In chemistry, accurately and precisely measuring the amount of substance is crucial in virtually every task, which is why it’s an important topic at A level.
Measurement is key to the analysis of substances and also equally important in the synthesis of substances. Various types of measurements, units, and concepts are used in determining the amount of substance. These include mass, volume, density, atomic weight, mole, and Avogadro’s number.
In this post:
Standard of Measurement
Chemistry requires measurements to enable validation through peer reviews. Quantitative data facilitates the repeatability of experiments and reproducibility of results.
Unlike pure mathematics and theoretical physics, chemistry is highly empirical in its approach. While some approximations and errors in measurements are inevitable, they can be contained within a reasonable range of degrees of errors.
However, without a standard set of measurements, repeatability of experiments and reproducibility of results would be very difficult, if not impossible. Thankfully, chemists and other scientists have devised an international standard of measurements: the metric system.
Also known as the International System of Units (SI), the metric system expresses the amount of substance as in base ten. This is a more convenient way of converting units into smaller or larger units. It also avoids the awkwardness and complexity of the conversion of units in the imperial system. For example, kilograms can easily be converted into grams by simply multiplying the number by 1,000. Conversely, to convert grams to kilograms, you only need to divide the number by 1,000.
In the imperial system, on the other hand, there’s no definite base number for all the different types of measurements. For example, converting a pound to ounces is a bit clunky: you need to multiply a pound by 16. It becomes even more awkward if you want to convert pounds to kilograms, which involves multiplying the pound unit by 0.45359237.
For chemistry A level, these three important units of measurement are used in determining the amount of substance:
- Kilogram (and its derivatives) for mass: This is approximately defined as equivalent to the mass of 1,000 cubic cm of pure water at room temperature and at one atmospheric pressure. The more technical and precise definition involves the Planck constant and the speed of light.
- Litre (and its derivatives) for volume: The SI unit of volume is actually the cubic meter, which is a derived unit. It’s approximately equivalent to 1 kg of pure water at room temperature and at one atmospheric pressure. Litre and millilitre are more commonly used in laboratory settings when measuring liquids with the use of graduated cylinders and other graduated glassware.
- Density: Density is simply the ratio between the mass per unit volume. Therefore, it’s a derived unit. It’s very useful in determining how much matter is packed in a given space. It’s also a good predictor of miscibility and buoyancy. For example, hydrocarbons have lower density than water, which is why oil floats on water.
Lorenzo Romano Amedeo Carlo Avogadro was an Italian aristocrat (Count of Quaregna and Cerreto – but that’s something you probably won’t need to remember for your A level chemistry exam) and scientist who is now widely recognised because of this constant named in his honor. Avogadro’s number, which is 6.02214154 x 1023 particles per mole, is named after the Italian count – but not because he was the one who derived it.
Avogadro is recognised for his important contribution to molecular theory, a contribution that is now known as Avogradro’s law. This law states that the number of molecules in gases of the same volume under the same pressure and temperature is equal.
Avogadro died in 1856, but it took more than half a century before the term Avogadro’s number was used. In fact, it was the French physicist Jean Baptise Perrin who coined the term in 1909. He reported the first estimate of the number based on his research on Brownian motion.
Various techniques have been developed over the decades to derive Avogadro’s number. Accurately determining the number requires a high level of precision in terms of measuring a single pure quantity of an element or compound both on the atomic and macroscopic scales. The same unit of measurement must be used to get the correct proportionality. From there, the number can be calculated.
American physicist, Robert Millikan, was the first to measure Avogadro’s constant in his work on determining the electron charge. In his famous oil droplet experiment, Millikan was able to precisely measure the charge of an electron, which earned him the Nobel Prize in 1923.
However, the charge of a mole of electrons had been known before Millikan made the measurements. It was referred to as the Faraday unit of charge or Faraday constant, named after English scientist Michael Faraday.
Furthermore, J.J. Thomson had already discovered the mass-to-charge ratio of the electron, but the actual values of the mass and charge were unknown. Therefore, the experiments of Millikan paved the way for measuring the mass of the electrons and other subatomic particles. In turn, Avogadro’s number was accurately determined.
Methods of Computing
Our current best estimate of Avogadro’s number is based on the value of the Faraday and the measured charge of one electron:
- Faraday = 96,485.3383 coulombs per mole of electrons
- Electron charge = 1.60217653 x 10-19 coulombs per electron
By simply dividing the charge in a mole of electrons (Faraday constant) by the charge of one electron, you’ll get Avogadro’s number.
Both the Faraday constant and the electron charge values are experimentally determined. The National Institute of Standards and Technology (NIST) is among the institutions that set the standards of measurement for chemistry, which also provide the most accurate and updated measurements of values like the electron charge.
X-ray diffraction techniques are also used to determine Avogadro’s number. Here, the density of an ultrapure sample of a substance on a macroscopic scale is measured. Then, the density of the same sample is measured on a microscopic scale using X-ray diffraction based on the crystalline structure of the substance.
Molarity of Substance
Avogadro’s number is directly related to the molar mass of a substance or a solution. It’s particularly useful in calculating the concentration of a substance. Molarity is the number of moles in one litre of solution, and is crucial in calculating the amount of reactants needed to produce a specific amount of product.
One mole of any substance is equivalent to Avogadro’s number in terms of the number of particles of that substance, which can either be atoms or molecules. It’s a precise way of predicting chemical reactions based on the balanced equation. The molarity law is applicable in all types of solutions, whether liquid, gas, or even solid.
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