A sounding balloon is a rubber bag filled with H₂(g) and carrying a set of instruments (the payload). Because this combination of bag, gas, and payload has a smaller mass than a corresponding volume of air, the balloon rises. As the balloon rises, it expands. From the table below, estimate the maximum height to which a spherical balloon can rise given the mass of balloon, 1200 g; payload, 1700 g: quantity of H₂(g)in balloon, 120 ft³ at 0.00 °C and 1.00 atm; diameter of balloon at maximum height, 25 ft. Air pressure and temperature as functions of altitude are:

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Altitude, km 0 5 10 20 30 40 50 60 Pressure, mbar 1.0 × 10³ 5.4 x 10² 2.7 x 10² 5.5 x 10¹ 1.2 x 10¹ 2.9 × 10⁰ 8.1 x 10-1 2.3 × 10-1 Temperature, K 288 256 223 217 230 250 250 256