Final answer:
Using Charles's Law, the volume of methane gas in the balloon will increase from 5.73 L at 47.0 °C to 6.53 L at 94.0 °C.
Step-by-step explanation:
The question relates to the change in volume of a gas due to a change in temperature while the pressure remains constant. This is a direct application of Charles's Law, which states that, for a given amount of gas at constant pressure, the volume of a gas is directly proportional to its temperature measured in Kelvin.
To calculate the new volume of the balloon at 94.0 °C, we must first convert the temperatures from Celsius to Kelvin by adding 273.15, then use the following formula: V1/T1 = V2/T2, where V1 is the initial volume, T1 is the initial temperature in Kelvin, V2 is the final volume, and T2 is the final temperature in Kelvin.
Initial volume (V1): 5.73 L
Initial temperature (T1): 47.0 °C + 273.15 = 320.15 K
Final temperature (T2): 94.0 °C + 273.15 = 367.15 K
Following Charles's Law and rearranging the formula to solve for V2, we get:
V2 = V1 × (T2/T1)
V2 = 5.73 L × (367.15 K / 320.15 K)
Calculating this gives us the final volume:
V2 = 6.53 L (rounded to two decimal places)
Therefore, the new volume of the balloon would be 6.53 L at 94.0 °C.