Video Transcript
What is the general formula for the group of compounds to which the following displayed formula is related?
First of all, we need to know what a general formula is. A general formula is a simple mathematical formula that describes the abundance of different elements within a compound. Let’s start by looking at the general formula for alkanes. Here are the displayed formulas for three example alkanes. By counting the number of carbon atoms, we find out their names to be methane, ethane, and hexane. Each of these molecules will have a different molecular formula. Methane has one carbon atom and four hydrogen atoms. So it has the molecular formula CH4. Ethane has the molecular formula C2H6, and hexane has the molecular formula C6H14.
The formulas that we have derived are specific to each molecule. But we’re looking for the general formula. The general formula for linear and branched alkanes is C𝑛H2𝑛+2 , where 𝑛 is the number of carbon atoms. So this means that in a linear alkane molecule the number of hydrogen atoms is double the number of carbon atoms plus two.
Let’s check that this general formula applies to the example alkane molecules. Methane has one carbon atom, so 𝑛 is one. When we substitute 𝑛 as one, we get C1H2×1+2 This gives us C1H2+2, which is equivalent to CH4. CH4 is the molecular formula for methane. So we know that this general formula does work for methane. Similarly, if we substitute 𝑛 as two for ethane, we get C2H6. This is the molecular formula for ethane. So we know that the general formula works for this alkane too.
Substituting 𝑛 as six into the general formula gives us the molecular formula of hexane. So the general formula applies to these three molecules and all other linear alkanes. When the displayed formulas are drawn like this, it’s actually quite easy to see where the general formula comes from. If we have 𝑛 number of carbon atoms, then we will also have 𝑛 hydrogen atoms above these carbon atoms, 𝑛 hydrogen atoms below these carbon atoms, giving us two 𝑛 hydrogen atoms so far. And each molecule has an extra hydrogen atom bonded to each end, giving us the plus two.
We have now confirmed that the general formula for a linear alkane is C𝑛H2𝑛+2. But the molecule given to us in the question is an alkene because it’s a hydrocarbon containing a carbon-carbon double bond. And it is monounsaturated because it only contains one carbon-carbon double bond. Let’s draw out the displayed formulas for a few monounsaturated alkenes.
The alkenes shown have two, three, four, and nine carbon atoms, respectively. So the name of the first molecule is ethene. The second is a propene. The third is a butene. And the fourth is a nonene. If we also count up the number of hydrogen atoms they have, we find out that these molecules have the molecular formulas C2H4, C3H6, C4H8, and C9H18. If we pay close attention to these molecular formulas, we will see that the number of hydrogen atoms is double that of the number of carbon atoms. So for every 𝑛 carbon atoms, there are two 𝑛 hydrogen atoms. Therefore, the general formula for monounsaturated alkenes is C𝑛H2𝑛.
As this is the general formula for the group of compounds to which the molecule in the question is related, it is our answer. But just to confirm, let’s check that this general formula works for the molecule given in the question. The molecule in the question has six carbon atoms. So 𝑛 is six. If we put 𝑛 is six into the general formula, we get C6H6×2. This is equivalent to C6H12. If we count up all the hydrogen atoms in this molecule, we find that there are 12. So we can be sure that the general formula C𝑛H2𝑛 is the general formula for monounsaturated alkenes, which is the group of compounds to which the displayed formula in the question is related. So our final answer is C𝑛H2𝑛.
