Final answer:
Using Charles's law, the initial temperature of the gas before it was submerged in ice water and reduced to a volume of 2.57 L was calculated to be 17.44 °C. This calculation assumes constant pressure throughout the process.
Step-by-step explanation:
The subject of this question is the thermal expansion of gases, which relates to Charles's law. This law states that at constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature (in Kelvin) increases or decreases. Given that the initial volume of the gas is 2.80 L and the final volume when submerged in ice water is 2.57 L, we can find the initial temperature by setting up the equation based on Charles's law:
V1/T1 = V2/T2
Where:
- V1 is the initial volume = 2.80 L
- V2 is the final volume = 2.57 L
- T1 is the unknown initial temperature in Kelvin
- T2 is the final known temperature = 273.15 K (0.00 °C converted to Kelvin)
By rearranging the equation to solve for T1, we get:
T1 = V1 * T2 / V2
Plugging in the values we get:
T1 = (2.80 L * 273.15 K) / 2.57 L
T1 = 747.02 K / 2.57 L = 290.59 K
To convert from Kelvin to Celsius, we subtract 273.15 from the temperature in Kelvin:
Initial temperature (in °C) = 290.59 K - 273.15 = 17.44 °C
Therefore, the initial temperature of the gas was 17.44 °C.