You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds 0.900 L. The pressure of the gas inside the balloon equals air pressure (1.00 atm). (a) If the air inside the balloon is at a constant 22.0o C and behaves as an ideal gas, what mass of air can you blow into one of the balloons before it bursts? (b) Repeat part (a) if the gas is helium rather than air.
Solution 6E The ideal gas equation is PV = nRT , where n = number of moles of gas, P = pressure of gas, V= volume of gas, R= universal gas constant, T= temperature in absolute scale. We have to calculate n first and then we can find the the mass of air to be filled in the balloon to get the required pressure. (a) Given, P = 1.0 atm = 1.013 × 10 Pa5 3 3 4 3 3 V = 0.9 L = 0.9 × 10 m = 9.0 × 10 m = 0.0009 m R = 8.314 J/mol.K 0 T = 22 C = 273.15 + 22 K = 295.15 K Substituting these values in the equation PV = nRT 1.013 × 10 Pa × 0.0009 m = n × 8.314 J/mol.K × 295.15 K n = 0.037 moles Now, molar mass of air is = 28.97 g/mol The mass of 0.037 moles of air is = 0.037 × 28.97 g = 1.07 g Therefore, the mass of air that has to be blown into a balloon is approximately 1.07 g. (b) Molar mass of helium is = 4.00 g/mol Therefore, the mass of 0.037 moles of helium is = 0.037 × 4.00 g = 0.148 g So, the amount of helium that has to be blown into a balloon is 0.148 g.