Answer to Question #153095 in Chemistry for Krishna Pradhan

Question

A steel cylinder of 50 L capacity contains helium gas at a pressure of
200 atm and temperature of 27 oC. Assume that all of the gas can be
used to fill a weather balloon which is released in air. At a height of
100000 ft, the volume of the balloon is 200 m3 and its temperature is
-73 o C. What is the pressure of the gas inside the balloon?

Answer 1

P₁ = 200 atm

V₁ = 50 L = 0.05 m³

T₁ = 27^oC = 300 K

P₂ = unknown

V₂ = 200 m³

T₂ = -73^oC = 200 K

Solution:

The Combined Gas Law:

P₁V₁/T₁ = P₂V₂/T₂

Cross-multiply to clear the fractions:

P₁V₁T₂ = P₂V₂T₁

Divide to isolate P₂:

P₂ = (P₁V₁T₂) / (V₂T₁)

Plug in the numbers and solve for P₂:

P₂ = (200 atm × 0.05 m³ × 200 K) / (200 m³ × 300 K) = 0.033 atm

P₂ = 0.033 atm

Answer: 0.033 atm is the pressure of the gas inside the balloon.