In 1897 the Swedish explorer Andreé tried to reach the North Pole in a balloon. The balloon was filled with hydrogen gas. The hydrogen gas was prepared from iron splints and diluted sulfuric acid. The reaction is $$ \mathrm{Fe}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{FeSO}_{4}(a q)+\mathrm{H}_{2}(g) $$ The volume of the balloon was \(4800 \mathrm{~m}^{3}\) and the loss of hydrogen gas during filling was estimated at \(20 . \%\). What mass of iron splints and \(98 \%\) (by mass) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) were needed to ensure the complete filling of the balloon? Assume a temperature of \(0^{\circ} \mathrm{C}, \mathrm{a}\) pressure of \(1.0\) atm during filling, and \(100 \%\) yield.

To find the mass of iron splints and the mass of diluted H₂SO₄ needed to completely fill the balloon, follow these steps: 1. Calculate the actual volume of hydrogen gas needed, considering the 20% loss: \(4800\,\text{m}^{3} / (1 - 20/100) = 6000\,\text{m}^{3}\) 2. Convert the volume to moles of hydrogen gas using the ideal gas law: \(n = PV / (RT) = (101325 \times 6000) / (8.314 \times 273.15) = 266,585.96 \, \text{mol}\) 3. Determine the moles of iron and H₂SO₄ needed, which are equal to the moles of hydrogen gas: 266,585.96 mol 4. Calculate the mass of iron needed: \((266,585.96 \, \text{mol}) \times (55.85 \, \text{g/mol}) = 14,889,473.56 \, \text{g}\) 5. Calculate the mass of the diluted H₂SO₄ solution needed: \((266,585.96 \, \text{mol}) \times (98.08 \, \text{g/mol}) / 0.98 = 26,673,301.56 \, \text{g}\) The mass of iron splints needed is approximately 14,889,473.56 g and the mass of the diluted H₂SO₄ is approximately 26,673,301.56 g.