Final answer:
The new pressure of the gas sample when the temperature rises from 25.0 °C to 100 °C is about 250.5 torr, calculated using Gay-Lussac's Law, which states that gas pressure is directly proportional to temperature in Kelvin.
Step-by-step explanation:
Assuming the volume and the amount of gas remain constant, the relationship between pressure and temperature is described by Gay-Lussac's Law, which states that the pressure of a given mass of gas is directly proportional to its Kelvin temperature when the volume is held constant. To find the new pressure, the temperatures must first be converted to Kelvin by adding 273.15. Thus: Initial temperature (T1) = 25.0 °C = 298.15 K, Final temperature (T2) = 100 °C = 373.15 K, Initial pressure (P1) = 200.0 torr. Applying Gay-Lussac's Law (P1/T1 = P2/T2), we can solve for the new pressure (P2): P2 = P1 * (T2/T1), P2 = 200.0 torr * (373.15 K / 298.15 K). P2 is calculated to be approximately 250.5 torr. Therefore, the new pressure of the gas after the temperature rises to 100 °C is about 250.5 torr. This demonstrates how the pressure of a gas changes in direct proportion to its temperature in Kelvin.