Once more into the world of hydronium and logarithm; but never mind the mole

By Associate Professor Allan Blackman

This article was orignally published in the Otago Daily Times on Wednesday 4 July 2012.

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What was hopefully obvious from last month’s column was that pH is far from a simple concept. For starters, it is a logarithmic function. In simple terms, this means that a change of 1 pH unit corresponds to a 10-fold change in the hydronium ion concentration – at the risk of upsetting the chemistry purists, one could say that a solution of pH 3 is 10 times as acidic as one of pH 4. To put this in a more understandable context, suppose we had 1 litre of a solution of pH 3 – if we added 9 litres of water to this (i.e. a 10-fold dilution) the final solution would have a pH of 4.

The useful pH scale ranges from 0 (a very acidic solution) to 14 (a very basic solution). Because of its logarithmic nature, this means that it spans a hydronium ion concentration range of 1 × 10¹⁴, or 100,000,000,000,000, between these pH values. To give some idea of the pH values of common substances, lemon juice, for example, has a pH around 2.3, orange juice, around 3.5, milk, around 6.7, seawater, around 8, household ammonia, around 11.5, and oven cleaner can be as high as 13, depending on its composition. Although it is supposedly common knowledge that pure water at 25 °C has a pH of 7.00, measurement of the pH of a sample of any water under all but the most stringently controlled conditions will yield a value somewhere between 5 and 6; this is because the water sample will contain dissolved carbon dioxide from the air, which renders the water very slightly acidic through formation of small amounts of ‘carbonic acid’.

So this is where we get to the importance of pH. Nature has evolved so that many of its important chemical reactions, particularly those that occur in living systems, are optimised to occur at particular pH values. If the pH of the system becomes too high or too low, then critical chemical reactions are impeded, and this can be fatal for the organism. For example, normal human blood has a pH between 7.35 and 7.45 – if our blood pH lowered to 7 or increased to 8, we would probably die. Nature has therefore developed a series of chemical species we call buffers, which ensure that the pH of blood does not change significantly.

Sadly, despite all I have written here, a true appreciation of exactly what pH means is contingent on understanding the mole, a chemical concept which is usually first introduced in 6th form (Year 12) Chemistry and is not necessarily understood by all even when University rolls around. My explanation of pH has only scratched the surface and is extremely simplistic – but hopefully it had given you some idea of what pH is all about.

Of course, the fact that pH is conceptually difficult doesn’t stop advertisers telling us that their clients’ products are ‘pH balanced’ ‘pH neutralising’, and other such meaningless terms. Treat all such claims with caution.

It is a tragedy that the cities of Fukushima, Hiroshima, Nagasaki and Chernobyl will for ever be associated with the word “radioactivity”. It is, in my opinion, fair to say that a significant number of people think of radioactivity as resulting solely from the actions of human beings, by way of nuclear power stations or nuclear weapons, and that it didn’t exist prior to the 20th century. So it may come as some surprise to you that your body, my body, and, indeed, the bodies of everybody on planet Earth, are teeming with radioactive atoms, the majority of which derive from a natural source – the element potassium.

Potassium (elemental symbol K) is an essential element for life. Humans require around two to four grams a day, and this is generally obtained from such foods as potatoes, spinach and bananas. But it turns out that, of all the potassium atoms we ingest, a small percentage are radioactive. Natural potassium consists of three isotopes, ³⁹K, ⁴⁰K and ⁴¹K. All three contain 19 positively-charged protons in their nucleus, but differ in the number of neutrons – 20, 21 and 22, respectively. The ⁴⁰K isotope is radioactive, and comprises about 0.012% of all the atoms of potassium on Earth. It has a half-life of just over one billion years, meaning that one half of any sample of ⁴⁰K will disappear over this time, and it decays by emitting beta particles and gamma rays, both of which are potentially harmful to humans.

An ‘average’ 75 kg person contains about 150 g of potassium. Of that 150 g, 0.018 g is due to the radioactive ⁴⁰K isotope. This might not sound much, but when this mass is converted to an actual number of atoms, we find that it corresponds to about 270,000,000,000,000,000,000 atoms of radioactive potassium in the body. That’s a lot. Given the billion year half-life of this isotope, you might perhaps expect that not many of these atoms would decay over our lifetime, but again, you may be surprised to find that around 7000 ⁴⁰K atoms decay per second. Each of these decays can potentially lead to DNA mutation, and there’s absolutely nothing we can do about it! Obviously it is impossible for us to gauge the health effects of these radioactive decays, as it’s rather difficult to prepare a potassium-free human.

Like it or not, natural radioactivity, whether it be in the form of ⁴⁰K, the most abundant radioactive isotope in the body, ¹⁴C, which we ingest primarily through breathing in _¹⁴CO₂ from the air, or literally hundreds of other radioactive isotopes, is ubiquitous, and will always be with us – well, at least for the next few billion years, anyway.