In organic chemistry, what is the general formula for a straight chain saturated hydrocarbon (alkane) containing n carbon atoms?

Introduction / Context:
Alkanes are the simplest class of hydrocarbons and consist of carbon and hydrogen atoms joined by single covalent bonds. Straight chain alkanes follow a simple general formula that relates the number of carbon atoms to the number of hydrogen atoms. This formula is widely used in writing molecular formulas, predicting patterns in homologous series and solving stoichiometry problems. The question asks for the general formula of a straight chain alkane with n carbon atoms.

Given Data / Assumptions:
- Alkanes are saturated hydrocarbons, meaning all carbon carbon bonds are single bonds and each carbon satisfies its valency with hydrogen or other carbons.
- We consider straight chain alkanes with no rings or double bonds, such as methane, ethane, propane and butane.
- The variable n represents the number of carbon atoms in the chain.
- The options propose different algebraic expressions for the relationship between carbon and hydrogen atoms.

Concept / Approach:
For a straight chain alkane with n carbon atoms, each interior carbon is bonded to two other carbons and two hydrogens, while the two terminal carbons are each bonded to one carbon and three hydrogens. Counting carefully, we find that the total number of hydrogen atoms is always 2n + 2 for an acyclic saturated hydrocarbon. This leads to the general formula CnH2n+2. Other formulas, such as CnH2n, correspond to alkenes or cycloalkanes, while CnH2n-2 can correspond to alkynes or cycloalkadienes. The formula CnH2n+2 is specific to open chain alkanes.

Step-by-Step Solution:
Step 1: Check simple examples of straight chain alkanes to see the pattern. Methane is CH4, ethane is C2H6, propane is C3H8 and butane is C4H10. Step 2: For methane, n equals 1 and the formula CH4 fits the pattern C1H2(1)+2, which is CH4. Step 3: For ethane, n equals 2 and the formula C2H6 fits C2H2(2)+2, which is C2H6. Step 4: For propane, n equals 3 and the formula C3H8 fits C3H2(3)+2, which is C3H8, confirming the pattern. Step 5: From this pattern, conclude that the general formula for a straight chain alkane with n carbon atoms is CnH2n+2.

Verification / Alternative check:
We can also verify the formula by counting bonds. In an open chain saturated hydrocarbon, each carbon forms four bonds. The chain of n carbons has (n - 1) carbon carbon single bonds. If we count all valence bonds and recognise that each carbon provides four bonds and each carbon carbon bond connects two carbons, we can derive that the remaining bonds must connect to hydrogen atoms. Solving this simple counting leads to the relationship that there are 2n + 2 hydrogen atoms. This bond counting argument is a standard derivation in organic chemistry and supports the formula CnH2n+2 for acyclic alkanes.

Why Other Options Are Wrong:
Option A, C2nH2n+3, does not match the formula for known simple alkanes and gives incorrect hydrogen counts. Option C, CnH2n, corresponds to alkenes with one double bond or to cycloalkanes, which are unsaturated or cyclic and not simple straight chain alkanes. Option D, CnH3n+2, gives hydrogen numbers that are too high for saturated carbon frameworks. Option E, C2nH2n-2, resembles formulas for alkynes or other unsaturated compounds with multiple bonds. None of these alternatives correctly describe straight chain saturated hydrocarbons.

Common Pitfalls:
Students sometimes mix up the general formulas for different homologous series, especially alkanes, alkenes and alkynes. Another pitfall is to apply the alkane formula to cyclic compounds without considering the effect of ring closure on hydrogen count. To avoid these mistakes, it is useful to remember the key patterns: CnH2n+2 for open chain alkanes, CnH2n for alkenes and cycloalkanes and CnH2n-2 for alkynes and some dienes. Working through a few concrete examples, as shown above, can also reinforce the correct formula for straight chain alkanes.

Final Answer:
The general formula for a straight chain saturated hydrocarbon (alkane) with n carbon atoms is CnH2n+2.