given the reaction -
Fe(s)+H2SO4(aq)->FeSO4(aq) + H2(g)
the volume of the balloon was 4400m^3 and the loss of hydrogen gas during filling was est. at 20%. what mass of iron splints and 87% (by mass) H2SO4 were needed to ensure complete filling of the balloon? assume temp of 0C pressure of 1.0atm and 100% yeild.
I would first divide 4400 m^3 by 0.80 (only 80% efficient in filling). Then
use PV = nRT to calculate n, the mols of H2 required to fill the balloon. P is in atm, V in liters (use the value above which you calculated but change to liters), R is 0.08205, T is in Kelvin.
Convert mols H2 gas needed to mols Fe(s) and mols H2SO4.
Convert mols Fe to grams Fe.
Convert mols H2SO4 to grams H2SO4, then divide that by 0.87 (since it's only 87% by mass good stuff).
Check my thinking.
To find the mass of iron splints and 87% H2SO4 needed to fill the balloon completely, we need to calculate the amount of hydrogen gas produced and then determine the amount of iron and H2SO4 required based on the stoichiometry of the reaction.
1. Calculate the volume of hydrogen gas produced:
Given that the volume of the balloon is 4400 m^3, and there was a 20% loss during filling, the actual volume of hydrogen gas produced is 80% of the balloon volume:
Actual volume of H2 gas = 80% of 4400 m^3 = 0.8 * 4400 m^3 = 3520 m^3
2. Convert the volume of hydrogen gas to moles:
We can use the ideal gas law to convert the volume of hydrogen gas to moles. The ideal gas law equation is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Since we are given a temperature of 0°C, we need to convert it to Kelvin:
Temperature (T) = 0°C + 273.15 = 273.15 K
Using the ideal gas law, we can rearrange it to solve for moles:
n = PV / RT
Substituting the values:
n = (1.0 atm) * (3520 m^3) / [(0.0821 L * atm / K * mol) * 273.15 K]
n ≈ 152.70 mol
3. Determine the molar ratio of Fe(s) to H2(g):
From the balanced chemical equation, we can see that the molar ratio of Fe(s) to H2(g) is 1:1. This means that the same number of moles of iron (Fe) and hydrogen gas (H2) are produced.
4. Calculate the mass of iron needed:
Since the molar ratio of Fe(s) to H2(g) is 1:1, the mass of iron needed is equal to the molar mass of iron (Fe) multiplied by the number of moles of hydrogen gas produced:
Mass of Fe = 55.85 g/mol * 152.70 mol ≈ 8528.15 g ≈ 8.53 kg
5. Calculate the mass of 87% H2SO4 required:
Since the molar ratio of H2SO4 to H2(g) is 1:1, the mass of 87% H2SO4 needed is equal to the molar mass of H2SO4 multiplied by the number of moles of hydrogen gas produced:
Molar mass of H2SO4 = 98.09 g/mol
To find the mass of H2SO4 in 87% H2SO4, we need to consider that 87% indicates the mass of H2SO4 in 100 g of the solution. Therefore, the mass of H2SO4 is 87 g in every 100 g of the solution.
Now, calculate the mass of 87% H2SO4 needed:
Mass of 87% H2SO4 = (87 g H2SO4/100 g solution) * (152.70 mol H2SO4) * (98.09 g/mol) ≈ 1255.29 g ≈ 1.26 kg
Therefore, to ensure complete filling of the balloon, approximately 8.53 kg of iron splints and 1.26 kg of 87% H2SO4 (by mass) are needed.