Final answer:
To find the final pressure of ethylene gas when transferred from a larger tank to a smaller tank, Boyle's Law is used. The initial volume and pressure of the gas and the volume of the smaller tank are given, allowing for the calculation of the final pressure to be approximately 133 atm.
Step-by-step explanation:
The question is related to the ideal gas law, which can be represented by the formula PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature. Since the question assumes constant temperature and amount of gas, the relationship between pressure and volume is described by Boyle's Law (P1V1 = P2V2), which says that the product of the initial pressure (P1) and volume (V1) equals the product of the final pressure (P2) and volume (V2).
In this case, we are looking to find the final pressure when a certain volume of gas at known pressure is transferred to a smaller tank. Given that the initial volume (V1) of ethylene gas is 7980.3 L and the initial pressure (P1) is 0.96 atm, and the final volume (V2) is 58.1 L, we need to solve for the final pressure (P2).
Applying Boyle's Law:
- P1V1 = P2V2
- (0.96 atm) × (7980.3 L) = P2 × (58.1 L)
- Solving for P2, we get:
P2 = (0.96 atm × 7980.3 L) / 58.1 L
P2 = 133 atm (approximately)
Therefore, the correct answer is a) 133 atm.