chemistry question

Question

A weather balloon is filled with 180.0 L of He and launched from sea level (T = 20.0°C, P = 755 torr). The balloon is designed to continue its ascent to an altitude of 30.0 km where it bursts, releasing a package of meteorological instruments that parachute back to Earth.

If the atmospheric pressure at 30.0 km is 28.0 torr and the temperature is -42.0 °C, what is the volume of the balloon when it bursts?

Answer in Liters

Answer 1

P₁V₁ / T₁ = P₂V₂ / T₂

P₁ = 755 torr

P₂ = 28.0 torr

V₁ = 180.0 L

V₂ = ?

T₁ = 20.0 °C + 273 = 293 K

T₂ = -42.0 °C + 273 = 231 K

Rearrange the above equation and solve for V2

P₁V₁ / T₁ = P₂V₂ / T₂

V₂ = P₁V₁T₂ / P₂T₁

= (755 torr x 180.0 L x 231 K) / (28.0 torr x 293 K) = 3827 L ~ 3830 L (rounded to 3 significant figures)