Final answer:
To increase the pressure of argon from 3.5 atm to 557.15 kPa, the volume would need to be approximately 1.9065 L, as determined using Boyle's Law after converting the initial pressure to kPa.
Step-by-step explanation:
To find the new volume required to increase the pressure of argon to 557.15 kPa, we can use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when the temperature and the amount of gas are held constant. First, we need to make sure that the pressure units are consistent.
To convert 3.5 atm to kPa, we use the conversion factor: 1 atm = 101.325 kPa. Thus, 3.5 atm converts to 3.5 × 101.325 = 354.6375 kPa.
Now, we can set up the equation using Boyle's Law:
P1 × V1 = P2 × V2
Substituting the known values:
354.6375 kPa × 3.0 L = 557.15 kPa × V2
To solve for V2 (the new volume), we rearrange the equation:
V2 = (354.6375 kPa × 3.0 L) / 557.15 kPa
V2 = 1.9065 L (rounded to four decimal places)
Therefore, to increase the pressure to 557.15 kPa, the volume would need to be approximately 1.9065 L.