Which of the following ideal gas relationships is illustrated by curve (a)?

• A. Gay-Lussac's Law: P / T = constant (at constant V and n)
• B. Charles's Law: V / T = constant (at constant P and n)
• C. Avogadro's Law: V / n = constant (at constant P and T)
• D. Boyle's Law: P V = constant (at constant T and n)

Answer: (D)

Verified step by step guidance

1. Identify the variables involved in the curve (a) from the graph or problem context. Typically, Boyle's Law relates pressure (P) and volume (V) at constant temperature (T) and amount of gas (n).
2. Recall Boyle's Law formula: \(P \times V = \text{constant}\) when temperature and moles of gas are held constant.
3. Check if the curve (a) shows an inverse relationship between pressure and volume, meaning as pressure increases, volume decreases, or vice versa, which is characteristic of Boyle's Law.
4. Compare this behavior with the other laws: Gay-Lussac's Law relates pressure and temperature at constant volume and moles, Charles's Law relates volume and temperature at constant pressure and moles, and Avogadro's Law relates volume and moles at constant pressure and temperature.
5. Conclude that if the curve (a) shows \(P\) and \(V\) changing inversely while \(T\) and \(n\) remain constant, then the relationship illustrated is Boyle's Law: \(P \times V = \text{constant}\).