How to Measure Small Things
Measurement of vast distances is a straightforward job. We use large units of length such as kilometres for inland applications, light years for stellar applications and 1 parsec (3.26 light-years) for intergalactic applications. On another end of the scale, we have minimal measures. We can only understand millimetres and our naked eyes can sense up to 0.1 mm, but after that, it becomes tough to visualize. We have only recently begun to explore and understand the miniature world out there with modern technological development. To measure small things, we need to understand the Avogadro number and his hypothesis to know and how to measure the small distances.
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Avogadro Hypothesis
An electron microscope is a particular type of microscope that illuminates the sample with a beam of accelerated electrons. This electron will be needed to have a very short wavelength, approximately 100,000 times shorter than the visible light, hence, giving the electron microscope a better resolution characteristic than an optical microscope. This can be heavily used to observe tiny things such as atoms and molecules. A transmission electron microscope can extensively achieve better than 50 Picometer (10-12) resolution, and we should also remember that atoms range from 30 – 300 Pico meters. There is another interesting fact that the radius of an atom is approximately more than 10000 times the radius of the nucleus and the atom is 99.999999% space. Before any of the technological advancements in the peripheries, we had only come to know about the rough estimate of the size of the atom even after the Rutherford alpha particle which on scattering experiment gave us the size of the nucleus in an approximate measurement. Now, we have to understand some of these methods about how to measure small things.
Explain Avogadro's Number
The actual volume which is occupied by the particular atom of a substance is every timeless than the volume of that important substance because the packaging of atoms is inefficient. Due to this, there are empty spaces between atoms which results in an inflated volume. According to Avogadro's number, the actual volume which is occupied by the particular atoms in a certain mass of a denoted substance is two-thirds the volume which is occupied by that mass of the substance. Suppose if we take a mole of a substance, let us say Carbon. A mole generally refers to the amount of the substance in grams which is equivalent to the atomic weight of the substance. So if we keep talking of Carbon, one mole of Carbon consists of 12 g of pure carbon-12 (12C). There is another interesting fact about Avogadro's number unit that is: the definition of Avogadro's number is the same as of a mole which is given as the Avogadro uses Carbon as the standard for mole.
We previously know that volume is the ratio of mass divided by density. We can easily calculate the atomic volume of the whole mole.
By the Avogadro's number definition,
Molar Volume = Molar Mass (gm)/ Density (gm/cm3)
Solved Examples
1. How is Avogadro's Number Used?
The mole system allows the scientists to accurately calculate the number of elementary entities (usually atoms or molecules) in a particular mass of a given substance. Avogadro's number is absolute and constant: there are 6.022×1023 elementary particles in one mole. This can extensively be written as 6.022×1023 mol-1.
Did You Know?
This is a fantastic fact that Amedeo Avogadro comes into the territory, of course, his real name is Lorenzo Romano Amedeo Carlo Avogadro di Quaregna e di Cerreto—but everyone calls him Avogadro for apparent reasons. Avogadro developed the idea which is given:
If we think that Avogadro just introduced just a version of the Ideal Gas Law, then we are correct—but we have to move on to a useful example. Suppose if we take water (that is H2O) and run a short streak of electric current through it, it is called electrolysis. This process can easily break the water molecules into hydrogen gas and oxygen gas (which we could collect). If we had these two gases at the same temperature and pressure, the hydrogen gas would surely take up twice the volume compared to the oxygen gas. Why? Well, when we have to break up the water molecule, we get twice as much hydrogen as oxygen.
FAQs on Avogadro Hypothesis and Measurement
1. What is the fundamental statement of Avogadro's hypothesis?
Avogadro's hypothesis states that under the same conditions of temperature and pressure, equal volumes of all gases contain an equal number of molecules. This principle is crucial as it connects macroscopic properties of gases, like volume, to their microscopic properties, like the number of particles.
2. What is the mathematical formula that represents Avogadro's Law?
Avogadro's Law is mathematically expressed as V ∝ n, where 'V' is the volume of the gas and 'n' is the number of moles of the gas, provided temperature and pressure are constant. For comparing two different states of a gas, the formula is written as V₁/n₁ = V₂/n₂.
3. What are the main applications of Avogadro's hypothesis in Physics and Chemistry?
Avogadro's hypothesis has several important applications, including:
- Helping to determine the atomicity of gases (the number of atoms in one molecule).
- Establishing the relationship between a gas's molecular mass and its vapour density.
- Calculating the molar volume of any ideal gas at Standard Temperature and Pressure (STP), which is approximately 22.4 litres.
- Providing a method to estimate the approximate size of individual atoms and molecules.
4. How can Avogadro's number be used to estimate the size of a single carbon atom?
To estimate the size of a carbon atom, we can relate its macroscopic properties to the atomic scale using Avogadro's number. First, we find the volume of one mole of carbon (Molar Volume = Molar Mass / Density). Then, we divide this molar volume by Avogadro's number (6.022 × 10²³) to get the approximate volume occupied by a single carbon atom. By assuming the atom is a sphere (V = 4/3πr³), we can then calculate its approximate radius.
5. What is the important difference between a 'mole' and 'Avogadro's number'?
This is a common point of confusion. A mole is a unit of measurement for an amount of a substance, similar to how a 'dozen' is a unit for the number 12. Avogadro's number, on the other hand, is the actual count of particles (atoms, molecules, ions) in one mole of any substance. Its value is approximately 6.022 x 10²³ particles per mole. So, the mole is the unit, and Avogadro's number is the quantity that defines the unit.
6. How is Avogadro's hypothesis connected to the Ideal Gas Law?
Avogadro's hypothesis (V ∝ n) is a foundational component of the Ideal Gas Law (PV = nRT). The Ideal Gas Law combines Avogadro's Law with Boyle's Law (V ∝ 1/P) and Charles's Law (V ∝ T) into a single, comprehensive equation that describes the behaviour of most gases under various conditions. Therefore, Avogadro's work was essential for developing this universal law.
7. Why is the actual volume occupied by atoms in a substance less than the total volume of that substance?
The total volume of a substance is greater than the sum of its atoms' volumes due to inefficient packing. Atoms are not perfect cubes that fit together without gaps. In solids and liquids, there are always small empty spaces between the atoms, known as interstitial voids. This empty space contributes to the overall volume of the substance, making it larger than the combined volume of the atoms themselves.
8. Is Avogadro's 'hypothesis' still just a hypothesis, or is it a proven law?
When Amedeo Avogadro first proposed the idea in 1811, it was a 'hypothesis'—a theoretical proposal without direct experimental proof. However, over the following century, overwhelming evidence from various experiments, especially from the kinetic theory of gases, confirmed its validity. Today, it is universally accepted and treated as a fundamental scientific 'law'. The original name 'hypothesis' is often retained for historical reasons.
