Notes to a video lecture on http://www.unizor.com
For a short introduction to the International System of units (SI) see the previous lecture "SI Intro & Time" within this topic.
Amount of Substance Units
Consider a rocket in space that works on hydrogen. It needs certain amount of hydrogen and certain amount of oxygen. Hydrogen, burning with oxygen, produces vapors of water and energy needed to move the rocket.
Hydrogen occurs in molecules of two atoms paired together as represented by formula H2.
Similarly, molecules of oxygen also consist of two atoms O2.
The molecule of water consists of two atoms of hydrogen connected with one atom of oxygen as represented by a structure H−O−H and formula H2O.
Therefore, to make a reaction between molecules of hydrogen and oxygen, we have to take 2 molecules of hydrogen (2·H2) for each molecule of oxygen (O2).
So, the reaction we want to make in a rocket, operating with molecules, can be represented by the following equation
H2 + H2 + O2 = 2·H2O
From the practical viewpoint, how can we measure the proper quantities of hydrogen and oxygen to take on board in a rocket to make sure that all molecules will react with each other and there would be no excess of either gas?
A relatively good approach is to compare masses of atoms of hydrogen and oxygen.
An atom of hydrogen consists of a single proton in its nucleus and one electron flying on an orbit around a nucleus.
An atom of oxygen consists of eight protons and eight neutrons in a nucleus plus eight orbiting electrons.
For simplicity, assume that the mass of electrons in an atom is negligent relatively to the mass of proton or neutron, and masses of protons and neutrons are practically the same. We will correct this assumption later.
Therefore, we can say that the mass of one atom of oxygen is greater than the mass of one atom of hydrogen in approximately 16 times. Same proportion exists between their molecules because each molecule of either gas consists of two atoms.
Hence, there are as many molecules in 1 gram of hydrogen as in 16 grams of oxygen.
It's true for any other measure of mass, like kilogram or tonne. The proportion of the amounts of these two substances that contain the same number of molecules will always be 1:16.
Since we need two molecules of hydrogen for each molecule of oxygen to complete the reaction of all molecules, it seems reasonable to take 2 measures of hydrogen (by mass) per 16 measures of oxygen.
Generally speaking, if we deal with some substance that consists of uniform molecules X, and we know that the number of protons and neutrons of each such molecule is NX, then in NX grams (or any other unit of mass) of this substance will be the same number of molecules as in NY grams (or, correspondingly, other unit of mass) of substance Y that consists of molecules with NY protons and neutrons.
For example, a molecule of hydrochloric acid HCl contains one proton in the hydrogen atom plus 17 protons and 18 neutrons in the chlorine atom. This totals to 36 nucleons (protons+neutrons) per molecule of this substance.
The principle we spoke about states that in 36 units of mass of hydrochloric acid HCl there are approximately the same number of molecules as in 2 same unit of mass of molecular hydrogen H2 or in 32 same units of mass of molecular oxygen O2.
Experimentally it was determined that in N gram of any uniform substance, having N protons and neutrons in each molecule, there are about 6.02214076·1023 molecules. This number is called Avogadro constant.
So, if a uniform substance has molecular weight (number of nucleons) N, its amount of N grams contains, approximately, Avogadro number of molecules. This amount of this substance is called a mole.
Thus, one mole of molecules of hydrogen (2 protons in a molecule H2) is two grams, one mole of molecules of oxygen (8·2=16 protons, 8·2=16 neutrons in a molecule O2) is 32 gram, one mole of molecules of carbon (6 protons, 6 neutrons in a molecule C) is 12 gram, one mole of hydrochloric acid (1+17=18 protons, 18 neutrons in a molecule HCl) is 36 gram.
The obvious improvement is to calculate the molecular weight precisely, taking into consideration all particles inside. The unit of atomic mass, as was discussed in earlier lectures, was 1/12th of the mass of an atom of carbon-12. For example, the molecular weight of hydrochloric acid is not 36, but 36.458. So, strictly speaking, one mole of hydrochloric acid is 36.458 gram. This amount of acid contains Avogadro number of molecules.
To avoid imprecision, in 2019 there was a revision of the unit mole and physicists declared that one mole of any substance is EXACTLY the Avogadro number of its molecules.
That definition is much more precise and not connected to molecular weight, which is always approximate.
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