Final answer:
By applying Boyle's Law and the conversion between mmHg and atm, we find that after increasing the volume from 4.90 L to 9.90 L at constant temperature, the final pressure of the gas in atmospheres is approximately 0.495 atm. The closest match among the provided options is A. 0.448 atm
Step-by-step explanation:
The question involves applying Boyle's Law, which states that for a given mass of gas at constant temperature, the volume of the gas is inversely proportional to the pressure. This can be expressed as P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume respectively.
To solve for the final pressure of the gas after the volume increases from 4.90 L to 9.90 L at constant temperature, we can rearrange Boyle's Law to solve for P2: P2 = P1 * V1 / V2.
Inserting the values provided, P2 = (755 mmHg) * (4.90 L) / (9.90 L). Calculating this gives us P2 = 3725.50 mmHg * L / 9.90 L = 376.3131 mmHg. To convert to atmospheres (atm), we use the conversion factor 1 atm = 760 mmHg. Thus, P2 = 376.3131 mmHg / 760 mmHg/atm = 0.495 atm. The closest answer to our calculation is option a. 0.448 atm, considering that some rounding may have occurred in the options provided.