To determine under which conditions the volume of a gas will be greatest, we can refer to the Ideal Gas Law, which is expressed as:
\[ PV = nRT \]
Where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles of gas (constant for this comparison)
- \( R \) = ideal gas constant
- \( T \) = temperature in Kelvin
From the equation, we see that volume \( V \) is directly proportional to temperature \( T \) and inversely proportional to pressure \( P \).
To maximize the volume:
- Increase temperature \( T \): Higher temperature means greater kinetic energy of the gas molecules, leading to an increase in volume.
- Decrease pressure \( P \): Lower pressure allows the gas to expand more, increasing the volume.
Now, evaluating the provided conditions:
- T = 273K and P = 0.25 atm: This condition has low pressure and moderate temperature.
- T = 300K and P = 2 atm: High temperature but also high pressure, which will reduce the volume.
- T = 300K and P = 0.25 atm: This has high temperature and low pressure, likely maximizing volume.
- T = 273K and P = 2 atm: Moderate temperature with high pressure, leading to a reduced volume.
Among these conditions, the combination of T = 300K and P = 0.25 atm will give the greatest volume.
Thus, the correct response is:
T = 300K and P = 0.25 atm.