finding molecular formula

Question

A is a compound of molecular formula RCOOH, where R contains C and H only. On complete combustion A gave CO₂ and H₂O in the mass ratio of 44:9. The r.m.m. of A is approximately 160. Determine the molecular formula of A.

 Please give me a method to solve this

Answer 1

Here's what I did:

 

First figure out the molecular ratio of H₂O and CO₂ in the output.

 

The rmm of CO₂ is 12 + 2*16 = 44.

The rmm of H₂O is 2 + 16 = 18.

 

So in order to get a mass ratio of 44:9, you'd have to have 2 CO₂ for every 1 H₂O. That gives a ratio of 2 C for every 2 H in the output.  But we know that all the C and H in the combustion output comes from A.  So that means that the number of C's and H's in A must be equal.  Since the number of C and H in COOH are the same, that means that the number of C's and H's in R must also be the same.

 

The rmm of RCOOH is 160.  We already know that the COOH component has an rmm of 12 + 2*16 + 1 = 45.  That means that the rmm of R is 115.  Since the number of C and H in R must be equal, there must be some number of pairs of C and H, with their rmm adding to 115.  Each pair of C and H has an rmm of 12 + 1 = 13.  115 / 13 = 8.85.  That's not a round number of CH pairs.

 

HOWEVER, if by "approximately 160" you mean it could be as high as 162, then you could have 9 C and 9H in R.  That would give a molecular formula for A of C₉H₉COOH or C₉H₁₀O₂.