Analysis of a sample of an unknown hydrocarbon yields 3.6 grams of carbon and 0.3 grams of hydrogen, indicating an empirical formula of CH. Which of the following formulas could be the molecular formula of the unknown hydrocarbon if the atoms involved have the usual bonding patterns? (A) C2H2, (B) C3H3, (C) C4H5, (D) C5H6, or (E) C6H9.
In this question, we’ve been given the empirical formula of an unknown hydrocarbon. An empirical formula is a formula with the simplest integer ratio of atoms in a compound. But we’ve been tasked with finding the molecular formula for this unknown hydrocarbon, which tells us the amount of atoms of each element within a compound. For example, the molecule hydrogen peroxide is composed of two oxygens bonded together and each of the oxygen atoms are bonded to a hydrogen atom. The empirical formula for hydrogen peroxide is HO because there is one hydrogen atom for every oxygen atom within a molecule of hydrogen peroxide. Hydrogen peroxide’s molecular formula, however, would be H2O2 because there are two hydrogen atoms and two oxygen atoms within every molecule of hydrogen peroxide.
So we can see from this example, the molecular formula will always be some integer multiple of the empirical formula. Since our unknown hydrocarbon has an empirical formula of CH, we can rule out answer choices (C), (D), and (E) because C4H5, C5H6, and C6H9 are not integer multiples of this empirical formula. So that leaves us with either C2H2 or C3H3. The question tells us that the atoms involved in our unknown hydrocarbon have the usual bonding patterns. The usual bonding pattern for carbon is that it forms four bonds. And the usual bonding pattern for hydrogen is that it only forms one.
So now, let’s look at the structure of our two answer choices and see if we can come up with a structure that has the usual bonding patterns for both carbon and hydrogen. The molecule C2H2 has 10 valence electrons. If we connect all our atoms with single bonds, that uses up six of the valence electrons. So we have four remaining to place in the structure. If we try placing these electrons around one of our atoms, we’ll run out of valence electrons before both of the carbons have a full octet. So we can create a full octet for both carbons by placing a triple bond in between them. This is the correct structure for C2H2.
If we look at the structure we’ve just created, each carbon has four bonds which means that it’s following the usual bonding patterns for carbon. And each of the hydrogens has one bond to a carbon. So the hydrogens are also following the usual bonding patterns. So it seems that answer choice (A) is likely our correct answer. But let’s look at answer choice (B) just to be sure. C3H3 would have 15 valence electrons. If we connect all the atoms with single bonds and place the remaining electrons as lone pairs around the carbons, we’ll run out of electrons before we complete each carbon’s octet.
If we attempt to remedy this structure by placing multiple bonds, we’re still not going to have a full octet on one of the carbons due to this extra electron that’s not paired. So no matter how hard we try to create a structure with C3H3 that follows the usual bonding patterns for carbon and hydrogen, we won’t be able to. So the molecular formula of the unknown hydrocarbon with the empirical formula of CH that has usual bonding patterns is most likely C2H2.