# 4.10: Molecular Weight: Conversions

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In the previous section, the molecular weights (MWs) of several compounds were calculated by adding the mass contributions of the constituent elements found within each corresponding compound. Upon completing each calculation, the resultant solution was then represented as a molar equality, a conversion factor, and a "hidden" conversion factor. As has been the case with the Avogadro's number, "component within," and atomic weight molar standards, a molecular weight conversion factor can be applied to bring about a desired unit transformation.

## Applying Molecular Weight Conversion Factors in Dimensional Analysis

As stated previously, the quantity containing the unit that is being canceled must be written in the *denominator *of a conversion factor, in order to bring about a desired unit transformation. Orienting the applied conversion factor in this way will cause the given unit, which appears in a numerator, to be divided by itself and, therefore, "cancel," since the same unit appears in the denominator of the conversion factor. Remember that all numerical values that have been discussed in this chapter are associated with *two *units. Therefore, in order to achieve complete unit cancelation, a conversion factor that results in the *simultaneous *elimination of *both units* must be applied.

For example, use a conversion factor based on the molecular weight of ZnBr_{2}, 225.19 g/mol ZnBr_{2}, to calculate how many grams of ZnBr_{2} are present in 0.25 moles of ZnBr_{2}.

The reference to a mass unit, "grams," in the given problem, coupled with the knowledge that ZnBr_{2}, zinc bromide, is a compound, indicates that a mass-based molecular weight conversion factor should be applied to solve this problem. The "/" in the given molecular weight unit is read as "per," which is the indicator word that is associated with identifying a "hidden" conversion factor. Because the word "per" implies a ratio, which is associated with the mathematical operation of division, the word "per" is represented as the fraction bar in a conversion factor. Any number or unit read *before* the word "per" becomes the numerator of the conversion, and any number or unit found *after* the word "per" is written in the denominator. The value "225.19 g/mol ZnBr_{2}" can, therefore, be written as

\( \dfrac{225.19 {\text{ g }} \ce{ZnBr_2}}{\text{ mol } \ce{ZnBr_2}} \) or \( \dfrac{\text{ mol } \ce{ZnBr_2}}{225.19 {\text{ g }} \ce{ZnBr_2}} \)

The conversion factor on the left is a direct representation of the given molecular weight, and the second conversion factor is derived by interchanging where each quantity is written, relative to the fraction bar. However, only the conversion factor on the left will allow for the complete cancelation of the given unit, "moles of ZnBr_{2}," since *both *of the units that are being canceled must be written in the denominator of the conversion factor that should be applied to solve the given problem. Therefore,

\( {0.25 \; \cancel{\rm{mol} \; \rm{ZnBr_2}}} \times\) \( \dfrac{225.19 \; \rm{g} \; \rm{ZnBr_2}}{\; \cancel{\rm{mol} \; \rm{ZnBr_2}}}\) = \( {\text {56.2975}}\) \({\rm{g} \; \rm{ZnBr_2}}\) ≈ \( {\text {56}}\) \({\rm{g} \; \rm{ZnBr_2}}\)

The solution is calculated by multiplying the given number by the value in each numerator, and then dividing by the quantity in each denominator. When using a calculator, each conversion factor should be entered in parentheses, * or* the "=" key should be used after

*division. Finally, the correct number of significant figures should be applied to any calculated quantity. Since the math involved in dimensional analysis is multiplication and division, the number of significant figures in each number being multiplied or divided must be counted, and the answer must be limited to the lesser count of significant figures. Neither the given number nor the molecular weight that was utilized above are exact numbers. As the given number contains fewer significant figures, the final answer should be rounded to two significant digits, as shown above.*

*each*