Final answer:
The gas will occupy a volume of 2.56 liters at 38.0°C under a pressure of 500 torr. The question involves calculating the change in volume of a gas sample under different temperature and pressure conditions using the combined gas law. The correct answer is A.
Step-by-step explanation:
To solve this problem, we can use the combined gas law, which relates the initial and final conditions of temperature, pressure, and volume of a gas. The combined gas law equation is:
P1 * V1 / T1 = P2 * V2 / T2
where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures, respectively.
Using the given information, we can plug in the values and solve for the final volume:
P1 = 660 torr, V1 = 1.83 L, T1 = 21.0°C = 294.15 K
P2 = 500 torr, T2 = 38.0°C = 311.15 K
Solving for V2:
V2 = (P1 * V1 * T2) / (P2 * T1)
Plugging in the values:
V2 = (660 torr * 1.83 L * 311.15 K) / (500 torr * 294.15 K) = 2.56 L
Therefore, the gas will occupy a volume of 2.56 liters at 38.0°C under a pressure of 500 torr.
Using the combined gas law, the new volume of the gas at 38.0°C and 500 torr is calculated to be approximately 2.56 liters, corresponding to option a.
The question involves calculating the change in volume of a gas sample under different temperature and pressure conditions using the combined gas law. To find the new volume at 38.0°C and 500 torr, we first need to convert the given temperatures to Kelvin by adding 273 to the Celsius temperature. Then, we use the combined gas law formula:
P1V1/T1 = P2V2/T2
Plugging in the values, we get
660 torr * 1.83 L / (21.0 + 273)K = 500 torr * V2 / (38.0 + 273)K
Solving for V2, we find that the new volume of the gas is approximately 2.56 liters, which corresponds to option a.