Question

A weather balloon with a volume of 231 L is launched at 20.0°C at sea level, where the atmospheric pressure is 1.00 atm. The balloon rises to an altitude of 2.00 × 10⁴ m, where atmospheric pressure is 57.0 mmHg and the temperature is 210.0 K. What is the volume of the balloon at 2.00 × 10⁴ m?

Answer 1

Answer – We are given,

Initial values -

Volume of balloon, V₁ = 231 L

Temperature, T₁ = 20.0^oC

Pressure , P₁ = 1.00 atm.

Final Values ,

Height, h = 2.00 x 10⁴ m

Pressure, P₂ = 57.0 mm Hg

Temperature, T₂ = 210.0 K

Volume, V₂ = ?

We are given the initial volume and initial and final value of temperature and pressure. We need to use a combine gas law to determine the final volume of the balloon.

The mathematical expression for combine gas law is,

PA XV PzXV T.

We need both phase values in the same unit.

T₁ in degree Celsius and required in Kelvin

T₁ = 20.0^oC + 273.15 = 293.15 K

P₂ is given mm Hg and P₁ in atm, hence we can convert the P₂ in atm from mm Hg

760 mm Hg= 1 atm

57.0 mm Hg =? atm

= 57.0 mm Hg x 1 atm / 760 mm Hg

=0.075 atm

By plugging the values,

  

1 atm x 231 L 293.15 K 0.075 atm x V2 210.0 K

1 atm x 231L x 210.5 K -= 2.21 % 103 L 293.15 KX 0.075 atm

Thus, the final volume of the balloon at 2.00 x 10⁴ m is 2.21 x 10³ L.