equivalents exactly because this problem you are encountering.
Fact number no. ...
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There will be many molecules collide with the walls and the molecules will hit another molecules after its collision with wall (right?), thus the pressure of the system should be low. How often the collision of what kind happens under what condition?
The collision condition doesn't need to be strictly in Boyle's law condition, that the elastic collision is ...
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Many of the articles from internet states that triplet state is of lower energy.In which case majority of molecules assume singlet state.Why is this so
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As an example if the reaction is $\ce{A + B -> C}$ the rate expression for the appearance of $\ce{C}$ is
$$\frac{\mathrm d[\ce{C}]}{\mathrm dt} = +k[\ce{A}][\ce{B}].$$
The units have to be the same on both sides of this equation, these are concentration/time on the left and to be the same on the right the rate constant $k$ has to have units $(1/\text{...
1
Since the change in internal energy for the cycle is zero, if you are using the form of the 1st law written as $\Delta U=Q+W$ (where work done on the system is regarded as positive), the heat for the entire cycle must equal minus the work for the entire cycle. The work done on the system in AB must be -(1)(1.5-1)=-0.5 L-atm. Therefore, the work done on the ...
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The document the OP references has most of the information: The overall measured dipole moment, the way bond dipoles add up to the molecule dipole, and how to calculate the bond dipole. Also, it states that a proton and an electron at a distance of 100 pm have a dipole moment of 4.80 D. From that information, we should be able to figure everything out.
Bond ...
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Is there a difference in interpretation of dipole moment in Physics and Chemistry?
Addressing the above part: The definition of dipole moment is the same in physics and chemistry. However, the chemist's dipole moment has opposite directions as compared to the physicist. Which one is right? Of course, the physicists draw it correctly, which is consistent ...
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There are excellent answers already, but I wanted to address the following question
[...] how would we mathematically define a normal coordinate for the oxygen(s) and hydrogen during a normal mode vibration of water molecule?
The first step is to switch from cartesian coordinates to internal coordinates. For water, it would be the two bond lengths $L_1$ ...
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Will these changes result in the molar mass of a substance no longer being exactly equal to the molecular mass expressed in grams?
Yes. The ratio between the molar mass and the relative molecular mass is called the molar mass constant, and it used to be 1 g/mol exactly. Now that Avogadro's constant is set to a fixed value, it's value has to be determined ...
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Since I was reviewing this in some detail recently, I will try to supplement Prof. Hutchison's already good answer with some more detail as to why one would choose to work with normal coordinates, rather than the already quite simple Cartesian coordinates.
The short answer is that, under the assumption of small displacements, normal coordinates decouple the ...
2
Radio waves $10^4$ to $10^{11}$ Hz are not that innocent as is commonly purported. Long time ago there was an demonstration that radio waves of certain frequency can decompose salt water into hydrogen and oxygen (and ignite). There was an article in Popular Mechanics. No other type of radiation can cause this effect. See the video of burning here Burning ...
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Infinite dilution is a hypothetical construct. Only homeopathy believes in a practical infinite dilution but for the rest of scientific world, infinite dilution means that the concentration has been mathematically extrapolated to zero.
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The phrase "infinite dilution" is to introduce the idea that the only intermolecular interactions the solute experiences are from the solvent while dissolved in it.
This is understood to be a solution at "infinite" dilution — or a solution where the interaction between solvent and solute physically and energetically does not change upon further dilution.
...
3
This is a bit of a stretch, but the Zeeman and Stark effects are linked to radio frequencies, in that line splitting of a visible spectral frequency (~10^15 Hz) can give rise to a beat-frequency in the RF. Your answer of NMR, though, is more applicable. The most general term for precession in a magnetic field is Larmor precession.
1
Radio waves have a longer wavelength than infrared radiation and is classified between 3Hz and 300MHz frequencies. Due to its lower energy/longer wavelength, radio waves are able to penetrate deeper than higher energy radiation. For example, the skin depth is a function of frequency:
$$\delta = \sqrt{\frac{2 \rho}{\omega \mu}}$$
where $\rho$ is the ...
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If we consider N atoms in a non-linear molecule, then each atom can move independently on the X, Y, and Z axes. That's $3D \times N = 3N$ degrees of freedom.
But if I move the whole molecule 3 Å along the x-axis, that doesn't constitute a vibration - it's just a translation. So we have to remove 3 degrees of freedom for translations.
Similarly, if I ...
2
Chlorophyll (chl) is involved in two ways in photosynthetic organisms firstly as a light gathering pigment and second in electron transfer once the light is captured. It is unique in this role.
In the first case, that of gathering light there are pigment protein complexes containing many chl (100's) and work in such a way that energy absorbed in one ...
2
To answer the side question about German language terminology, I'll pick up terms from @porphyrin's answer.
But first of all, term = Term (same as in maths)
The word 'state' tends to be used colloquially to mean any of Term, Level or State.
All those colloquial states are Zustände (pl., sg. Zustand) in German or you can use Term, Niveau (level) and ...
1
If you calculate the equilibrium vapor pressure at 298K (25 C), you can calculate the change in Gibbs free energy of the vapor in going from this pressure to the hypothetical state of 1 bar and 298K using $dG=VdP=RTd\ln P$. Neglecting the Poynting correction, the free energy of the liquid at 298 and at the equilibrium vapor pressure is 0. And this is also ...
0
Standard Gibbs energy at normal boiling point
At the normal boiling point, all species are at standard state (pure liquid, gas at normal pressure). The system is at equilibrium, so the Gibbs energy of the process is zero. Because all species are at standard state, the standard Gibbs energy is zero as well.
Standard Gibbs energy at room temperature
The OP ...
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Based on the comments and extended chat, this is the kind of question the OP actually wanted to ask: Consider a mixture of Fe and FeO. The total percentage (by weight) of iron is 86.638%. What is the percentage of iron metal in the mixture?
Answer: For simplicity, assume exactly 100 g of the mixture. Hence the total iron is 86.638g and the remaining 13.362g ...
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The figure below shows the situation between configuration for a $p^2$ configuration, terms, levels and states. The word 'state' tends to be used colloquially to mean any of Term, Level or State.
The Configuration such as $(1s)^2$ or ...$(2p)^2$ etc. tell us which orbitals are occupied.
These are split with electrostatic (Coulomb) coupling to form Terms.
...
10
According to Skoog, Analytical Chemistry:
Using classical mechanics, assuming a diatomic molecule, the frequency of vibration $\nu$ may be described by
$$\nu = \frac{1}{2\pi} \sqrt{\frac{k}{\mu}} $$
where $k$ represents the force constant of this bond, and $\mu$ the reduced mass of the particles bond together, defined as
$$\mu = \frac{m_1 \cdot m_2} {...
28
A property of the harmonic oscillator is that the oscillation frequency, $\omega$, is dependent not only on $k$ (the spring constant) but also on the mass $m$ of the object:
$$\omega = \sqrt{\frac{k}{m}}$$
We can crudely model a chemical bond as a two-body harmonic oscillator, which largely obeys the same rule, except that the mass must be replaced with ...
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This image is from Atomic Spectra and Atomic Structure by Gerhard Herzberg, John William Tranter Spinks - 1944. It does not really have boxes (just boxes of a table), but spin +1/2 and spin -1/2 are shown as arrows. Of course, I am not claiming this is the first usage, just that in 1944 it existed.
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A neutral atom is an atom with an equal number of protons and electrons [...] The "neutral" in a neutral atom means electrically neutral.
Neutral in this case means net neutral. It does not mean that the opposite charges "destroy" each other. After all, the electrons are still attracted to the nucleus even though the overall system is net neutral.
We ...
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The mathematics of quantum mechanics predicts an unevenness of the observation, similar to wave equations in that there are points where high values of electron density/reaction and low (~zero) values occur. If you have places (~50% of the places) where "interference" has yielded zero electron density/reaction, then the other 50% of the places will have ...
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The electronegativity of atoms/elements is indeed an indication of the relative attractiveness of that atom/element for an electron.
But it seems to me that the question asks what force or energy is involved. In general, atoms and molecules are neutral. It takes energy to produce a free electron and hang it in space. If it detects a positive charge, it will ...
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The term mole is a short form of the German word Molekül which was coined by Ostwald in 1890s. At that time, the "atomic mass unit" did not exist. The common term at that time was gram atomic mass or gram-molecule. The original meaning of so-called was defined to be equal one gram molecule i.e, the mass of a molecule expressed in grams. Atomic mass unit came ...
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The answer lies in electronegativity. When a proton attracts an electron, the electron doesn't magically suck out the charge of the proton. The proton's charge is still distributed in all directions. The reason why 1 proton on average can attract only 1 electron is because electrons push each other out.
Now let's first take H - it has 1 proton which ...
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An atom is only neutral when viewed as a single object from large enough distance. But as an electron comes closer to the atom, it "notices" the electron cloud first. This cloud also "notices" the electron and deforms—the atom polarizes—so as to keep the atomic electrons farther on average from the extra electron, since like charges repel. But this ...
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Your analysis is correct, except that you don't account for how the the units cancel out in your calculation.
The initial reaction quotient, $Q_P$, is indeed 3, as you have calculated. And since $K_P$ is 1, the reaction will shift to the left, increasing $P_A$. Hence Statement-1 is nearly correct. I say "nearly" because $K_P$ is dimensionless, so it ...
1
Using Mathematica, I obtained $T=546 K$, as follows. One of the nice things about using Mathematica for physical calculations is that it has the ability to understand/keep track of/cancel out/convert units.
The volume is non-physically small -- about 750,000 x smaller than what we'd expect for a mole of, say, ideal gas at $P=100 Pa, T = 546 K$). One does ...
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