Final answer:
The percent difference in pressures is greater in a smaller volume due to Boyle's Law, where pressure and volume are inversely proportional. Additionally, the deviation from ideal gas behavior is more pronounced in smaller volumes.
Step-by-step explanation:
When considering why the percent difference in the pressures calculated with two different equations is greater when the gas is in a smaller vessel than a larger vessel, it's important to understand Boyle's law and the behavior of gases. Boyle's Law states that pressure and volume are inversely proportional (P = k/V), meaning that if the volume increases, the pressure decreases, and vice versa. Consequently, the small 3.90 L vessel would have a higher pressure compared to the larger 15.30 L vessel since there is less volume for the gas particles to move.
Furthermore, real gases deviate from ideal behavior at high pressures where the volume occupied by the gas molecules becomes significant compared to the volume of the container. In a smaller volume like a 3.90 L vessel, this deviation is pronounced, leading to a bigger percent difference in pressures calculated using ideal and real gas equations. In contrast, in larger volumes, the influence of gas particle volume is more distributed and thus results in a smaller percent difference. Answer (b) The smaller vessel has a higher pressure is correct because it aligns with Boyle's Law and accounts for deviations in real gas behavior.