Final answer:
The final volume of the balloon is 238.38 ml.
Step-by-step explanation:
The final volume of the balloon can be found using the combined gas law equation. The combined gas law states that:
P1V1/T1 = P2V2/T2
Where P1 and T1 are the initial pressure and temperature, P2 and T2 are the final pressure and temperature, and V1 and V2 are the initial and final volumes respectively.
In this case, the initial volume (V1) is given as 700 ml at a temperature (T1) of 20.0 C. The final temperature (T2) is given as 100 K. We need to find the final volume (V2).
First, convert the initial temperature from Celsius to Kelvin by adding 273.15: 20.0 C + 273.15 = 293.15 K.
Using the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
Substituting the given values: (1 atm * 700 ml) / 293.15 K = (P2 * V2) / 100 K
Simplifying and solving for V2:
V2 = (1 atm * 700 ml * 100 K) / (293.15 K)
V2 = 238.38 ml
Therefore, the final volume of the balloon is 238.38 ml.