Answer :
Final answer:
The volume of hydrogen gas produced when 98.5 g of iron reacts completely is approximately 45.9 liters.
Explanation:
To calculate the volume of hydrogen gas produced, we need to follow these steps:
- Convert the mass of iron to moles using its molar mass.
- Use the molar ratio between iron and hydrogen gas to determine the moles of hydrogen gas produced.
- Apply the ideal gas law to convert the moles of hydrogen gas to volume.
Step 1: Convert the mass of iron to moles:
The molar mass of iron (Fe) is 55.845 g/mol. We can use this value to convert the mass of iron to moles:
moles of iron = mass of iron / molar mass of iron
moles of iron = 98.5 g / 55.845 g/mol
moles of iron ≈ 1.763 mol
Step 2: Use the molar ratio to determine the moles of hydrogen gas:
According to the balanced chemical equation, the molar ratio between iron and hydrogen gas is 1:1. This means that for every 1 mole of iron reacted, 1 mole of hydrogen gas is produced.
moles of hydrogen gas = moles of iron ≈ 1.763 mol
Step 3: Apply the ideal gas law to convert moles of hydrogen gas to volume:
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 the pressure and temperature are given in the question (1 atm and 25°C), we can use these values in the equation:
V = (nRT) / P
Convert the temperature to Kelvin:
T = 25°C + 273.15 = 298.15 K
Substitute the values into the equation:
V = (1.763 mol * 0.0821 L·atm/(mol·K) * 298.15 K) / 1 atm
V ≈ 45.9 L
Therefore, the volume of hydrogen gas produced when 98.5 g of iron reacts completely is approximately 45.9 liters.
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