Answer:
the new volume of the sample gas at 745.0 torr and 30.0°C is approximately 37.59 mL.
Explanation:
To solve this problem, we can use the combined gas law, which states that the ratio of the initial pressure, volume, and temperature to the final pressure, volume, and temperature of a gas remains constant, as long as the number of moles and the gas itself remain constant.
The combined gas law formula is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
where P1, V1, and T1 are the initial pressure, volume, and temperature, and P2, V2, and T2 are the final pressure, volume, and temperature.
Let's substitute the given values into the formula:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
(785 torr * 45.5 mL) / (15°C + 273.15) = (745.0 torr * V2) / (30.0°C + 273.15)
Simplifying the equation, we get:
(35767.75) / (288.15) = (745.0 * V2) / (303.15)
Now, let's solve for V2, the new volume of the sample gas:
(745.0 * V2) = (35767.75 * 303.15) / (288.15)
V2 = (35767.75 * 303.15) / (288.15 * 745.0)
V2 ≈ 37.59 mL
Therefore, the new volume of the sample gas at 745.0 torr and 30.0°C is approximately 37.59 mL.
