Empirical and Molecular Formula

Question

A compound containing only phosphorous and oxygen was found to have 43.64 % phosphorous by mass and 56.36 % oxygen by mass. The molecular formula has a molar mass of 141.94 g/mol.  Determine the empirical formula and the molecular formula of the compound.

Answer 1

There are several ways of doing this, Here is a "mathy" way:

Let "m_T" be the total mass of the compound, let m_P be the mass of the phosphorous, and let m_O be the mass of the oxygen

Then, by the conservation of mass, m_P + m_O = m_T

We can also say that m_T = (molar mass of the compound)(number of moles of the compound)

And we can say m_P = (molar mass of phosphorous)(number of atoms of phosphorous)

And we can say m_O = (molar mass of oxygen)(number of atoms of oxygen)

So, because m_P + m_O = m_T then:

(molar mass of phosphorous)(number of atoms of phosphorous) + (molar mass of oxygen)(number of atoms of oxygen) = (molar mass of the compound)(number of moles of the compound) or:

(30.974)(number of atoms of phosphorous) + (15.999)(number of atoms of oxygen) = (141.94)(number of moles of the compound)

Ley x = number of atoms of phosphorous and let y = number of atoms of oxygen and let us assume we will get 1 mole of the compound. Then:

30.974x + 15.999y = 141.94

Since both x and y must be integers, we can create a little table and suppose various integer values for x then calculate a corresponding value of y and look for y to be an integer:

Integer Value Corresponding Value

of x of y

1 6.939

2 4.9998

3 3.064

4 1.128

5 -0.808

Notice the value of 5 results is a negative so cannot be since negative values don't make sense in this application. Also notice that x = 2 gave us almost a perfect 5 for the integer value of y.

Therefore, there must be a ratio of 2 atoms of phosphorous to 5 atoms of oxygen making the compound formula P₂O₅ and since this cannot be reduced, it is also the empirical formula.