# Monthly Archives: April 2016

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 decillion uneventful collisions per second to be precise – not much else is happening in our ten-litre vessel at this stage.

### Conclusion

• Hydrogen gas, H2(g): 1.00 mol

Next week, we’ll add some helium to the vessel and see what happens.

# Periodic Table Smoothie

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.

Join me next week to start the experiment.

# What if we put 200 g ice into 1.00 L hot water?

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.

# Shut off Your Digital Screens by 9PM

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.

### Tips for getting a better night’s sleep

1. Limit screen time within the two hours before falling asleep
2. Remove computers and mobile devices from the bedroom
3. Use iOS Night Mode (available on iOS 9.3 and later)
4. Use Flux for Mac
5. Limit screen time for children under 13 to just two hours per day