Question

which of the following equations properly describes the ratio of the molecular formula mass to the empirical formula mass?

molecular or molar mass (amu or \\( \frac{8}{\text{mol}} \\)) / empirical formula mass (amu or \\( \frac{8}{\text{mol}} \\)) = n formula units/molecule

n formula units/molecule / molecular or molar mass (amu or \\( \frac{8}{\text{mol}} \\)) = empirical formula mass (amu or \\( \frac{8}{\text{mol}} \\))

empirical formula mass (amu or \\( \frac{8}{\text{mol}} \\)) / molecular or molar mass (amu or \\( \frac{8}{\text{mol}} \\)) = n formula units/molecule

(n formula unit/molecule) x molecular or molar mass (amu or \\( \frac{\text{g}}{\text{mol}} \\)) = empirical formula mass (amu or \\( \frac{\text{g}}{\text{mol}} \\))

Explanation:

Step1: Recall the relationship between molecular formula and empirical formula

The molecular formula is a multiple \(n\) of the empirical formula. Mathematically, \(Molecular\ formula=(Empirical\ formula)_n\). In terms of mass, \(Molecular\ mass = n\times Empirical\ formula\ mass\), where \(n=\frac{Molecular\ mass}{Empirical\ formula\ mass}\) and \(n\) represents the number of formula units per molecule.

Step2: Analyze each option

• Option 1: \(\frac{molecular\ or\ molar\ mass(amu\ or\frac{g}{mol})}{empirical\ formula\ mass(amu\ or\frac{g}{mol})}=n\ formula\ units/molecule\). This is consistent with the relationship \(n = \frac{Molecular\ mass}{Empirical\ formula\ mass}\) derived from \(Molecular\ mass=n\times Empirical\ formula\ mass\).
• Option 2: \(\frac{n\ formula\ units/molecule}{molecular\ or\ molar\ mass(amu\ or\frac{g}{mol})}=empirical\ formula\ mass(amu\ or\frac{g}{mol})\). Rearranging gives \(n = empirical\ formula\ mass\times molecular\ mass\), which is incorrect.
• Option 3: \(\frac{empirical\ formula\ mass(amu\ or\frac{g}{mol})}{molecular\ or\ molar\ mass(amu\ or\frac{g}{mol})}=n\ formula\ units/molecule\). This would imply \(n=\frac{Empirical\ formula\ mass}{Molecular\ mass}\), which is the reverse of the correct relationship.
• Option 4: \((n\ formula\ unit/molecule)\times molecular\ or\ molar\ mass(amu\ or\frac{g}{mol})=empirical\ formula\ mass(amu\ or\frac{g}{mol})\). Rearranging gives \(n=\frac{Empirical\ formula\ mass}{Molecular\ mass}\), which is incorrect.

Answer:

First option: \(\frac{molecular\ or\ molar\ mass(amu\ or\frac{g}{mol})}{empirical\ formula\ mass(amu\ or\frac{g}{mol})}=n\ formula\ units/molecule\)