Final answer:
Using Charles's Law, the volume of a balloon filled with gas will be approximately 1.588 L at -60°C and 3.824 L at 240°C when the initial conditions are 2.20 L at 22°C, assuming constant pressure.
Step-by-step explanation:
To predict the volume of the balloon at different temperatures, we can use the combined gas law which shows that if the pressure remains constant, the volume of a gas is directly proportional to its temperature in Kelvins. This concept is based on Charles's law, part of the ideal gas laws. To use the law, we need to make sure the temperatures are in Kelvins, and the formula to convert Celsius to Kelvin is K = °C + 273.15.
First, let's convert the temperatures:
-60°C is -60 + 273.15 = 213.15 K
240°C is 240 + 273.15 = 513.15 K
The original volume (2.20 L) and original temperature (22°C) must also be converted to Kelvins: 22°C + 273.15 = 295.15 K.
Now, using Charles's Law which is V1/T1 = V2/T2, where V1 is the original volume and T1 is the original temperature, we can solve for V2, the new volume, at the two different temperatures.
For -60°C (213.15 K):
V2 = V1 * (T2/T1)
V2 = 2.20 L * (213.15 K / 295.15 K)
V2 = 2.20 L * 0.722
V2 = 1.588 L (approximately)
For 240°C (513.15 K):
V2 = V1 * (T2/T1)
V2 = 2.20 L * (513.15 K / 295.15 K)
V2 = 2.20 L * 1.738
V2 = 3.824 L (approximately)
Thus, the predicted volumes are approximately 1.588 L at -60°C and 3.824 L at 240°C.