Final answer:
The final pressure of the heated and expanded gas sample, calculated using the combined gas law, is approximately 524 torr.
Step-by-step explanation:
The question pertains to the behavior of a gas sample undergoing changes in volume, pressure, and temperature. To compute the final pressure of the gas after it is heated and expands, we can apply the combined gas law, which states that the ratio of the product of pressure and volume to the temperature of a system remains constant for a given amount of gas: P1V1/T1 = P2V2/T2. Observing that temperature must be in Kelvin for gas law calculations, we convert the temperatures from °C to K by adding 273.15 to each. Consequently, T1 = 25°C = 298.15 K and T2 = 40°C = 313.15 K. Plugging in the initial conditions (P1 = 970 torr, V1 = 3.50 L, T1 = 298.15 K) and the final conditions (V2 = 6.80 L, T2 = 313.15 K) while solving for P2, the final pressure, we find:
P2 = (P1V1T2) / (V2T1)
P2 = (970 torr × 3.50 L × 313.15 K) / (6.80 L × 298.15 K)
P2 = ≈ 524 torr
Therefore, the final pressure of the gas sample after being heated and expanded is approximately 524 torr.