Final answer:
The order of increasing energy for the conformations of butane from lowest to highest is anti (A) < gauche (B) < first eclipsed (C) < cis eclipsed (D).
Step-by-step explanation:
The question asks us to rank the conformations of butane in terms of increasing energy. Starting from the most stable conformation, we have the anti conformation labeled as 'A,' which is the lowest in energy because it has the bulky methyl groups (-CH3) farthest apart. As we rotate the molecule 60°, we reach an eclipsed conformation labeled 'C,' which is 16 kJ/mol higher in energy than 'A' due to torsional strain. A further 60° rotation brings us to another staggered conformation called the gauche conformation, labeled 'B,' which is 3.8 kJ/mol higher than the anti conformation. Lastly, another 60° rotation leads to a conformation where the methyl groups are eclipsing each other, labeled 'D,' which is the highest energy conformation. Therefore, the order of increasing energy for the given conformations is A (anti) < B (gauche) < C (first eclipsed) < D (cis eclipsed).