- 2987 - AVOGADRO’S - kilogram has how many moles? To measure the mass in kilograms we need to have a kilogram standard. Science would like to have a standard defined in some way tied to nature’s fundamental constants. Like the length of the meter is defined in terms of the constant speed of light.
-------------------- 2987 - AVOGADRO’S - kilogram has how many moles?
- Mass is one of the fundamental constants in nature. Mass is believed to be caused by the Higgs Field existing in the vacuum of space. It is like a field of molasses that resists the change of motion of an object moving through it.
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- The Force needed to move the object equals the mass times the acceleration, F = m*a, or, the mass time the rate of change of velocity. A Force needed to start a mass in motion that is at rest, or zero velocity , is called Inertial Mass. Since F = m*a, then , mass = Force / acceleration. Mass is the Force required to cause a rate of change to the rate of change of distance per unit time.
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- When we say mass is a fundamental constant, we refer to the constant mass of all protons that occupy the nucleus of all atoms.
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--------------------- Proton = 1.67*10^-27 kilograms
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- The mass of every electron that occupies every neutral atom is 1,833 times smaller.
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------------------- Electron = 9.11 * 10^-31 kilograms.
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- We do not know why these fundamental constants have the values they have. We can not derive them from physical theories or equations, they simply are what they are.
And, we believe they are the same every where in the Universe and throughout all time in the Universe. OK, you might ask. What determines the mass of a kilogram?
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- You might be surprised to learn that is totally arbitrary. It happens to be the weight of a platinum cylinder stored in a vault outside of Paris, France. By consensus and definition this cylinder is one kilogram and all mass measured is related to it.
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- Since 1889 the cylinder has gathered dust. It is carefully washed and weighed in comparison with 6 other cylinders, similarly maintained. These cylinders maintained and measured with the highest precision can still change relative to each other on the order of micrograms per century. 0.000001 grams per 100 years.
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- That all seems to be precise enough, however, science would like to have something even better. The cylinder is 1 kilogram to within 0.000000020 kilograms, or precise to 20 parts in a billion.
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- Science would rather have mass defined in terms of another fundamental constant, like the speed of light defines the length of a meter. Instead of using a meter long platinum rod stored in a vault in Paris, a meter is defined as the distance light would travel in 1 / 299,792,458th of a second.
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- Protons and electrons are the fundamental constants of mass, why can’t we define the kilogram is those terms? Well we can. All we need to know is how many atoms there are in a kilogram.
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- Of course, that depends on what atoms we use to be in the kilogram. It makes a big difference whether we choose hydrogen atoms or gold atoms. So, how do we learn how much each atom weighs?
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- The answer to this question all started with Amedeo Avagadro in 1811. He determined that the number of molecules in a gas with a given volume, a given temperature, and a given pressure is always the same number. ( See Review #1072 - Avogadro’s Number - for more details.)
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- He calculated the number of molecules to a mole of gas to be:
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------------- Avogadro’s Number = 6.022 * 10^23 molecules.
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------------- Avogadro’s Number = 602,200,000,000,000,000,000,000 molecules
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- In order to expand this number to include the other gases and other elements he needed to define a consistent quantity equal to the atomic weight, or molecular weight, for each element measured in grams.
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- For example, the number of molecules in one gram-molecule, or mole, of oxygen is 32 grams. There are two atoms of oxygen in each molecule of oxygen. So there are 6.022^10^23 molecules of oxygen in 32 grams of oxygen.
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- Let’s take the carbon-12 atom. From the Periodic Table of Elements the carbon-12 atomic weight is 12.01. One mole of carbon would weigh 12.01 grams. The number of atoms in that mole of carbon would be Avogadro’s number, 6.022 * 10^23 atoms.
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- To calculate how much each atoms weighs:
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------------------------ carbon atom = 12.01 grams / 6.022*10^23 = 1.994*10^-23 grams.
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- One mole of oxygen weighs 15.999 grams.
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------------------ oxygen atom = 15.999 grams / 6.022*10^23 = 2.677 * 10^-23 grams
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- Oxygen is 33% heavier than carbon:
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------------------- 2.677 * 10^-23 grams / 1.994*10^-23 grams = 1.33
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- To define the mass of a kilogram by the number of atoms scientists have chosen a sphere of pure “silicon-28“. One mole of silicon 28 weighs 28 grams. Therefore a kilogram would contain 1,000 grams / 28 grams per mole = 35.7142857 moles of silicon-28 atoms need to be in the sphere that weighs exactly one kilogram.
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- Silicon-28 is two atoms of silicon-14 bond together. Silicon-14 has 4 electrons in its outer shell and naturally binds to another silicon-14 atom to fill the outer shells of each with 8 electrons.
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- A single silicon crystal of extremely high purity has very few lattice defects and each single lattice contains 8 atoms. The dimensions of each lattice cell is measured with an X-ray interferometer.
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- We need to calculate the volume that contains 35.7 moles. Each mole containing 6.022 * 10^23 atoms. Divide by 8 to get the number of silicon crystal cells. Multiply the volume dimensions for each cell to get the dimensions needed for a silicon sphere of exactly 1 kilogram mass. In this way the kilogram mass is calculated from the bottom up, atom by atom, to an accuracy of 30 parts in a billion.
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- The number calculated for Avogadro’s Constant becomes somewhere near 6.02214084 *10^23 + or - 30 parts per billion.
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- The number of silicon-28 atoms in the sphere is:
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--------------- 21,507,645,850,000,015,000,000,000 atoms
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and --------- 21,507,645,849,000,985,000,000,000 atoms
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- We need the count to be within + or - 15 trillion atoms in order to be better than 30 parts per billion. ( 35.7 moles * 6.022*10^23 + or - the uncertainties). Avogadro Constant is defined as the number of molecules contained in a “mole” of any substance. The Constant is a proportionality factor and is the same for all substances, 6.022*10^23 per mole.
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- Mole, that has the symbol “mol”, is an amount of substance that contains as many elementary entities as there are atoms in 0.012 kilograms of carbon-12. In other words, the number of atoms in the atomic weight of carbon-12 measured in grams. The elementary entities must be specified as atoms, molecules, ions, electrons, or other particles. There is always confusion between atoms and molecules, atomic weights and molecular weights, but, Avogadro’s Number of Proportionality works for either.
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- You may have already noticed. After all that work the metal cylinder in Paris is a still a better standard with an accuracy of 20 parts per billion.
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- However to by honest about this. We do not need the number of atoms to be exactly accurate. What we need for the standard is for it to be “constant“. Regardless of the number we need to get the same answer every time. Remember, the number is arbitrary.
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- Being a fundamental constant that we can always count on to repeat is what is important. Is anyone up for the task?
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------------------------------- See Review:
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- 1072 “Avogadro’s Number”. This review answers the question, Are there as many oxygen atoms in a single breath as there are breaths in all the Earth’s atmosphere? What’s your guess, “i.e. calculation“?
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January 20, 2021 AVOGADRO’S - kilogram moles? 1238 2987
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