### Mathematical Issues for Chemists

A brief outline of the mathematical issues faced by chemistry students.

### Reaction Rates

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

### Mixed up Mixture

Can you fill in the mixed up numbers in this dilution calculation?

# The Amazing Properties of Water

##### Stage: 4 and 5 Challenge Level:

Why do people say that water is necessary for life? Why have we never found any living organism that can flourish in a completely dry environment? How is it that something odourless, colourless, tasteless and relatively unreactive makes up 60% of our body mass? Why could another liquid not be used? Why water?

Water has several properties that make it unique amongst compounds and make it possible for all forms of known life to function.

It is the only natural substance found in all three physical states at the temperatures that naturally occur on Earth.

This means that we see water as a liquid, in rivers and seas, a solid, as snow and ice, and as a gas, as clouds or steam. If this was not the case the water cycle would be completely different (what if water didn't evaporate in the sun?); snow and ice might not exist (and thousands of species would now be homeless) and weather would be very different (would it still rain?). Can you think of anything else that would be different? Do you think we could still live if water was only a liquid at the temperatures that occur naturally on Earth? What about only a gas/solid?

Ice is less dense than water

This just means that ice floats on water and that lakes freeze from the top down to the bottom. This is clearly important for animals that live on ice, as their habitats would be greatly reduced or not exist at all if ice sank. Similarly, fish and other pond-life would be affected if lakes and ponds froze from the bottom upwards - the layer of frozen water at the top of the pond provides some insulation and prevents the rest of the water getting cold as quickly. It does this by making a barrier between the cold air and the water below. This means that large bodies of water don't get cold deeper down as fast as they might if ice sank and helps wildlife survive in ponds over winter. In fact, water gets more dense at it is cooled until it reaches $4^\circ$ C (which you can see on the graph), after which it gets less dense again. Most substances get progressively more dense as they are cooled. The graph below shows how density of water changes with temperature.

Water has a very high melting and boiling point compared to other similar molecules

This is what means it is seen as a solid, a liquid and a gas on Earth. If water was not a liquid at most of the temperatures we see on Earth the seas would all be ice, there would be no rain, nothing for plants to collect and animals to drink. Even our cells are filled with liquid water, which would not be possible either.

It is called the 'universal solvent' because it is capable of dissolving so many substances.

The water in our bodies is mostly contained in our cells, where it gives them a clear shape as well as having billions of useful molecules dissolved in it. Our cells need to be filled with water to work properly because the enzymes inside them only work in solution. Water is also the means by which transport occurs in our bodies' blood is mostly water and has hormones and gasses dissolved in it as well as toxins such as urea, which are removed from the body with yet more water. Transport in water also occurs on a much smaller scale: when something is dissolved it can move around in the solvent. For example, if an enzyme needs calcium ions to be activated and start working it will meet these as they move about in the solution inside a cell. The higher the concentration of calcium in the cell, the more likely the enzyme will meet an ion sooner. You may also have learnt about diffusion and osmosis, which are key concepts in understanding how cells function and rely on the presence of water

Water has a high specific heat capacity.

While this idea sounds a bit intimidating it is actually very simple - all it means is that it takes a lot of energy to make water a little bit warmer. This is why on a hot day the sand on a beach can be too hot to walk on but the sea still feels cool; the energy from the sun is enough to heat the sand a lot but the water only a little. This has some very important implications, especially for organisms that live in water. Seas, lakes and rivers maintain a much more constant temperature than air, which means that animals can live in water all year round without having to adapt to large temperature changes (What do you think would happen if water cooled more easily? What problems might this pose to organisms living in a small pond?). This also means that our body temperature is reasonably difficult to change quickly and hence makes our brain's job of maintaining a constant body temperature much easier (What might happen if our body temperature changed quickly and easily?).

Surface tension

You might have noticed that if you put a needle on the surface of a bowl of water it floats but if you throw it in it sinks. This is because the needle is denser than water so wants to sink but is held up by the surface tension of the water. Surface tension is a property that means the surface of water does not want to break - it is 'sticky'. You can also see this when you fill a cup to the brim, as the surface of the water will hold together and resist spilling. The high surface tension of water is the reason that some flies can land on its surface without sinking. This concept is also very closely related to another, the idea of capillary action.

Capillary action

Similarly to surface tension, this revolves around the idea that molecules of water 'stick' together. If you put a very fine tube into a beaker of water you will see that some of the water travels a short way up the tube; this is called capillary action and is caused by the water clinging to the sides of the tube and to other molecules of water, pulling them up the tube with it. Eventually the weight of the water being pulled is too great to be supported and the water stops moving, having reached an equilibrium. This same principle allows plants to draw water up from the ground; as water molecules travel up the stem more water molecules stick to them and more stick to those and so on until a column of water is being transported in the xylem (to find out more about this, look up 'transpiration').

But why?

All of these properties of water are critical for life as we know it but why does water have them? Does no other substance also do these things? What is it about water that makes it different? To understand the answers to these questions you have to study the molecular structure of water. The chemical formula for water is H2O, meaning that it contains two hydrogen atoms covalently bonded to one oxygen atom, like this:

The 95.84pm shows the length of the bond between the oxygen and the hydrogen; one pm is short for a picometre, which is one trillionth of a metre. The angle shown is the acute angle between the two hydrogen nuclei (do you have any ideas about why it isn't $180^\circ$ ? Why should it be $180^\circ$ ?) This diagram represents the bonds as lines, which makes it look like they are the same at every point ? this is not the case. Because oxygen is more electronegative than hydrogen it attracts the electrons in the O-H bond towards itself. If the thickness of the line represents electron density (the amount of time electrons spend in that part of the bond), the O-H bond actually looks more like this:

PICTURE showing polarisation of bond

As you can see the electrons spend most of their time nearer to the oxygen nucleus. This means that the oxygen is slightly negatively charged and that the hydrogens are slightly positively charged. This is called polarity and is the key concept behind the properties of water

PICTURE TO BE  RE SIZED -

This means that weak ionic interactions can occur between neighbouring water molecules as the slightly positive hydrogen from one molecule is attracted to the slightly negative oxygen on another. These are called hydrogen bonds.

This is why water 'sticks' to itself, giving it high surface tension and the ability to move by capillary action.

A great deal of energy is required to break down the hydrogen bonds, which is why the melting and boiling points of water are high and why it has a high specific heat capacity

A substance will dissolve in water if it is polar or ionic. This is because it dissolves by forming hydrogen bonds with the water. Oil is not polar, which is why it will not dissolve. Salt, NaCl, does dissolve because it is ionic. Can you think of some other substances that are soluble in water? How do they form hydrogen bonds with it? Can you draw a similar picture to the one below showing why glucose is soluble? Is it more or less soluble in water than salt? Why do you think this is?

A diagram of what happens to NaCl in solution:

This is an image of the chemical structure of glucose. There is a C (carbon atom) at each vertex - this is a common way of drawing organic molecules.