exchemist

Erm the numerator should be the product of the concentrations of the dissociated ions: [ A ]x[ B ]/[AB] = Kd And I think the questioner is asking about the situation in which [A]=/= [ B ] , e.g. an acetic acid/acetate buffer, or something like that. I suppose what the statement in question is driving at is that is if [ B ] << Kd, then the ratio [A]/[AB] will have to be >> Kd, so that when multiplied by [ B ] it gives Kd. But since, for weak acids and bases, K <<1 , it is not necessary for [A] >> [AB] to achieve that. .......I think...... For example, with acetic acid, Kd = 1.8 x 10⁻⁵ = [H+] x [acetate]/[acetic acid]. So if, for the sake of argument, [H+] is also 1.8 x 10⁻⁵, then the [acetate]/acetic acid] ratio would be 1/1. So I too am a bit baffled by the statement our questioner is querying.

Though the findings of that one, non peer reviewed, preprint seem to be contradicted by the link provided in @swansont 's post. As I say, it seems to be a fine balance of very low risks rather than a choice that is obvious. And then the parents might also to consider the increase in risk to themselves from an unvaccinated child bringing the virus home from school.

The decision as to whether or not to vaccinate secondary school age children seems to be quite finely balanced, if one considers only the risk to each individual child. What may tilt the balance in favour of vaccinating them is the reduction it produces in the level of infection circulating in the population as a whole. UK experience is that levels of infection have shot up since the school term started. Throughout this epidemic it has been remarkably hard to get certain segments of US society to recognise that the virus countermeasures are not applied just for the good of the individual, but also for the good of other people who they would otherwise infect. Given that vaccination cannot prevent infection completely, suppressing it by vaccinating this age group as well seems to be a sensible strategy.

From the article it appears the trains have been returned to service, without being repaired first, subject to careful monitoring to see if the cracks develop further, which they have not. So it does not look as if there is judged to be a risk of accidents due to these cracks. (The "yaw dampers" will, I presume, be the dampers that prevent the bogies from hunting at high speed.)

Why can't you do an internet search and contact the numerous companies listed which do this?

As an addendum, when I was on holiday in Tiree last week, staying with a rather back-to-nature niece, she washed some clothes using "soap nuts", a sort of brown nuggets that she put in the machine in a little bag along with the washing. I had never heard of these. It turns out these contain saponin, a triterpene glycoside which, having an oleophilic and a hydrophilic end, is a natural surfactant and has been used for centuries in the Indian subcontinent. Soap nuts come from the soapberry plant, Sapindus. The clothes seemed to be clean and odour-free after washing, though obviously as the soap nuts remained in contact with the clothes until then end, there was not much effective rinsing off of the saponin. (Possibly the lower temperature at the end of the rinse cycle will have reduced the amount leaching from the nuts.) Be that as it may, I have not developed any rashes or skin irritation, so it seems to work fine.

I’d agree that there is entropy in black body radiation, but I’d take some persuading that a solar cell is a heat engine. If it’s not a heat engine then I don’t think Carnot efficiency applies. For instance we don’t apply Carnot efficiency to the electricity production from an electrochemical cell, do we? But you pose an interesting question. I found this about analysing the entropy in solar radiation, which seems to address what you have in mind: https://www.nature.com/articles/s41598-017-01622-6 This does not seem to make any reference to Carnot efficiency, I notice.

Electrons flow in response to a voltage gradient. They do not produce energy when they flow, but transmit it from whatever is responsible for the voltage gradient. So there is no violation of conservation of energy.

I don’t think the issue of *beating* Carnot efficiency arises, because this system is not a heat engine, I.e. it does not rely on converting heat to work. So it isn’t limited by Carnot efficiency any more than, say, a hydroelectric turbine, is it?

There is nothing about nd1 in the paper you linked, so far as I can see, and it has no special meaning that I am aware of. I suspect it has a meaning in the context of the problem you have been asked to solve. I can't comment more without seeing the text of the actual problem you have been given.

Yes, page 21 and 22 describes the standard splitting of the energy levels of d orbitals in an octahedral and in a tetrahedral ligand field, into E and T groups, the tetrahedral case being the opposite way round from the octahedral case. Any text on crystal field theory or ligand field theory will explain how this arises. What's the issue?

I'm sorry but I am not downloading attached files from unknown sources. You will need to post a relevant extract directly in a post. I assume this is something to do with how the energy levels of the d orbitals are split, according to crystal field theory.

ρ = r.(μe²/hbar²4πε₀). So it is r multiplied by a constant, made up of these various physical and mathematical quantities. Yes of course. But none of this is the subject of this thread.

Well no, it is proportional to r, surely? a is a constant, but ρ =r/a, right? By the way, are you in Brazil or Portugal?

Er, I've just confirmed what ρ is.What are you asking? My understanding of the VB model is that you make hybridised atomic orbitals from the atomic orbitals of the free atom and you then attribute bonding to the overlap of these hybridised atomic orbitals with those of neighbouring atoms. This is what your book is saying. Our questioner is engaged in constructing graphs, using some maths software, of these hybridised atomic orbitals, that's all.

Obrigado! 😀 According to my old Atkins QM book, ρ = r.(μe²/hbar²4πε₀) for the hydrogen atom, so that seems to fit. What is the problem?

Reputation points seem to have disappeared. And I don't remember seeing the rocket thingie on people's icons.

Well exactly. Hence my suggestion of hailing driverless cars when you want them...................... 😄

No. Read the post by @TheVat. The difference is that a 40kg rock is not aligned with the skeleton to load it in the same way as body weight would. Furthermore it is dead weight, unlike body weight, which is a mass of bone, fat and muscle that moves dynamically in response to the action of walking. Both things make a huge difference to how the knees and other joints are loaded, during the action of walking or other movements. (It is noteworthy that people used to carrying heavy loads in many parts of the world choose to place them on their heads. This will be because having the extra load taken by the spine is the best way to avoid off-centre loading of the joints.)

I think he has been asked to graph them, to see how the shapes arise from the linear combinations, or something.

Yes it would need to be either green hydrogen, by electrolysis, or blue hydrogen (from methane but with CCS). Some are sceptical that blue hydrogen actually achieves the goal, by the time losses of methane (a powerful greenhouse gas) etc., are taken into account. But it seems to me one can't be too choosy at the start: the main thing is to get something at commercial scale in place and see where imaginative people can take it. Home heating is a hell of an issue and nobody is tackling it at the moment. Where is the Elon Musk of central heating, eh? I've looked at heat pumps, but since the cost/kWh of electricity is 4 x that of gas in the UK, it's tough to make that stand up economically, even in terms of running costs only. When you factor in the higher capital cost and the possible need to change radiators in the house due to the lower heating water temperature, or else the need for a conventional booster heater to get it up to the temperature for the existing radiator system, it makes no sense. Regarding hydrogen embrittlement, I don't know about that, but I am old enough to remember that we used to run "town gas" (basically synthesis gas: CO + H2) through all the gas mains in Britain before "North Sea gas" (methane) came along in the 60s. It seemed to work. When N Sea gas came in, a guy from the gas board came round to change over the burners on our gas cooker - and that was it.

My understanding is that hydrogen may have a place for heavy goods vehicles, for which battery weight could be prohibitive. Hydrogen is also being talked about - and piloted - as a full or partial replacement for gas in home heating. Keele university has a pilot in which hydrogen is blended with natural gas and burns successfully without the need for changing burners: https://www.keele.ac.uk/discover/news/2020/june/hydeploy-update/pilot-positive-results.php This currently only blends it in at 20%, but that still saves a lot of carbon emission and equally importantly provides a pathway, using existing infrastructure, for the commercial production of hydrogen to get started. We will need a low-barrier way to break into hydrogen production or everyone will just wait for everyone else. No one will build trucks until hydrogen supply exists, no one will put in refuelling points until trucks are built, etc., etc.

Yes you have a point there. But the young family stage is quite brief. I'm in a quandary myself about a new car. I really only use it for visiting my aged father in his nursing home once a week, which I could do by bike and train if I had to, and for our annual trips to Brittany. I have no actual need to keep stuff permanently in the car. So maybe I'll go electric in a couple of years, or maybe I won't get one at all and just use Zipcar when I need to take stuff to the rubbish dump etc, as my friend does. The peak demand issue I don't see as invalidating the approach. Given that I am talking about cities, there is little need for commuting by car. Furthermore, catering for demand peaks via a collective pool of vehicles obviously requires far fewer than one per household. I'm not sure I understand the safety issue you raise. You seem to be base this on reducing vehicle weight by cutting back on the safety of the construction. I don't think anyone in this thread has suggested such a thing, and certainly not me.

This is intellectual masturbation.

If you really need the full solutions, then these will involve the product of the Laguerre functions (expressing the radial wave function) and the spherical harmonics that express the angular dependence. You should be able to find these on the internet for 2s, 2p, 3d etc. but I confess I don't know where. Here is an explanation of how they are used: https://demonstrations.wolfram.com/HydrogenAtomRadialFunctions/ As you can see, it is not simple. I did an entire quantum chemistry supplementary subject at university without being required to master exact solutions. The reason is that exact solutions are only possible for the hydrogen atom. For multi-electron atoms and molecules one has to resort to approximate solutions anyway, so it is far better to focus on symmetry properties etc., rather than getting enmeshed in the algebra of analytical solutions. So I'm still a bit sceptical that anyone expects you to get into all this. Like @studiotI too think it would be a good idea if can post the text of the task you have been assigned (if it is in English - or maybe I could decipher it in French).