Final answer:
To find the expanded volume of a gas when heated, Charles's law is used. For a sample heated from 20.0°C to 200.0°C, the expanded volume is calculated to be approximately 3.74 L.
Step-by-step explanation:
The student's question relates to the expansion of a gas sample when heated from one temperature to a higher temperature, and this can be answered using Charles's law. Charles's law states that, at constant pressure, the volume of a gas is directly proportional to its Kelvin temperature.
To find the new volume V2 after heating the gas, we can set up the equation V1/T1 = V2/T2 where V1 is the initial volume and T1 and T2 are the initial and final temperatures in Kelvin, respectively. First, we need to convert the temperatures from Celsius to Kelvin (K = °C + 273.15).
For the student's problem: Initial volume V1 = 2.33 L, initial temperature T1 = 20.0°C (293.15 K), and final temperature T2 = 200.0°C (473.15 K). Therefore, the equation to solve for V2 becomes:
2.33 L / 293.15 K = V2 / 473.15 K
By solving for V2, we find that the expanded volume is approximately 3.74 L.