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The modern approach to chemical calculations is based on the principles of stoichiometry, which is the quantitative study of chemical reactions. It involves using balanced chemical equations to determine the amounts of reactants and products involved in a chemical reaction.

The key concept in stoichiometry is the mole, which is a unit of measurement used to express the amount of a substance. One mole of a substance contains Avogadro's number of particles (6.022 x 10^23).

To perform chemical calculations, it is necessary to know the molar mass of the substance, which is the mass of one mole of the substance. This can be calculated by adding up the atomic masses of the elements in the compound.

The modern approach to chemical calculations also involves the use of dimensional analysis, which is a method of converting units and quantities using conversion factors. This involves multiplying the given quantity by a conversion factor that relates the starting unit to the desired unit.

Other important concepts in chemical calculations include limiting reactants, which are the reactants that are completely consumed in a reaction, and theoretical yield, which is the maximum amount of product that can be obtained from a reaction based on the amount of limiting reactant present.

Overall, the modern approach to chemical calculations involves a combination of mathematical concepts and chemical principles to quantitatively analyze chemical reactions.
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