Shaun Holt and I recently co-wrote a paper for Research Review on the ingredients found in personal care products (e.g. shampoos, lotions and cosmetics). We analyse the recent surge in demand for ‘natural’ products and the beliefs that have been driving it.
We’re not saying that natural products don’t work – in fact, quite the opposite. We’re saying that natural products, just like synthetic ones, can be harmful, beneficial or neutral depending on the dose and upon how they’re used.
The terms “natural”, “chemical free” and “organic” are used frequently to market personal care products. However, the exact meaning of these terms is still unclear for consumers, and the use of these terms on labels is still unregulated in some markets. The purpose of this review is to provide clarity on the meanings of these terms and the implications of their application in the marketing of personal care products. The importance of applying a science-based approach to the assessment and recommendation of personal care products is also emphasised. This review is intended as an educational resource for healthcare professionals (HCPs), including nurses, midwives, pharmacists, and pharmacy assistants.
In a debut podcast, Sam Howarth discusses with chemophobia research-enthusiast and chemistry teacher, James Kennedy, the evolution of fearing chemicals and the people who are driving it behind the scenes.
Sam Howarth is a self-taught nutrition and fitness enthusiast – a fanatic learned through trial and error over 3 years of research and over 10 years of personal struggles with food and body image.
In the podcast, we talk about chemophobia, its origins and the money that keeps it alive.
We all feel a profound connection with the natural world. E O Wilson called this sensation biophilia: ‘the urge to affiliate with other forms of life’. That sense of connection brings great emotional satisfaction. It can decrease levels of anger, anxiety and pain. It has undoubtedly helped our species to survive, since we are fundamentally dependent on our surrounding environment and ecosystem. But lately, biophilia has spawned an extreme variant: chemophobia, a reflexive rejection of modern synthetic chemicals.
Recall from last week that our Periodic Table Smoothie contains the following species:
Amount present (moles)
Pressure: 718 kPa Temperature: 350 °C
Reactions of nitrogen in our 10-litre vessel
Our freshly-added 1.00 mol of nitrogen gas, N2(g), reacts with hydrogen gas to make ammonia in the following reversible (equilibrium) reaction. We will assume that the interior metal surface of the vessel is a suitable catalyst for this reaction (e.g. iron).
There are three other reactions below that might have occurred at higher temperature, but I’ve chosen not to raise the temperature of the vessel at this point. Rather, we’ll keep it at 350 °C to keep things manageable.*
*I was tempted at this point to elevate the temperature of our vessel to 500 °C so that the second reaction could take place as well. This would produce copious amounts of smelly ammonia gas, which would allow for larger quantities of interesting organic compounds to be produced later on. To keep our simulation safe and (relatively) simple, I’ve decided to keep the vessel at 350 °C. Interesting compounds organic will still form – only in smaller amounts.
The ammonia reaction above (the first equation) is actually an equilibrium reaction. That means that the reactants are never completely used up, and the yield is not 100%.
Recall from Le Châtelier’s principle that removing product from an equilibrium reaction causes the position of equilibrium to shift to the right, forming more product. This is because:
“If an equilibrium system is subjected to a change, the system will adjust itself to partially oppose the effect of the change.” – Le Châtelier’s principle
There are three reactions that will remove ammonia from our vessel while it’s being produced, and I’ve put all three of these into the simulation. One of these is the reverse of the reaction above (producing hydrogen and nitrogen gases) and the other two are described below. Let’s take a look at those other two reactions.
With what will the ammonia react in our vessel?
Ammonia can undergo the following reactions with the other things in our vessel**
**The ammonia does react with methane and beryllium as well, but only at temperatures of 1200 °C and 600 °C, respectively.
Two compounds will be formed: lithium amide and borazine. Lithium amide reacts with nothing else in the vessel, so the reaction chain stops there. Borazine, on the other hand, is much more interesting.
We’ve made borazine!
Borazine is a colourless liquid at room at temperature. It boils at 53 °C and has a structure that resembles that of benzene.
Because of the electronegativity difference of about 1.0 between the B and N atoms in the ring, borazine has a mesomer structure:
Like benzene, there is partial delocalisation of the lone pair of electrons on the nitrogen atoms.
Borazine polymerises into polyborazine!
Fascinatingly, borazine polymerises into polyborazine at temperatures above 70 °C, releasing an equal number of moles of hydrogen gas. Polyborazine isn’t particularly well-understood or well-documented, but one recent paper suggested it might play a role in the creation of potential ceramics such as boron carbonitrides. Borazine can also be used as a precursor to grow boron nitride thin films on surfaces, such as the nanomesh structure which is formed on rhodium.
Like several of the other compounds we’ve created in our Periodic Table Smoothie, polyborazine has also been proposed as a hydrogen storage medium for hydrogen cars, whereby polyborazine utilises a “single pot” process for digestion and reduction to recreate ammonia borane.
The hydrogen released during the polymerisation process will then react further with a little bit of the remaining nitrogen to produce a little more NH3(g) – but not much. Recall from earlier that the ammonia reaction is an equilibrium one, and the yield of NH3(g) at pressures under 30 atmospheres is very low. Pressure in our vessel is still only around 7 atmospheres.
Once polymerised, this would form about 12 grams of polyborazine:
As far as I’m aware, no further reactions will take place in the vessel this week.
Conclusion after adding 1.00 mole of nitrogen gas
Amount in mol
Pressure: 891 kPa (higher than before due to the addition of nitrogen gas) Temperature: 350 °C (vessel is still being maintained at constant temperature)
Next week, we’ll add a mole of oxygen gas to the vessel. Warning: it might explode.
Stock, Alfred and Erich Pohland. “Borwasserstoffe, VIII. Zur Kenntnis Des B 2 H 6 Und Des B 5 H 11”. Berichte der deutschen chemischen Gesellschaft (A and B Series) 59.9 (1926): 2210-2215. Web.
Today, we’re going to add 1.00 mole of carbon to our vessel. After adding boron last week, we left our vessel locked at 350 °C and with a pressure of 638 kPa. These reactions are taking place at 350 °C and constant volume (exactly 10 litres). Pressure inside the vessel will therefore change over time.
Allotropes of carbon
Carbon has various allotropes (structural arrangements of an element). Diamond is extremely strong and highly unreactive, while graphite is soft and brittle. The differences are all due to the type of bonding between carbon atoms. In diamond, carbon atoms are bonded by four strong covalent bonds with the surrounding atoms in a strong, hard three-dimensional ‘network lattice’. Graphite owes its softness and brittleness to the fact that its carbon atoms are bonded by only three strong covalent bonds in a two-dimensional ‘layer lattice’. Individual layers are very strong, but the layers can be separated by just the slightest disturbance. Touching graphite lightly onto paper will remove layers of carbon atoms and place them onto the page (such as in a pencil). Using a diamond the same way would likely tear the paper instead.
For this reason, I’m going to put graphite into the vessel instead of diamond. Diamond is so strong and inert that it’s unlikely to do any interesting chemistry in our experiment. Graphite, on the other hand, will.
The following seven chemical reactions will take place after adding carbon (graphite) powder
As soon as the carbon powder enters the vessel, it will begin to react with the following three species as follows:
The ethyne produced in the third reaction will then react with any lithium and beryllium remaining in the vessel as follows:
The hydrogen gas produced by the above two reactions will then react with lithium and carbon (if there’s any left) as follows:
These reactions have the potential to all occur at the same time. Tracking them properly would require calculus and lots of kinetics data including the activation energy of each reaction and the rate constant for each equation. Quick searches on the National Chemical Kinetics Database yields no results for most of these equations, which means we won’t be able to use a computer model to calculate exact quantities of each product. Instead, I’m going to run a computer simulation using Excel that makes the following three assumptions:
all these reactions occur at the same rate;
all these reactions are first-order with respect to the limiting reagent;
all these reactions are zeroth-order with respect to reagents in excess.
The results will be a close approximation of reality – they’ll be as close to reality as we can get with the data that’s available.
Here are the results of the simulation
Here’s a graph of the simulation running for 24 steps. Exactly one mole of carbon powder is added at step 5.
Summary of results
The results are incredible! We’ve made ethyne and methane, both of which have the potential to do some really interesting chemistry later on. I’m hoping that we can make some more complex organic molecules after nitrogen and oxygen are added – maybe even aminoethane – let’s see.
Hydrogen has also re-formed. I’m hoping that this gas lingers for long enough to react with our next element, nitrogen: we might end up making ammonia, NH3(g).
You may have noticed that I removed the “boron-lithium system” from the vessel. The 0.178 moles we created are now stored separately and will not be allowed to react any further. With such little literature about the reactivity of B3Li, it’s impossible to predict what compounds it’ll form later on. B3Li is so rare that doesn’t even have a Wikipedia page.
Here’s what’s present in the vessel after adding carbon
Moles present after 500 ‘steps’
We also have 0.178 moles of B3Li stored separately in another vessel.
Next week, we’ll add nitrogen and see what happens.
Boron is a metalloid: an intermediate between the metals and non-metals. It exists in many polymorphs (different crystal lattice structures), some of which exhibit more metallic character than others. Metallic boron is non-toxic, extremely hard and has a very high melting point: only 11 elements have a higher melting point than boron.
British scientist Sir Humphrey Davy described boron thus:
“[Boron is] of the darkest shades of olive. It is opake[sic], very friable, and its powder does not scratch glass. If heated in the atmosphere, it takes fire at a temperature below the boiling point of olive oil, and burns with a red light and with scintillations like charcoal” – Sir Humphrey Davy in 1809
Before we add the 1.00 mol of boron into our reaction vessel, we need to recall what’s already in there from our experiments so far:
H2(g): 0.70 mol
He(g): 1.00 mol
Li(s): 0.40 mol
LiH(s): 0.60 mol
Be(s): 1.00 mol
The temperature of our vessel is 99 °C and the pressure of the gaseous phase is 525.5 kPa.
Now, let’s add our 1.00 mol of boron powder.
Which reactions take place?
Boron reacts with hydrogen gas to produce a colourless gas called borane, BH3(g), according to the following equation:
Boron also reacts with lithium in very complex ways. If we heat the vessel up to 350 °C, we’d expect to see the formation of a boron-lithium system with chemical formula B3Li according to this equation:
Notice that now we’ve heated up our vessel to 350 °C to allow this reaction to happen, the lithium at the bottom of the vessel has melted.
Boron reacts with lithium hydride as well, but only at temperatures around 688 °C. With our vessel’s temperature set at 350 °C, we won’t observe this particular reaction in our experiment.
Some allotropes of boron – in particular, the alpha allotrope that was discovered in 1958 – is capable of reacting with beryllium to form BeB12. Because we’re using beryllium powder, which has semi-random symmetry, we won’t see any BeB12 forming in our vessel. Alpha-boron only exists at pressures higher than around 3500 kPa. At our moderate pressure of only 525.5 kPa, powdered (semi-random) boron will prevail and no BeB12 will form.
For simplicity’s sake, let’s assume that the two reactions above take place with equal preference.
Boron powder reacts with hydrogen gas
Let’s do an ice table to find out how much borane we make.
A quick n/ratio calculation shows us that the hydrogen gas is limiting in this reaction:
We can expect all of the hydrogen gas to react with the boron powder.
units are mol
Borane is very unstable as BH3, and it would probably dimerise into B2H6(g). This is still a gas at 350 °C and is much more stable than BH3. For the rest of this experiment we’ll assume that our 0.466 mol of BH3 has dimerised completely into 0.233 mol of B2H6.
Boron powder reacts with lithium
With the molar ratios present in our vessel, at 350 °C, we’d expect to witness the formation of a boron-lithium system, with chemical formula B3Li.
A quick n/ratio calculation shows that in this reaction, the boron powder is limiting.
All of the remaining boron therefore reacts with lithium. To calculate exactly how much B3Li we’ve created, let’s do another ice table:
units are mol
What’s in our vessel after adding boron?
We have the following gas mixture in our vessel:
Helium gas, He(g): 1.00 mol
Helium is an inert noble gas that will probably remain in the vessel until the end of the experiment. It’s used in party balloons.
Borane gas, B2H6(g): 0.233 mol
We made this today. Borane is used in the synthesis of organic chemicals via a process called hydroboration. An example of hydroboration is shown below.
At the bottom of the vessel, there’s a sludge, which contains the following liquids and solids:
Molten lithium, Li(l): 0.22 mol
Lithium is used in the production of ceramics, batteries, grease, pharmaceuticals and many other applications. We’ve got 0.22 moles of lithium, which is about 1.5 grams.
Beryllium powder, Be(s): 1.00 mol
Beryllium is used as an alloying agent in producing beryllium copper, which is used in springs, electrical contacts, spot-welding electrodes, and non-sparking tools.
Lithium hydride, LiH(s): 0.60 mol
Lithium hydride is used in shielding nuclear reactors and also has the potential to store hydrogen gas in vehicles. Lithium hydride is highly reactive with water.
Boron-lithium system, B3Li(s): 0.178 mol
We made this today… but what is it? Not much is known about this compound – in fact, it doesn’t even have a name other than “boron-lithium system, B3Li”. It’ll probably decompose eventually in our experiment – maybe when we alter the pressure or temperature of the vessel at some later stage. We’ll need to keep an eye on this one.
The original H2(g) and B(s) have been reacted completely in our experiment.
What’s the pressure in our vessel now?
At the end of our reaction, the temperature of our vessel is still set at 350 °C and the pressure of the gaseous phase inside the vessel can be calculated to be a moderate 638 kPa as follows:
*It should also be noted that some evidence exists for a reaction between LiH and BH3, forming Li(BH4). The reaction seems to take place stepwise with increasing temperature. A quick read of this paper suggests that in our vessel, which is at 350 °C, any Li(BH4) formed would actually break back down into boron powder and hydrogen gas, which would in turn react with each other and with lithium metal to form BH3 and LiH again. The net result would be a negligible net gain of LiH and a negligible net loss of boron powder. We will continue calculating this Periodic Table Smoothie under the assumption that if any Li(BH4) forms, it breaks down before we add the next element, and the overall effect on our system is negligible.
**Li(BH4) is an interesting compound: it’s been touted as a potential means of storing hydrogen gas in vehicles – it’s safer and releases hydrogen more readily than LiH, which was mentioned above.
Next week, we’ll add element number 6, carbon, and see what happens.
Li(s): 0.40 mol (still solid: it melts at 180.5 degrees)
LiH(s): 0.60 mol
Pressure = 525.5 kPa
Temperature = 99°C
Beryllium doesn’t react with any of the things in the vessel: H2(g), He(g), Li(s) or LiH(s). My one mole of beryllium powder (which would cost me over $70) would just sit at the bottom of the vessel doing nothing.
With not much else to write about in the Periodic Table Smoothie this week, it might be a good idea to calculate how much this Periodic Table Smoothie would have cost in real life.
Last week, our vessel contained a mixture of hydrogen and helium gases. No chemical reactions have occurred so far, but that is about to change. Today, we’ll add 1.00 mole of lithium powder to the mixture and observe our first chemical reaction.
What does lithium look like?
Lithium is a soft, silvery metal with the consistency of Parmesan cheese. Lumps of lithium can be cut with a knife and it’s so light that it floats on oil. It would float on water as well if it weren’t for the violent reaction that would take place. Lithium is very well-known by science students for its ability to react with water, producing hydrogen gas and an alkaline solution of lithium hydroxide.
There’s no water in our vessel so the above reaction won’t actually take place. We’ve only got hydrogen gas and helium gas inside. Let’s see if our powdered lithium reacts with either of those gases.
Will the lithium powder react in our vessel?
Yes! Lithium reacts with hydrogen gas very slowly. One paper by NASA cited a reaction occurring at 29°C but the yield and rate were both very low. Because I want to initiate as many reactions as possible in this experiment, I’m going to heat my vessel to 99°C by immersing it in a bath of hot water. According to the NASA paper, this temperature would give my reaction a 60% yield after two hours.
Lithium hydride is beginning to collect in the bottom of my 10-litre vessel. It’s a grey-to-colourless solid with a high melting point.
How much of each substance do we now have in the vessel?
First, we need to know which reagent is limiting. We can calculate this by using the following rule:
Let’s substitute the values into the expression for all the reactants in this reaction: Li(s) and H2(g).
If the yield was 100% (i.e. a complete reaction), I’d expect to make 1.00 mole of lithium hydride. However, we’re only going to get 0.60 moles because according to the NASA paper, the yield of this reaction is only 60% at my chosen temperature.
Let’s do an ‘ice’ table to find out how much of each reactant reacts, and hence how much of each substance we have left in our reactor vessel.
units are mol
By the end of our reaction, we’d have:
H2(g): 0.70 mol
He(g): 1.00 mol
Li(s): 0.40 mol (still solid: it melts at 180.5 degrees)
LiH(s): 0.60 mol
What does 0.60 mol LiH look like?
Let’s use the density formula to try find out how many spoonfuls of LiH we’ve created.
We’ve made 6.11 millilitres of lithium hydride powder! That’s a heaped teaspoon of LiH.
What’s the resulting pressure in the vessel?
Our elevated temperature of 99°C will have caused a considerable pressure increase inside the vessel.
That’s 5.2 atmospheres (atm) of pressure, which is quite high. A typical car tyre is about 2 atm for comparison.
What if the vessel exploded?
BANG. The contents of the vessel, after they’ve rained down on an unsuspecting crowd, would react explosively with the water and other compounds in our bodies to produce caustic lithium hydroxide and toxic lithium salts. I recommend stepping away from the vessel and behind a thick safety screen at this point. Even though our imaginary vessel is quite strong, we better put on a lab coat and safety glasses as well—just in case.
Conclusion after adding lithium powder
H2(g): 0.70 mol
He(g): 1.00 mol
Li(s): 0.40 mol (still solid: it melts at 180.5 degrees)
LiH(s): 0.60 mol
Pressure = 525.5 kPa
Temperature = 99°C
Next week, we’ll add 1.00 mole of beryllium to the vessel and see what happens.
Last week, we put 1.00 mole of hydrogen gas into a cylinder. The resulting pressure was 243 kPa and the temperature was maintained steady at 20°C. This week, we’ll add 1.00 mol of helium gas, He(g), to the vessel and see what happens.
Will the helium react with the hydrogen?
No. Helium is completely inert. Hydrogen and helium will co-exist without undergoing any chemical reactions.
What will the resulting pressure be?
This is a very simple calculation. With 2.00 moles of gas in the vessel, the pressure would be double what it was before. This is known as Dalton’s law of partial pressures: the total pressure in a vessel is equal to the sum of all the pressure of the individual gases in the vessel.
Let’s convert that into pounds per square inch (psi) for easy comparison with everyday objects.
That’s about the same as a hard bicycle tyre.
How fast are the molecules moving?
Remember from last week that when our vessel contained only hydrogen gas, the molecules were moving around randomly with an average speed of 1760 metres per second.
Kinetic molecular theory states that the kinetic energy of a gas is directly proportional to the temperature of that gas. The formula for kinetic energy is shown below:
At constant temperature, heavier particles move more slowly than lighter ones. Even though they have the same kinetic energy, helium atoms at 20 °C move slower than hydrogen molecules at 20 °C because they have almost exactly double the mass. How much slower does the helium move? Let’s find out.
The molecules are moving at 1245 metres per second, or 4482 km/h. This is slower than the hydrogen gas by a factor of exactly root 2.
The molecules in our vessel could orbit the Earth in just 6 hours if they were to move in a single direction at this speed. Because the motion of particles in our gas mixture is random – they jiggle about rather than move in a single direction – they stay securely in the vessel.
Conclusion after adding helium
No chemistry’s happening in the vessel – not yet. Molecules of hydrogen and helium are simply co-existing in our vessel, bouncing off each other at different speeds and not interacting in any other way.
Hydrogen gas, H2(g): 1.00 mol
Helium gas, He(g): 1.00 mol
For some chemistry to happen, we’ll need to add the next element, lithium. We’ll do that next week.
I’m going to add 1.00 mol of hydrogen gas, H2(g), to our 10-litre vessel. We’ll assume that the entire experiment is carried out at normal room temperature – let’s say it’s 20°C.
How much does a mole of hydrogen cost?
Hydrogen gas is a relatively cheap element, and my one mole of H2(g) would cost less than one cent at wholesale prices. That said, the shipping, handling and service fee would be a couple of orders of magnitude greater than the cost of the gas itself, and I’d probably need to give the store about a dollar for the privilege of taking one cent’s worth of hydrogen gas.
What does a mole of hydrogen look like?
We’ll assume the temperature is 20°C and the atmospheric pressure is 102.3 kPa, which is what the Weather app on my phone is reading right now. After the hydrogen gas has been released from its high-pressure storage cylinder, my one mole of H2(g) would have a volume of 23.8 litres at these conditions. That’s about enough hydrogen gas to fill up a party balloon.
Hydrogen is a colourless, odourless gas that’s lighter than air. It’d float upwards very quickly if I opened the valve in the store. I’m now going to squeeze all that gas into my 10-litre vessel.
What’s the resulting pressure of the vessel?
If I squeeze that 23.8 litres of hydrogen gas into my 10-litre vessel, the resulting pressure in the vessel must be greater than atmospheric pressure (1 atm) because I’ve compressed the gas. We can calculate the final pressure precisely by using the ideal gas law: PV=nRT.
That’s significantly higher pressure than atmospheric pressure, which varies from 100 kPa to 102 kPa under normal weather conditions.
Interestingly, the pressure in the vessel, 243 kPa, is equal to 35.2 pounds per square inch (psi), which is the same as the recommended pressure for a car tyre.
Other than making random movements inside the vessel, the hydrogen molecules won’t really do anything else.
How fast are the molecules moving about?
We can calculate the average speed of the molecules by using the following equation:
*Note that R is the gas constant, 8.31, and M is the molar mass in kg/mol
The molecules are travelling at about 1760 metres per second (on average).
How much distance will the gas molecules travel before they collide with one another?
For this question, we need to calculate something called mean free path. The mean free path is the average distance we can expect each molecule to travel before it collides with another molecule. Mean free path is quite long in a vacuum, and very short at high pressure conditions. One of the formulae used to calculate mean free path, λ, is shown below.
**Note that in this formula, pressure (P) must be measured in pascals (Pa)- not kilopascals (kPa). We therefore need to multiply our kilopascal pressure by 1000 to convert it from kPa to Pa.
*** Note also that d is the diameter of the molecules being studied in metres. Wikipedia tells us that hydrogen molecules have a diameter of 120 picometres. I’ve used this value in the equation below.
The molecules in our vessel collide with each other roughly every 260 nanometres. That’s tiny: it’s just a few percent of the width of a cell nucleus!
How often do the molecules collide?
Let’s go right back to Year 10 Physics for this one. The time between collisions will be equal to the average distance travelled between collisions divided by the average speed of the molecules:
The molecules collide with each other roughly every 0.1478 nanoseconds.
How many times do the molecules bump into each other each second?
By taking the reciprocal of the average collision time, we can find out how many times the molecules collide with each other every second, on average:
Each molecule in our ten-litre vessel makes 6.765 billion collisions per second with neighbouring molecules.
Apart from lots of uneventful particle collisions – a total of 4.07 decillionuneventful collisions per second to be precise – not much else is happening in our ten-litre vessel at this stage.
Hydrogen gas, H2(g): 1.00 mol
Next week, we’ll add some helium to the vessel and see what happens.
Yesterday, I was wondering what would happen if we mixed the entire periodic table of elements together in a blender. Unsurprisingly, it would explode, scattering radioactive dust and debris for miles around in a red-hot fireball formed from the simultaneous fission of the entire seventh row. The periodic table would only need to be the size of a matchbox in order for this explosion to happen.
Calculating exactly what would happen would be incredibly difficult. There are so many simultaneous reactions – including nuclear reactions – taking place that it’s almost impossible to predict the outcome in any more detail than “KABOOM”.
Making a real Periodic Table Smoothie would be prohibitively expensive. You’d need 118 particle accelerators (costing $1 billion each) all pointing at the same target just to get single atoms of each element to collide at the same time. This is even more difficult than it sounds: those elements near the bottom of the periodic table (numbers 105 and above) are so unstable that they’d break down before they even reach the target. There are massive financial and physical challenges to mixing an entire periodic table up in a blender.
Instead of adding all the elements at the same time, I’ll be adding one element each week to an imaginary 10-litre vessel and documenting – as a theoretical exercise – what happens. Ultimately, we all know it’s going to explode at some point. But when will it do that? How many elements are we able to add before it finally explodes? Will we create anything interesting along the way?
This very idea was floated on Reddit’s AskScience forum in 2013 but nobody actually figured out (seriously) what would happen.
Today, we’re going to answer the following question:
When 200 grams of ice is added to a bucket containing 1.00 litre of hot water, what’s the final temperature of the water?
To answer the question, we’re going to need to make some assumptions. We’ll take 1.000 litre of pure water at 80.00°C and add 200.0 g of ice (at -10.00°C) to it. What’s the final temperature of the water?
Part 1: Heat transfer method
The following equation can calculate the temperature at thermal equilibrium of any number of objects in thermal contact.
I love this equation because it’s several lines of maths shorter than the version taught in school. With this equation, you don’t even need to convert the temperatures into kelvin. Celsius works just fine.
Let’s set up the equation so that the addition series contains the variables in the question.
Now, let’s substitute the gives values into the equation. The specific heat capacity of water is 4200 J kg-1 K-1, and that of ice is 2100 J kg-1 K-1.
Great! Adding 200.0 g of ice to 1.000 L of water decreases the temperature from 80.00°C to 71.80°C.
But we’ve forgotten something. The ice will melt as soon as it hits the hot water. Since melting is an endothermic process, heat energy from the water will actually be absorbed, thus reducing the final temperature even further.
Part 2: Let’s take into account the fact that the ice melts!
Remember our formula from part 1.
The amount of energy required to melt ice can be calculated using the latent heat equation:
Removing that amount of heat energy from the system results in the following equation:
Great! Now, we’ve calculated that the final temperature of the water would be 57.36°C after the addition of the ice. That’s equal to 330.5 kelvin, which will be useful later.
However, we’ve forgotten to take something else into account: how much heat will be lost as radiation from the surface of the bucket?
Part 3: What’s the rate of heat loss from the bucket by radiation?
The rate of heat lost by radiation can be calculated by using the Stefan-Boltzmann equation, below.
P is the rate at which heat energy is radiated from the surface of the bucket in watts. Emissivity, e, of water is 0.95, and the surface area, A, should be around 0.0707 m2 for a one-litre bucket. Calculation of A is shown below. Assuming that the radius of the surface of the bucket is 6cm:
Plugging that value into the equation, we can find P. We’ll assume that the experiment is being conducted at room temperature and the temperature of the surroundings is 20.00°C (29.03 K).
This means that 2.928 joules of energy are emitted from the surface of the bucket every second. Ten minutes later, the bucket would have lost 1756.8 joules of energy due to radiation from the surface. But what about emission of radiation from the sides of the bucket?
Let’s say that our bucket is made from highly polished aluminium (which has emissivity 0.035) and it holds exactly 1.2 litres of water. We need to calculate the dimensions of the bucket.
Assuming it has straight sides (i.e. it’s a cylinder), the bucket had volume equal to the following formula:
The surface area of our bucket (excluding the open surface at the top) is:
The rate of energy radiation from the sides would therefore be:
It’s interesting to note how very little radiation is emitted from the shiny aluminium bucket, while lots more radiation is emitted from the surface of the water. This is because relatively ‘dark’ water has a much higher emissivity than shiny aluminium. Total emission from the bucket is therefore:
After ten minutes, the bucket would have lost the following amount of energy:
Let’s factor this amount of energy loss into our final temperature equation.
Not much energy is lost via radiation! Finally, let’s find the peak wavelength of the radiation emitted by the object using Wien’s law.
Part 4: What’s the wavelength of the radiation being emitted by the bucket?
Here’s Wien’s law from Unit 1 Physics…
The radiation emitted from the resulting bucket of water lies firmly in the infra-red part of the electromagnetic spectrum. The bucket would be clearly visible on an infra-red camera!
Next week, we’ll begin a new a Chemistry-themed project called Periodic Table Smoothie. More next week.
Sleep is an essential part of our development and wellbeing. It is important for learning and memory, emotions and behaviours, and our health more generally. Yet the total amount of sleep that children and adolescents are getting is continuing to decrease. Why?
Although there are potentially many reasons behind this trend, it is emerging that screen time – by way of watching television or using computers, mobile phones and other electronic mobile devices – may be having a large and negative impact on children’s sleep.
It has also been suggested that longer screen times may be affecting sleep by reducing the time spent doing other activities – such as exercise – that may be beneficial for sleep and sleep regulation.
Screen time in the hours directly prior to sleep is problematic in a number of ways other than just displacing the bed and sleep times of children and adolescents. The content of the screen time, as well as the light that these devices emit, may also be responsible for poorer sleep.
The content, or what we are actually engaging with on the screen, can be detrimental to sleep. For example, exciting video games, dramatic or scary television shows, or even stimulating phone conversations can engage the brain and lead to the release of hormones such as adrenaline. This can in turn make it more difficult to fall asleep or maintain sleep.
The number of devices and amount of screen time children and adolescents are exposed to is continually increasing. Given these early associations with reduced sleep quality, and the importance of sleep in healthy development and ageing, this is an issue that is not likely to go away any time soon.
Sleep should be made a priority, and we can combat this growing problem in a number of ways.
I was recently accepted as a contributor to Apple News. This means that readers can now access this website’s content via the Apple News app from any iOS device. The latest posts will appear directly in readers’ Apple News feeds. This is quicker and much more convenient than using the mobile version of this website.
I’ve been using Apple News for a while now, and I love having quick access to important news from various sources. You can customise which news sources you want to appear in your news feed: there are around 2000 news sources to choose from, and this website has now been added to the mix.
Chad Jones works at Intel Corp. in Utah, USA. He’s the founder and chief science writer for The Collapsed Wavefunction, a science advocacy podcast featuring episodes on science instruction, science in popular culture, and current science news items.
In 2016, Chad’s launched his latest venture in chemistry outreach with a fantastic new podcast called Chemical Dependence. In each of the podcast’s punchy, 5-minute episodes, Chad explores interesting chemical compounds and how they’re used in society. The podcast is a great source of interesting facts to liven up any chemistry lesson. All Chemistry teachers should subscribe!
He’s even teamed up with Andy Brunning from Compound Interest for his latest episode on pipeline. Check it out here.
Check out all the episodes and subscribe to the podcast on iTunes here. Support the podcast via Patreon here.