Question

Scuba diving tanks are filled with compressed air for use underwater. Calculate the unknown quantity in each of the following situations using the appropriate gas law, then complete the related sentences. Round all of your answers to the nearest whole number.

1. A 10 L scuba tank is filled with air at a temperature of 21°C and pressure of 174 atmospheres at the surface. What volume of air would such a tank be able to deliver to a diver at an ocean depth of 30 m where the pressure is 4 atmospheres? Assume that the water temperature at 30 m deep is the same as at the surface.
2.Before being used for a scuba dive, the tank was stored in a room where the temperature was 3°C. What was the pressure of the gas in the tank while it was in the room assuming volume stays constant.

Answer 1

1. Using Boyle's Law: V₂ = V₁(P₁/P₂) = 10 L * (174 atm/4 atm) = 435 L. Therefore, the scuba tank would be able to deliver 435 L of air to a diver at a depth of 30 m.
2. Using Charles's Law: (P₂/T₂) = (P₁/T₁) where P₁ = 174 atm and T₁ = 294K (21°C + 273.15) and T₂ = 276K (3°C + 273.15). Solving for P₂, we get P₂ = (P₁/T₁) * T₂ = (174 atm/294K) * 276K = 164 atm. Therefore, the pressure of the gas in the tank while it was in the room was approximately 164 atm.