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.
answer in kg
To determine the mass of iron splints and 87% H2SO4 needed to ensure complete filling of the balloon, let's follow these steps:
Step 1: Calculate the volume of hydrogen gas produced.
According to the given reaction, 1 mole of Fe reacts with 1 mole of H2 to produce 1 mole of H2 gas. Therefore, the volume of H2 gas produced will be equal to the volume of the balloon, which is 4400 m^3.
Step 2: Adjust for the 20% loss of hydrogen gas during filling.
Since 20% of the hydrogen gas will be lost during filling, we need to adjust the volume of H2 gas produced. Multiply the volume by 1.20 to account for the loss:
4400 m^3 * 1.20 = 5280 m^3
Step 3: Convert the volume of H2 gas to moles using the ideal gas law.
The ideal gas law is given by PV = nRT, where:
P = pressure (1.0 atm)
V = volume (5280 m^3)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (0°C + 273.15 = 273.15 K)
n = PV / RT
n = (1.0 atm * 5280 m^3) / (0.0821 L·atm/(mol·K) * 273.15 K)
n ≈ 207728 moles
Step 4: Determine the mass of iron (Fe) needed.
From the balanced equation, we know that 1 mole of Fe reacts with 1 mole of H2. Therefore, the moles of Fe needed will be equal to the moles of H2 produced:
moles of Fe = 207728 moles
Step 5: Convert moles of Fe to mass using the molar mass of Fe.
The molar mass of Fe is 55.845 g/mol.
mass of Fe = moles of Fe * molar mass of Fe
mass of Fe = 207728 moles * 55.845 g/mol
mass of Fe ≈ 11,589,500 g
Step 6: Convert the mass of iron (Fe) to kilograms.
The final answer is desired in kilograms, so divide the mass of Fe by 1000 to convert it to kg:
mass of Fe ≈ 11,589,500 g / 1000
mass of Fe ≈ 11,589.5 kg
Therefore, approximately 11,589.5 kilograms of iron (Fe) splints and 87% (by mass) H2SO4 are needed to ensure complete filling of the balloon.
To determine the mass of iron splints and 87% H2SO4 needed to ensure complete filling of the balloon, we'll need to calculate the number of moles of H2 gas required based on the given volume of the balloon and the percentage loss during filling.
Step 1: Calculate the volume of H2 gas required
The given volume of the balloon is 4400 m^3. However, there was an estimated loss of 20% during filling. So, we need to calculate the volume of H2 gas considering the loss.
Volume of H2 gas = Volume of the balloon * (100% - percentage loss during filling)
Volume of H2 gas = 4400 m^3 * (100% - 20%) = 4400 m^3 * 80%
Step 2: Convert the volume of H2 gas to moles
To convert the volume of H2 gas into moles, we need to use the Ideal Gas Law: PV = nRT
Assuming a temperature of 0°C (or 273 K) and a pressure of 1.0 atm, we have:
(1.0 atm) * (volume of H2 gas in liters) = (moles of H2 gas) * (0.0821 L·atm/mol·K) * (273 K)
Let's convert the given volume of H2 gas (in m^3) to liters:
1 m^3 = 1000 L
So, the volume of H2 gas in liters = 4400 m^3 * 1000 L/m^3 = 4,400,000 L
With these values, we can solve for the moles of H2 gas:
(1.0 atm) * (4,400,000 L) = (moles of H2 gas) * (0.0821 L·atm/mol·K) * (273 K)
Simplifying:
moles of H2 gas = (1.0 atm * 4,400,000 L) / (0.0821 L·atm/mol·K * 273 K)
Step 3: Calculate the mass of iron splints and H2SO4 needed
Based on the balanced chemical equation provided, we see that the molar ratio between Fe and H2 is 1:1. Therefore, the number of moles of iron splints needed is equal to the number of moles of H2 gas.
Similarly, the molar ratio between H2SO4 and H2 is 1:1, according to the balanced chemical equation. However, the given H2SO4 is 87% by mass. So, we need to consider the mass percentage to calculate the required mass.
To calculate the required mass of iron splints and H2SO4:
Mass of iron splints = (moles of H2 gas) * (molar mass of Fe)
Mass of H2SO4 = (moles of H2 gas) * (molar mass of H2SO4) * (100% mass of H2SO4 / 87% H2SO4)
The molar masses of Fe and H2SO4 can be found from the periodic table:
Molar mass of Fe = 55.845 g/mol
Molar mass of H2SO4 = (2 * 1.0078 g/mol for H) + (32.065 g/mol for S) + (4 * 16.00 g/mol for O)
By substituting the calculated moles of H2 gas obtained in Step 2 into the equations for the mass of iron splints and H2SO4, you can find the required mass.