Solving applications of Boyle’s Law

Question

a marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures 78.0 cm wide. The biologist estimates she will need 2600. L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit in to the air tank. Write you answer in atmospheres. 

Answer 1

Volume of a sphere = 4/3 πr³

r = 78.0 cm/2 = 39 cm

V = 248475 cm³ = 248.5 L = volume of the storage tank

Assuming the 2600. L of air is measured at 1 atmosphere pressure, then you have the following relationship:

From P₁V₁ = P₂V₂

(1 atm)(2600 L) = (P₂)(248.5 L)

P₂ = 10.46 atmospheres = 10.5 atm (to 3 significant figures)