Step 1: Understanding the Question:
The question asks which listed antibiotic lacks activity against Pseudomonas aeruginosa, a gram-negative organism notorious for antibiotic resistance and for causing infections in hospitalised and immunocompromised patients.
Step 2: Key Concept or Approach:
The key is knowing which antibiotic classes cover gram-negative organisms with an outer membrane versus which ones only work on gram-positive bacteria. Anti-pseudomonal activity requires drugs that can penetrate the gram-negative outer membrane and resist or evade Pseudomonas efflux pumps and beta-lactamases.
Step 3: Working Through the Options:
Ceftazidime is a third-generation cephalosporin specifically developed for its anti-pseudomonal activity and is a mainstay for Pseudomonas infections. Piperacillin is an extended-spectrum penicillin with reliable anti-pseudomonal coverage, commonly combined with tazobactam for the same purpose. Aztreonam, a monobactam, acts on gram-negative aerobes including Pseudomonas and is often used in penicillin-allergic patients needing gram-negative cover. Vancomycin, however, is a glycopeptide that only binds the D-ala-D-ala terminus of peptidoglycan in gram-positive cell walls; it cannot cross the outer membrane of gram-negative bacteria like Pseudomonas, so it has no useful activity against it.
Step 4: Conclusion:
Vancomycin is not effective against Pseudomonas aeruginosa because it is a gram-positive-only agent, making it the correct answer.