Under which condition does the volume of an ideal gas approach zero according to the ideal gas law?

• A. When the pressure approaches zero at constant temperature
• B. When the temperature increases at constant pressure
• C. When the temperature approaches absolute zero (0 K) at constant pressure
• D. When the number of moles increases at constant temperature and pressure

Answer: (C)

Verified step by step guidance

1. Recall the ideal gas law: \(P \times V = n \times R \times T\), where \(P\) is pressure, \(V\) is volume, \(n\) is number of moles, \(R\) is the gas constant, and \(T\) is temperature in Kelvin.
2. To understand when volume \(V\) approaches zero, rearrange the ideal gas law to solve for \(V\): \(V = \frac{n \times R \times T}{P}\).
3. Analyze how \(V\) changes with each variable: volume is directly proportional to temperature \(T\) and number of moles \(n\), and inversely proportional to pressure \(P\).
4. Consider the effect of temperature approaching absolute zero (\(T \to 0\) K) at constant pressure and number of moles: since \(V\) is proportional to \(T\), \(V\) will approach zero.
5. Check other options: if pressure approaches zero, volume would increase; if temperature increases, volume increases; if number of moles increases, volume increases. Therefore, only temperature approaching absolute zero at constant pressure causes volume to approach zero.