Final answer:
To find the gas's new volume at different temperature and pressure conditions, we first convert temperatures to Kelvin and pressures to atmospheres, and then use the combined gas law. The final volume is calculated to be 308.3 cm³.
Step-by-step explanation:
The question involves calculating the change in volume of a gas when both temperature and pressure are changed. To solve this, we can use the combined gas law, which combines Charles's Law, Boyle's Law, and Gay-Lussac's Law.
The combined gas law is represented by the formula: (P1 × V1) / T1 = (P2 × V2) / T2, where P is pressure, V is volume, and T is temperature (in Kelvin). We need to convert all units into consistent ones, specifically temperatures to Kelvin and pressure to the same units.
First step, we convert the temperatures to Kelvin: T1 = 27 °C + 273 = 300K and T2 = 36 °C + 273 = 309K. Next, convert pressures to atmospheres: P1 = 700 mmHg × (1 atm / 760 mmHg) = 0.9211 atm and P2 = 750 mmHg × (1 atm / 760 mmHg) = 0.9868 atm.
Now use the combined gas law and solve for V2:
(0.9211 atm × 300 cm³) / 300K = (0.9868 atm × V2) / 309K
Solving for V2 gives us: V2 ≈ 308.3 cm³. So, the answer is option A. 308.3 cm³.