Unit conversions mathematical equations

The system of atomic units was developed to simplify mathematical equations by setting many fundamental constants equal to 1. This is a means for theorists to save on pencil lead and thus possible errors. It also reduces the amount of computer time necessary to perform chemical computations, which can be considerable. The third advantage is that any changes in the measured values of physical constants do not affect the theoretical results. Some theorists work entirely in atomic units, but many researchers convert the theoretical results into more familiar unit systems. Table 2.1 gives some conversion factors for atomic units. 

This balanced equation can be read as 4 iron atoms react with 3 oxygen molecules to produce 2 iron(III) oxide units. However, the coefficients can stand not only for the number of atoms or molecules (microscopic level) but they can also stand for the number of moles of reactants or products. So the equation can also be read as 4 mol of iron react with 3 mol of oxygen to produce 2 mol ofiron(III) oxide. In addition, if we know the number of moles, the number of grams or molecules may be calculated. This is stoichiometry, the calculation of the amount (mass, moles, particles) of one substance in the chemical equation from another. The coefficients in the balanced chemical equation define the mathematical relationship between the reactants and products and allow the conversion from moles of one chemical species in the reaction to another. 

Mathematics is an important part of operating a process unit. Flow rates must be calculated, filling ratios checked, conversion tables used, additive recipes blended, and special equations applied to industrial processes. The following is a review of some basic mathematical skills and operations. 

Notice that each conversion factor equals 1. That is because the two quantities divided in any conversion factor are equivalent to each other— as in this case, where 4 quarters equal 1 dollar. Because conversion factors are equal to 1, they can be multiplied by other factors in equations without changing the validity of the equations. You can use conversion factors to solve problems through dimensional analysis. Dimensional analysis is a mathematical technique that allows you to use units to solve problems involving measurements. When you want to use a conversion factor to change a unit in a problem, you can set up the problem in the following way. 

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