Main Concept The number of particles in a given chemical substance is an important quantity in the analysis of chemical and nuclear reactions. However, in most practical situations, the precise number is impossible to count, and an estimate of the number is typically a large enough number to make calculations more cumbersome than desired. To make calculations simpler, chemists introduced a new unit, the mole, defined as the amount of substance that contains the same number of elementary particles (atoms, molecules, ions, electrons) as there are atoms in 12 grams of carbon-12, carbon's most common isotope. The actual number (of atoms in 12 grams of carbon-12) has been experimentally determined to be $6.02214129×{10}^{23}$, and this is known as Avogadro's number. The amount of a substance in a chemical is an expression of how many moles the substance contains. Avogadro's constant, equal to Avogadro's number divided by one mole, or , is a factor which allows conversion between the expression of a quantity in terms of number of particles, and its expression in terms of amount of substance. The molar mass of a substance is its mass divided by the amount of substance. The molar mass of carbon-12 is , by definition. For other substances the molar mass is equal to the substance's mean molecular mass, where the average is taken over all the isotopes that make up that substance.   Avogadro's constant can be used as a conversion factor between mass, amount of substance and number of particles (usually atoms or molecules) as summarized by the following diagram: It just so happens that Avogadro's number is very close to (within .38% of) a power of $2$, namely . This allows for simple rough approximations in nuclear physics when considering chain reaction growth rates or particle decay.



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