How would you determine the molecular formula from the following empirical formula and molar mass: NPCl2, 348 g/mol?

Nov 26, 2015

${\left({\text{NPCl}}_{2}\right)}_{3}$

Explanation:

So, you know that the compound's empirical formula is ${\text{NPCl}}_{2}$.

As you know, a compound's empirical formula tells you the smallest whole number ratio that exists between the elements that make up said compound is.

In other words, the empirical formula doesn't tell you how many moles of each element the compound's molecule contains, it only tells you what the basic building block of the molecule is.

The molar mass, on the other hand, tells you what the mass of one mole of that compound is.

This means that the molar mass takes into account the molar mass of every atom that's a part of the molecule. So, if you know what the building block looks like, and what the mass of a mole of the compound is, you can use the molar mass of the building block to determine how many of those you need.

$\textcolor{b l u e}{\text{molecular formula" = "empirical formula} \times n}$

To get the molar mass of the empirical formula, add the molar mass of the atoms that are a part of the empirical formula - do not forget that you have 2 atoms of chlorine in there!

${M}_{\text{M empirical formula" = M_"M N" + M_"M P" + 2 xx M_"M Cl}}$

${M}_{\text{M empirical formula" = "14.00674 g/mol" + "30.9736 g/mol" + 2 xx "35.4527 g/mol}}$

${M}_{\text{M empirical formula" = "115.886 g/mol}}$

So, you now know that

$115.886 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{g/mol"))) * color(blue)(n) = 348 color(red)(cancel(color(black)("g/mol}}}}$

This means that $\textcolor{b l u e}{n}$ will be

color(blue)(n = 348/115.886 = 3.003 ~~ 3

The molecular formula of the compound will thus be

${\left({\text{NPCl}}_{2}\right)}_{\textcolor{b l u e}{3}} \to$ hexachlorophosphazene