Question

A 40.0L balloon is filled with air at sea level. (1.00 atm, 25.0C). It's tied to a rock and thrown into a cold body of water and it sinks to the point where the temperature is 4.0C and the pressure is 11.0 atm. What will its new volume be?

A) 14.0 L
B) 20.0 L
C) 25.0 L
D) 35.0 L

Answer 1

Using the combined gas law, the new volume of the balloon when it sinks to colder water with higher pressure is calculated to be 35.0 L.

Step-by-step explanation:

The student asked about the new volume of a balloon that was initially filled with air at sea level (1.00 atm, 25.0°C) and then sinks to where the temperature is 4.0°C and pressure is 11.0 atm.

To solve this, we use the combined gas law which is P1V1/T1 = P2V2/T2. Remember to convert all temperatures to Kelvin by adding 273.15.

Starting conditions: P1 = 1.00 atm, V1 = 40.0 L, T1 = 25.0°C + 273.15 = 298.15 K.
New conditions: P2 = 11.0 atm, T2 = 4.0°C + 273.15 = 277.15 K.

Solving for V2 we get:

V2 = (P1 × V1 × T2) / (P2 × T1)
V2 = (1.00 atm × 40.0 L × 277.15 K) / (11.0 atm × 298.15 K)
V2 = 35.0 L

Therefore, the new volume of the balloon would be option D) 35.0 L.