A scuba tank has a volume of 3820 cm 3 .For very deep dives, the tank is filled

Question

A scuba tank has a volume of 3820 cm3.For very deep dives, the tank is filled with 50 percent (by volume)pure oxygen and 50 percent pure helium.

How many oxygen molecules are there in the tank if it is filled at20°C to a gauge pressure of 12.6 atm?

How many helium molecules are there in the tank if itis filled at 20°C to a gauge pressure of 12.6 atm? A scuba tank has a volume of 3820 cm3.For very deep dives, the tank is filled with 50 percent (by volume)pure oxygen and 50 percent pure helium.

How many oxygen molecules are there in the tank if it is filled at20°C to a gauge pressure of 12.6 atm?

How many helium molecules are there in the tank if itis filled at 20°C to a gauge pressure of 12.6 atm?

Explanation / Answer

the equation of state for an ideal gas is P * V = N * kB * T ----------(1) the boltzmann constant kB is given by kB = R * (mo/M) R is universal gas constant,mo is the mass ofmolecules and M is the molar mass mo = * V is the density of gas and V is the volume of thegas density of oxygen gas is 1.429 kg/m3 and the volumeof the gas is V1 = 3820 * (10-2)3m3 = 3820 * 10-6 m3 from equation (1) we get N = (P * V/kB * T) = (P * V/R * (mo/M) *T) = (P * V * M/R * mo * T) or NO2 = (P * V * M/R * * V * T) = (P *M/R * * T) P = 12.6 atm = 12.6 * 1.013 * 105 Pa = 12.76 *105 Pa M = 16.00 g/mol = 16.00 * 10-3 kg/mol (foroxygen) R = 8.314 J/mol/K = 1.429 kg/m3 T = 20 oC = (20 + 273) K = 293 K the number of helium molecules that are there in the tankare NHe = (P * M/R * * T) M = 4.00 g/mol = 4.00 * 10-3 kg/mol = 0.1785 kg/m3 the values of P,R and T are same. the values of P,R and T are same.

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