Question

A weather balloon is inflated to a volume of 27.2 L at a pressure of 740. mmHg and a temperature of 29.2 °C. The balloon rises in the atmosphere to an altitude where the pressure is 375 mmHg and the temperature is -15.2 °C.

Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude.

A) 16.4 L
B) 20.8 L
C) 25.6 L
D) 32.2 L

Answer 1

Using the combined gas law, the volume of the weather balloon at the higher altitude with given conditions is approximately calculated to be 32.2 liters, which is answer choice (D).

Step-by-step explanation:

To calculate the new volume of the weather balloon at a higher altitude using the ideal gas law, we make use of the combined gas law equation, which is derived from the ideal gas law, PV = nRT. The combined gas law equation is P1V1/T1 = P2V2/T2, where P represents pressure, V represents volume, and T represents temperature in Kelvin. Since the number of moles (n) and the gas constant (R) remain constant, we can safely use this formula to find the volume (V2) of the balloon at the new conditions.

First, convert the temperatures to Kelvin:
T1 = 29.2 °C + 273.15 = 302.35 K
T2 = -15.2 °C + 273.15 = 257.95 K

Next, we rearrange the combined gas law formula to solve for V2:
V2 = (P1 × V1 × T2) / (T1 × P2)

Inserting the given values we have:
V2 = (740 mmHg × 27.2 L × 257.95 K) / (302.35 K × 375 mmHg)

After simplifying the above calculation, the answer is approximately V2 = 32.2 L, which corresponds to answer choice (D).