Question

A SCUBA tank, an air tank used for breathing under water, is initially filled with gas at a pressure of 2.3x10⁷ Pa and 25 ^oC. The tank has a volume of 16.0 L. If the tank will continue to provide air until it reaches a pressure of 2.5x10⁶ Pa, how many moles of gas will it provide to a diver diving in water at 6 ^oC? Give your answer in moles to at least three significant figures. Hint: There will be air left in the tank when the it reaches the lowest pressure the tank can deliver. The amount of air left might be useful in solving this problem.

Answer 1

PV = nRT

Initial mole:-

Pi*V = ni*R*Ti

2.3x10⁷ * 16 *10^-3   = n_i * 8.314 *(273.15 + 25)

n_i  = 2.3x10⁷ * 16 *10^-3 / 8.314 * 298.15

    = 148.457 mole initially

final mole :-

n_f   = P_f *V / R*T_f  

    = 2.5x10⁶ * 16 *10^-3 / 8.314 * 279.15

   = 17.235 mole

mole provided = n_i - n_f = 148.457 - 17.235

                                = 131.222 mole