Final answer:
To fill the 4800 m3 balloon to a pressure of 1 bar at 0°C using the given reaction, approximately 1,220.53 metric tons of iron are required.
Step-by-step explanation:
The first step in solving this problem is to calculate the number of moles of H2 gas that will be produced from the reaction. To do this, we use the ideal gas law equation:
n = PV / RT
where n is the number of moles, P is the pressure, V is the volume, R is the gas constant, and T is the temperature. Plugging in the given values:
n = (1 bar) * (4800 m^3) / ((8.3145 J/mol*K) * (273.15 K))
n = 21,829.19 moles
Now, we use the stoichiometry of the reaction to find the ratio between moles of H2 and iron:
Fe(s) + H2SO4(aq) → FeSO4(aq) + H2(g)
From the balanced equation, we can see that 1 mole of iron reacts with 1 mole of H2 gas. Therefore, the number of moles of iron required is also 21,829.19.
To convert these moles of iron to metric tons, we use the molar mass of iron:
mass = n * molar mass = 21,829.19 mol * 55.845 g/mol = 1,220,534.62 g
Finally, we convert grams to metric tons:
metric tons = 1,220,534.62 g / (1000 kg/g) = 1,220.53 metric tons