Which proportionality correctly represents the result of combining Avogadro's law with Boyle's law?

• A. V \propto 1/(nP)
• B. V \propto P/n
• C. V \propto nP
• D. V \propto n/P

Answer: (D)

Verified step by step guidance

1. Recall Avogadro's law, which states that at constant temperature and pressure, the volume \(V\) of a gas is directly proportional to the number of moles \(n\): \[V \propto n\]
2. Recall Boyle's law, which states that at constant temperature and number of moles, the volume \(V\) of a gas is inversely proportional to the pressure \(P\): \[V \propto \frac{1}{P}\]
3. To combine Avogadro's law and Boyle's law, consider that volume depends directly on \(n\) and inversely on \(P\), so you multiply the proportionalities: \[V \propto n \times \frac{1}{P}\]
4. Simplify the combined proportionality to get: \[V \propto \frac{n}{P}\]
5. This shows that volume increases with the number of moles and decreases with increasing pressure, which matches the combined gas law behavior when temperature is constant.