Final answer:
The volume a gas will occupy at 2.00 atm, when initially at 101.1 kPa and 896 mL, is calculated using Boyle's Law. Upon converting 2.00 atm to kPa and applying the formula P1V1 = P2V2, the new volume is found to be approximately 446.1 mL.
Step-by-step explanation:
The question you're asking is about the behavior of a gas under different pressures, and it can be answered using the ideal gas law and principles from chemistry, specifically the concept of Boyle's Law. Boyle's Law states that the volume of a given mass of gas is inversely proportional to its pressure, provided the temperature remains constant. So, to solve this problem, we need to apply Boyle's Law, which is usually stated as P1V1 = P2V2 where P represents pressure and V represents volume.
In your question, the initial conditions are a volume (V1) of 896 mL and a pressure (P1) of 101.1 kPa. We first need to convert the pressure you provided for the new condition (2.00 atm) to kPa because we need to keep our units consistent. Since 1 atm is equal to 101.325 kPa, 2.00 atm would be 202.65 kPa (2.00 * 101.325 kPa/atm).
Now, we can rearrange Boyle's Law to solve for the new volume (V2):
V2 = P1 * V1 / P2
Inserting the values, we get:
V2 = (101.1 kPa * 896 mL) / 202.65 kPa = 90414 / 202.65 = 446.1 mL
The new volume at 2.00 atm would therefore be approximately 446.1 mL if temperature and the amount of gas remain constant.