Is \(\mathrm{C}_{22} \mathrm{H}_{46}\) an alkane, an alkene, or an alkyne? How can you tell?

Alkanes have the general formula: \(\mathrm{C}_n \mathrm{H}_{2n+2}\) Alkenes have the general formula: \(\mathrm{C}_n \mathrm{H}_{2n}\) Alkynes have the general formula: \(\mathrm{C}_n \mathrm{H}_{2n-2}\)

We have \(\mathrm{C}_{22} \mathrm{H}_{46}\), and we want to determine which of the hydrocarbon classes it belongs to. Let's test if it's an alkane: If it is an alkane, then \(2n+2= 46\), with \(n = 22\). Solving for \(n\), we get \(n = \dfrac{46-2}{2} = 22\). Since we get the correct value for n, we can conclude that \(\mathrm{C}_{22} \mathrm{H}_{46}\) is an alkane. However, let's check for the other classes of hydrocarbons: Alkene: If it's an alkene, then \(2n = 46\), with \(n = 22\). In this case, we get \(n = 46/2= 23\), which does not match the given \(n\) value (22). Alkyne: If it's an alkyne, then \(2n-2 = 46\), with \(n = 22\). Solving for \(n\), we get \(n = \dfrac{46+2}{2} = 24\). Again, it does not match the given \(n\) value (22).

Based on the comparison of the given formula to the general formulas for alkanes, alkenes, and alkynes, we can conclude that \(\mathrm{C}_{22} \mathrm{H}_{46}\) is an alkane.